Yearly Itineraries Yearly Itinerary Summary Documents …curriculum.austinisd.org/schoolnetDocs/mathematics/general... · Grading Period Pacing Guide Assessment Texas Essential Knowledge

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Math Grade 3 © Austin ISD Yearly Itinerary 2014-2015

Grading Period Assessment

Pacing Guide Texas Essential Knowledge and Skills STAAR: DC = Dual Coded Skills; Readiness Standard;

Supporting Standard

The mathematical process standards TEKS should be taught in conjunction with the content TEKS; therefore, they are embedded throughout the year.

1st Nine Weeks 38 Days

August 25 – October 17

CRM 1 Place Value Concepts (14 days) August 25 – September 12

TEKS: 3.2A, 3.2B, 3.2C, 3.2D

CRM 2 Addition and Subtraction Concepts (15 days) September 15 – October 3

TEKS: 3.4A, 3.4B, 3.5A

CRM 3 Value of Coins and Bills and Personal Financial Literacy (9 days) October 6 – October 17

TEKS: 3.4C, 3.9A, 3.9B, 3.9C, 3.9D, 3.9E,

3.9F

2nd Nine Weeks 40 Days

October 20 – December 18 MOY I: CRM 1 – CRM 5 (Weeks 1 -11) November 10 – November 25

CRM 4 Time (10 days) October 20 – October 31

TEKS: 3.7C

CRM 5 Multiplication and Division Concepts (21 days) November 3 – December 5

TEKS: 3.4D, 3.4E, 3.4F, 3.4G, 3.4H, 3.4I,

3.4J, 3.4K, 3.5B, 3.5C, 3.5D

CRM 6 Patterns In a Table (9 days) December 8 – December 18

TEKS: 3.5E

3rd Nine Weeks 48 Days

January 5 – March 13

MOY II: CRM 1 – CRM 8 (Weeks 1 -23) February 17 – February 27

CRM 7 Fraction Concepts (24 days) January 5 – February 6

TEKS: 3.3A, 3.3B, 3.3C, 3.3D, 3.3E, 3.3F,

3.3G, 3.3H, 3.7A

CRM 8 Measurement Concepts and Attributes of Two-dimensional Figures/Three-dimensional Solids (19 days) February 9 – March 6

TEKS: 3.6A, 3.6B, 3.6C, 3.6D, 3.6E, 3.7B,

3.7D, 3.7E

CRM 9 Data Analysis and STAAR Review (5 days) March 9 – March 13

TEKS: 3.8A, 3.8B

4th Nine Weeks 51 Days

March 23 – June 4

CRM 9 Data Analysis and STAAR Review (21 days) March 23 – April 21

TEKS: 3.8A, 3.8B

CRM 10 Place Value Concepts (8 days) April 22 – May 1

TEKS: 3.2A, 3.2B, 3.2C, 3.2D

CRM 11 Fraction Concepts (14 days) May 4 – May 21

TEKS: 3.3F, 3.3G, 3.3H, 3.7A

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/Processstandards.pdf

Page 2 of 2

Grading Period Assessment

Pacing Guide Texas Essential Knowledge and Skills STAAR: DC = Dual Coded Skills; Readiness Standard;

Supporting Standard

The mathematical process standards TEKS should be taught in conjunction with the content TEKS; therefore, they are embedded throughout the year.

CRM 12 Multiplication and Division Concepts (8 days) May 26 – June 4

TEKS: 3.4G, 3.4J, 3.4K, 3.5B, 3.5D

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/Processstandards.pdf

3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 1: Place Value Concepts In this unit on place value, students will use knowledge of place value concepts to represent, order, compare, and round whole numbers. As you are teaching this unit, you should focus on the relationship between the value of digits and numbers as a whole. Students are expected to represent whole numbers to 100,000 with objects and pictorial models and compare and order whole numbers between 9,999 and 100,000. As you teach this unit, students should use manipulatives to develop the understanding of place value position as 10 times the position to the right and as one‐tenth of the value of the place to its left and use phrases such as “closer to,” “is about,” or “is nearly,” when representing numbers on a number line. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of place value concepts through real world experiences. This unit was strategically placed first because the concept is fundamental for understanding the value of numbers and how numbers are composed and decomposed as it relates to the four operations. Place value concepts and relationships should be spiraled throughout the school year.

Math Yearly Itinerary 2014‐2015

Process TEKS should be embedded through each content TEKS, therefore they are taught all year long. When

appropriate MoY questions will be dual‐coded with a content and a process TEKS.

1A 1B 1C 1D 1E 1F 1G apply mathematics to problems arising in everyday life, society, and the workplace

use a problem‐solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem‐solving process and the reasonableness of the solution

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

create and userepresentations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Page 1 of 3 Updated: July 29, 2014

© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 1st Nine Weeks

CRM 1 Place Value Concepts Pacing

14 days

August 25 – September 12 DESIRED RESULTS

Transfer: Students will independently use their learning to display, analyze, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication in order to connect mathematical ideas arising in problems in everyday life, society and careers.

Making Meaning

Enduring Understandings

Patterns in our number system and relationships between numbers are helpful in determining the value of a number.

Each decade of numbers has a symbolic pattern that is reflective of the 1-9 sequence.

The groupings of hundreds, tens, and ones can be taken apart in different ways based on patterns.

Patterns created by the base 10 system provide a framework for building number sense.

Essential Questions

How can you represent whole numbers using expanded notation?

How can you use base-tens, objects and pictures to compose and decompose whole numbers?

What are some ways that you can read and write numbers to 999,999?

What relationship can you find in the place value system?

How can you represent whole numbers through ten thousands on a number line to round?

What are some ways you can compare and order whole numbers?

Vocabulary Vocabulary Cards, word form, expanded form/notation, standard form, hundred thousands, ten thousands, thousands, hundreds, tens, ones, round, compose, decompose, place value, place, sum, nearest number, close to, about Student pre-requisite knowledge Reading, writing, composing/decomposing, and representing place Value to the thousands

Resources: MathBoard; Base-ten Blocks; Centimeter Grid Paper; Place Value chart to the Hundred Thousands; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos

Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners.

TEKS Knowledge & Skills Acquisition

STAAR: RC = Reporting Category; DC = Dual Coded Skills; Readiness Standard; Supporting Standard Concepts are addressed in another unit.

Students Will Know Students Will Be Able To

3.2 Number and operations: The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

A number is composed of one or more periods.

A number is composed of one or more digits.

Each digit in a number holds a “place.” (ie. place value)

Each place in a number represents ten times the value of the place to

Read, write, and describe numbers up to the hundred thousands place.

Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/Elementary/Vocabulary_Cards/m_4_Vocabulary_Cards_AtoZ_1415.pdf

http://www.thinkcentral.com/

http://curriculum.austinisd.org/adv_ac/preAP/curriculum.html

http://curriculum.austinisd.org/adv_ac/GT/curriculum.html

http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4



3.2B describe the mathematical relationships found in the base-10 place value system through the hundred thousands place 3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

its right.

The place of a digit represents its value.

The symbol for zero allows us to represent symbolically the absence of value in a digit.

There are different representations for the same whole number value.

Numbers are composed and decomposed by the sum of the digit value.

Composing is to create a number based on the value of the digit(s).

Decomposing is to break a number apart based on the value of its digit(s).

Objects, pictorial models,

numbers, and expanded notation

can be used to compose and

decompose numbers.

When you round a number you

find a number that tells you about

how much or about how many.

You can use a number line to

round numbers.

You can round by finding the

closest or nearest 10, 100, 1000,

10,000, 0r 100,000.

Numbers can be compared using symbols to represent greater than, less than, and equal to.

Whole numbers can be ordered from least to greatest on a number line.

Whole numbers become greater on a number line as you move from left to right.

Whole numbers become less on a number line as you move from right to left.

The closer a number is to “zero” the smaller the number.

The farther a number is from “zero” the larger the number.

The symbol > represents greater than.

The symbol < represents less than.

The symbol = represents equal to.

many ones using objects, pictorial models, and numbers.

Compose and decompose numbers using expanded notation.

Describe the mathematical relationships found in place value system through the hundred thousands place as 10 times the position to the right.

Represent numbers up to 999,999 using objects and pictorial models.

Represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000.

Use words such as “closer to, is about, and is nearly” to describe the relative size of numbers in order to round whole numbers.

Compare and order all whole numbers up to 9,999 and between 9,999 and 100,000.

Represent comparisons using the symbols greater than, less than, and equal to.


ASSESSMENT EVIDENCE

Student Work Products/Assessment Evidence

Performance Tasks Other Evidence (i.e. unit tests, open ended exams, quiz,

essay, student work samples, observations, etc.)

Task: Comparing and ordering numbers to 100,000

Write the number 86,391 on the board. Ask students to record on white boards the number that is 1,000 less than your number (85,391). Repeat this activity with other numbers up to 100,000 using 10, 100, 1,000, 10,000, or 100,000 more or less than your number.

Put students in groups of 5 or 6. Give each student a number card 0-9 or a playing card (take out face cards, aces are 1, jokers are 0.)

Have the groups arrange the cards to create the largest number possible and record it using numbers and words, then find the smallest number possible and record it. Use symbols to write a comparison of the two. Ask the group to a statement to justify that the number is the largest possible or smallest possible.

Then each member of the group holds up one of the cards and stands in an ordered line to show their number to the class. They must say the number out loud in words.

Short Cycle Assessment

SCA items are available under the Assessment tab in Schoolnet for use in teacher created assessments.

Additional Suggestions for Assessments

Houghton Mifflin Harcourt: Go Math Soar to Success Math

Houghton Mifflin Harcourt: Go Math Enrich, Homework, and Practice

Houghton Mifflin Harcourt: Go Math Grab and Go Differentiated Centers

Houghton Mifflin Harcourt: Go Math Personal Math Trainer

Teacher Created Exit slips

Teacher Created Assessments

Journal Prompts or Responses

Home/In class Projects

Interactive Online or Board Games

Webquest

LESSON PLANNING TOOLS

In the course of lesson planning, it is the expectation that teachers will include whole child considerations when planning such as differentiation, special education, English language learning, dual language, gifted and talented, social emotional

learning, physical activity, creative learning, and wellness.

Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Representing and Comparing Numbers to 100,000

http://curriculum.austinisd.org/schoolnetDocs/mathematics/3rd/M_3RD_IR_CRM1_1415.pdf

http://curriculum.austinisd.org/schoolnetDocs/mathematics/3rd/M_3RD_IR_CRM1_1415.zip

3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 2: Addition and Subtraction Concepts In this unit on addition and subtraction, students will use knowledge of place value concepts to add, subtract, and estimate to determine solutions to mathematical and real‐world problems involving addition and subtraction of whole numbers. As you are teaching this unit, you should focus on the student’s ability to determine how and when it is appropriate to use addition or subtraction. Students are expected to round and solve problems involving whole numbers to the nearest 10 or 100 using compatible numbers (with values that lend themselves to mental calculations) and rounding up or down to the nearest specified place value to solve problems flexibly, accurately, and efficiently. As you teach this unit, students should use manipulatives to represent one‐ and two‐step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, strip diagrams, and equations. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of addition and subtraction concepts through real world experiences. This unit was strategically placed so that students are able to use their knowledge of place value to solve problems involving the addition and subtraction. Addition and subtraction concepts should be spiraled throughout the school year.











Page 1 of 3 Updated: June 23, 2014


CRM 2 Addition and Subtraction Concepts Pacing

15 days

September 15 – October 3 DESIRED RESULTS


Making Meaning


Problems can be solved using many different strategies.

Addition and subtraction are related.

Computation can involve taking apart (decomposing) and combining (composing) numbers in a variety of ways.

Rounding and compatible numbers are strategies that can be used to estimate solutions to addition and subtraction problems.

Knowing the reasonableness of an answer comes from using good number sense and estimation strategies.

Essential Questions

How can you round numbers?

How can you use compatible numbers and rounding to estimate sums and differences?

How can you add more than two addends?

How can you use place value to add and subtract numbers?

What strategies can you use to solve one-step and two-step problems?

Vocabulary Vocabulary Cards, addend, sum, difference, join, separate, compare, operation, regroup, unknown, strategy, counting on, adding up to, estimate, rounding, compatible number, open number line, number line, properties of operations, commutative property of addition, associative property of addition, equation, relationship, inverse operations

Student pre-requisite knowledge Modeling addition and subtraction situations; solving joining, separating, and comparing problems; writing number sentences; working with basic facts; explaining strategies

Resources: Base-ten blocks; Part-Part-Whole Mats; 100 chart; MathBoard; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos

Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports

ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners.




3.4 Number and operations: The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. The student is expected to:

3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4B round to the nearest 10 or 100 or use compatible numbers to estimate

Compatible numbers are numbers that can be easily manipulated when adding or subtracting.

Place value and compatible numbers are used to generate an open number line.

Following the action in a problem helps to determine which operation to use to solve the problem.

Explain the relationship between addition and subtraction.

Choose the correct operation when fluently solving a one-step and two-step problems.

Use pictures, words, and numbers to model whole numbers in addition and subtraction situations up to 1,000.

Solve addition and subtraction

http://curriculum.austinisd.org/schoolnetDocs/mathematics/generalResources/Elementary/Vocabulary_Cards/4th_Grade/m_4_Vocabulary_Cards_AtoZ_1415.pdf







solutions to addition and subtraction problems

Problems can be solved using place value strategies and properties of operations.

Commutative property allows you to add numbers in any order.

Associative property allows you to group the addends in any order and still get the same sum.

An estimate is close to the exact answer.

We estimate by choosing compatible numbers that are easy to think about and work with.

Finding the nearest 10 or 100 is essential to rounding.

Estimation strategies can help determine reasonableness when problem solving.

Rounding must be completed before addition or subtraction operations are performed.

Look to the digit in the place immediately right of the place you are rounding to and use the rounding rules to decide whether you move it up or round to the lower multiple.

Rounding rules say that if the digit to the right of the place you are rounding is 5 or more “you up the score,” if it is 4 or less “you let it rest.”

problems using place value strategies and order of operations.

Use place value and compatible numbers to represent addition and subtraction on an open number line.

Represent addition and subtraction situations on a traditional number line.

Write an equation (number sentence) to represent an addition or subtraction situation of whole numbers up to 1,000.

Round to the nearest 10 or 100.

Use compatible numbers, number line, and rounding rules to estimate solutions to addition and subtraction problems

3.5 Algebraic reasoning: The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to:

3.5A represent one- and two-step

problems involving addition and

subtraction of whole numbers to 1,000

using pictorial models, number lines, and

equations

Addition and subtraction are related.

Addition names the whole by joining its parts, and subtraction names the part being removed or separated.

Addition and subtraction problems can require more than one step to solve.

Addition and subtraction situations can be modeled using base- ten blocks.

Addition and subtraction of whole numbers up to 1,000 can be represented using picture models, number lines (including open number lines), and equations (number sentences).

Open number lines are number

Use pictorial models, number lines, and equations to represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000.

Use addition to solve subtraction problems by counting on or adding up to a number.

Represent a number on a number line as being between two consecutive multiples of 10, 100, 1000, and 10,000.

Use strip diagrams to add and subtract problems.


lines without tick marks or numbers.

ASSESSMENT EVIDENCE




Tasks: Modeling Problems

Have students model each problem with base ten blocks, draw the models on the worksheet, then write a complete number sentence that fits model.

Read the story, The True Story of the Three Little Pigs or any other Fairy Tale favorite. On the back of 18-20 index cars write the word addition on half of the cards and subtraction on the remaining cards. Shuffle the cards so that when you pass them out to students they are distributed evenly. Give each student a card.

Have the student create addition or subtraction problems based on the story. The student should be able to explain why the problem is an addition or subtraction problem. (What was the mathematical language in the problem or situation that lets you know to add or subtract to solve the problem?) The problem below is an example of what the student could write:

“The first pig built his house out of bricks. He started with 48 bricks and then he bought 57 more to make his house really strong. “How many bricks did he use altogether to build the house?













Webquest




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Adding and Subtracting Within 1,000

http://www.austinschools.org/curriculum/math/elem/3rd/documents/3rdGradePerformanceTaskCRM2Arc12012.pdf



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 3: Value of Coins and Bills and Personal Financial Literacy In this unit on the value of coins and bills and personal financial literacy, students will use knowledge of place value relationships and concepts to add, subtract, and estimate to determine solutions to mathematical and real‐world problems involving money and personal finances. As you are teaching this unit, you should focus whole number computations so students are expected to determine the collection of coins in cents. As you teach this unit, students should use class projects and manipulatives to better understand the concepts found in this unit. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of money and financial concepts through real world experiences. This unit was strategically placed so that students are able to use addition and subtraction to solve problems involving money and finances. Money and personal financial literacy concepts should be spiraled throughout the school year.













CRM 3 Value of Coins and Bills and Personal Financial Literacy Pacing

9 days

October 6 – October 17 DESIRED RESULTS


Making Meaning


A person’s standard of living is established by money and income.

Financial literacy is critical in a global society.

Individuals must accept the responsibility for creating their own wealth.

Financial choices will have benefits, costs and future consequences.

Credit is an essential tool used to establish financial independence.

Essential Questions

What is the connection between your education, the amount of work you do, and the money you can earn?

How does the availability of resources affect their cost?

What are the benefits of planned spending decisions?

How does using credit to buy something that you want or need affect the cost?

How and why should you save money?

What kind of decisions can you make involving income, spending, saving, giving, and credit?

Vocabulary Vocabulary Cards, human capital, labor, scarcity of resources, cost, benefits, purchase, spending, savings, savings plan, credit, borrower, lender, interest, supply, demand, inflation, charitable giving , money, coins, add, subtract, income Student pre-requisite knowledge Coin collections; value of coins and bills; recall of basic addition and subtraction facts; adding and subtracting money

Resources: Play Money; Real Money; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos







3.4C determine the value of a collection of coins and bills

Amounts of money can be represented in multiple ways.

Each coin has a unique value.

Each coin has a different size.

Only pennies have a copper color.

Each dollar bill has a unique value.

Collections of dollar bills and coins can be received as payment for

Recognize each coin and bill and know the value of each.

Determine the value of a collection of coins and bills by skip counting by 5s, 10s and 25s and counting by 1s.

Select coins and bills for a given amount.

Represent currency amounts in








goods purchased or services received.

People count money or collections of bills and coins to determine the amount of money that they are spending or the amount of money they have earned from a task or job.

multiple ways (3 dimes or 6 nickels is 30¢).

Use the dollar sign and decimal point together, and cents sign independently when representing money ($0.34 or 34¢).

3.9 Personal financial literacy: The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:

3.9A explain the connection between

human capital/labor and income

3.9B describe the relationship between

the availability or scarcity of resources

and how that impacts cost

3.9C identify the costs and benefits of

planned and unplanned spending

decisions

3.9D explain that credit is used when

wants or needs exceed the ability to pay

and that it is the borrower's

responsibility to pay it back to the lender,

usually with interest

3.9E list reasons to save and explain the

benefit of a savings plan, including for

college

3.9F identify decisions involving income,

spending, saving, credit, and charitable

giving

Human capital is a person’s ability to invest in himself/herself through the knowledge and skills that he/she gains from education and experience.

People use money for many different reasons.

Money is also called currency.

Money looks different in different countries.

All money does not have the same value.

Capital is any human-made resource that is used to produce other goods and services.

Goods are things that we purchase from or sell to others such as a candy bar or an IPAD.

Services are things that are provided to others such as a checkup at the doctor’s office or a fireman putting out a fire.

Human capital is a person’s ability to invest in himself/herself through the knowledge and skills that he/she gains from education and experience.

Labor is the effort that a person devotes to a task (job) that he/she is paid to do.

Income is the money that a person earns from the task (job) that he/she performs.

People earn income or “money” by providing “goods” and “services” to others.

There are costs and benefits of planned and unplanned spending decisions.

Credit is used when wants or needs exceed the ability to pay.

The person that uses credit is called the borrower.

Identify and describe human capital as a person’s ability to invest in himself/herself through the knowledge and skills that he/she gains from education and experience.

Identify and describe income or “money” that a person can earn from the task (job) that he/she performs.

Identify and describe human-made resources that are used to produce other goods and services.

Identify and describe goods and services that are purchased or provided from or sold to others to earn (generate) income for themselves.

Identify and describe human capital as a person’s ability to invest in himself/herself through the knowledge and skills that he/she gains from education and experience.

Describe the relationship between the availability or scarcity of resources and how that impacts cost.

Identify and describe income or “money” that a person can earn from the task (job) that he/she performs.

List reasons to save and explain the benefit of a savings plan, including for college.

Identify decisions involving income, spending, saving, credit, and charitable giving that we make in our daily life.


The lender extends credit to the borrower.

It is the borrower's responsibility to pay money back to the lender, usually with interest.

Interest is the amount that a borrower pays back to the lender beyond what was initially loaned.

When you place money in a savings account at a banking institution, it earns interest.

People should save a portion (at least 20%) of what they earn.

The voluntary giving of help, typically money or time, to those in need is called charitable giving.

Scarcity of resources increases the demand either through the supply or demand of a product and this increases the cost for the good as people are willing to pay more to get something.

Scarcity of resources is how large companies make money for themselves. (ie. gasoline prices)

If a product is abundant and available to everyone this leads to lower cost.

This is called supply and demand.

ASSESSMENT EVIDENCE




Task: Hay Rides

Have students glue the following problem in the math journal and perform the following task:

All the sunshine this spring has been great for Dan and Carlos’s hay ride business! Over the holidays they were very busy. In one night alone, Dan and Carlos gave 4 rides! They took 6 people per ride and charged $4 for each person, how much money did they make?

1. Draw a pictorial model, array, or area model to represent and solve the problem.

2. Once the money is shared between the two boys, how much will they each receive?

3. How could the boys use their money wisely?














Webquest

Federal Reserve Education Activities

Practical Money Skills

Show Me the Future

Financial Literacy for Kids




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Collecting Coins

http://www.federalreserveeducation.org/

https://www.practicalmoneyskills.com/foreducators/lesson_plans/children.php

http://showmethefuture.org/

http://www.doughmain.com/odmpublic/financial-literacy/



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 4: Time In this unit on time, students will explore intervals of time. As you teach this unit, students should solve problems involving intervals of time. With the length of intervals provided, the focus is on the conversion of 60 minutes to an hour when considering time intervals. As you teach this unit, students should use manipulatives and tools such as analog and digital clocks, to solve problems related to the addition and subtraction of intervals of time in minutes. The skill of telling and writing time has moved to grade 2. This skill builds to the 4th grade standard 4.8C. The process TEKS should be partnered throughout this unit lending itself to the application of the measurement of time through real world experiences. This unit was strategically placed after units involving the addition and subtraction operations so that students are able to solve problems such as a 15‐minute event plus a 30‐minute event equals 45 minutes. The concepts learned in this unit should be spiraled throughout the school year.












© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 2nd Nine Weeks

CRM 4 Time Pacing

10 days

October 20 – October 31 DESIRED RESULTS


Making Meaning


Time can be given and shown in more than one way.

Telling time is an essential life skill.

Essential Questions

How can you measure elapsed time in minutes?

How can you find the starting time and ending time when you know the elapsed time?

What strategies can be used to solve problems about elapsed time?

Vocabulary Vocabulary Cards, hour, minute, hour hand, minute hand, a quarter after, a quarter to, half past, analog clock, digital clock, AM, PM, scale, intervals, elapsed time, event, a quarter after, a quarter to, half past the hour

Student pre-requisite knowledge Addition, subtraction, tell time to the half hour

Resources: Teacher and Student Analog Clocks; Digital Clock; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos






3.7 Geometry and measurement: The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement. The student is expected to:

3.7C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

The long hand on a clock measures the minutes. The short hand measures the hours.

When the hour hand is between numbers on the clock, the number read depends on whether it is before or after 30 minutes.

Elapsed time is the amount of time that passes from the start of an event until the end of the same event.

The passage of time can be measured through standard units (minutes, hours) and through non-standard methods.

Explain the difference between AM and PM.

Read and write the time shown on a digital clock and an analog clock to the minute.

Add and subtract minutes in intervals of time such as a 15-minute event plus a 30-minute event equals 45 minutes using pictorial models or tools.

Use the terms “a quarter after” and “a quarter to” and “half past” the hour.

Add and subtract time to determine the amount of time








The difference between A.M. and P.M. and how that affects problems involving elapsed time.

Time can be added or subtracted to find the amount of time that has passed.

Time is added when you move forward on a clock or when the hands turn clockwise.

Time is subtracted when you move backward on a clock or when the hands turn counter clockwise.

Finding elapsed time requires a multi-step problem solving process.

that has passed from the start of an event until the end of the event.

Determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools.

ASSESSMENT EVIDENCE




Task: 3rd Grade Picnic

Present the following problem to the class:

The third grade class picnic will begin at 2:00 o’clock

on the last day of school. Mrs. Curry told the third

graders they only had 40 minutes to eat and play with

their friends. When the students looked at the

outside clock they saw this time (below). Is the picnic

over, or do they still have time to play? Explain your

process.

Ask students to work with a shoulder partner to represent the time, solve the problem, and answer the question.

Ask students to show what the time would look like on a digital clock.

Ask students to decide if the picnic would take place during A.M. or P.M. How did they decide?

45 minutes before the start of the picnic, the class had storytime in the library. What time did storytime begin?













Webquest

Telling Time Games and Activities

http://www.aasd.k12.wi.us/staff/boldtkatherine/MathResources3-6/Math_Time.htm


Draw an analog and digital clock to show and label storytime.

Ask students to explain how they determined when storytime began.




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Measuring Time



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 5: Multiplication and Division Concepts In this unit on multiplication and division, students will use knowledge of place value relationships, recall of multiplication facts up to 10 X 10, and properties of operations to multiply, divide, and estimate to determine solutions to mathematical and real‐world problems involving multiplication and division of whole numbers within 100. The learning of facts related to 11s and 12s is not included in the Revised TEKS. As you are teaching this unit, you should focus on the student’s ability to determine how and when it is appropriate to use multiplication or division and strategies that support the learning of multiplication facts such as repeated addition, equal‐sized groups, arrays, area models, equal jumps on a number line, skip counting, mental math, partial products, the commutative, associative, and distributive properties, and the standard algorithm. Arrays should reflect the combination of equally‐sized groups of objects. As you teach this unit, students should use manipulatives and concrete models and objects. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of multiplication and division concepts through real world experiences. This unit was strategically placed so that students are able to use their knowledge of addition and subtraction to solve problems involving the four operations. Multiplication and division concepts should be spiraled throughout the school year.













CRM 5 Multiplication and Division Concepts Pacing

21 days

November 3 – December 5 DESIRED RESULTS


Making Meaning


Multiplication and division are related.

Multiplication and division involve counting groups of like size.

Models can be used to solve problems for multiplication and division and give meaning to equations (number sentences).

Basic facts are conceptually related.

Essential Questions

How is multiplication like/different addition?

How is division related to subtraction?

How are multiplication and division related?

How can you model multiplication and division problems to find products and quotients?

What strategies can be used to solve one and two step problems?

How can you use the properties of operations to solve multiplication problems?

What strategies can be used to determine if a number is even or odd?

How can you use strip diagrams top solve problems?

Vocabulary Vocabulary Cards, operation, multiplication, factor, product, array, area model, partial product, repeated addition, equal groups, multiple, division, divisor, dividend, quotient, partial quotient, repeated subtraction, equation, decompose, tens, ones, algorithm, expression, rows, columns, addition, subtraction, even, odd, equal groups, unequal groups, divide, multiply, commutative, associative, and distributive properties Student pre-requisite knowledge Basic multiplication and division facts; counting groups and the number in each group; building models of multiplication and division situations

Resources: Color tiles; Strip Diagrams; Snap Cubes; Counters; Centimeter Graph Paper; Base-ten Blocks; Number Lines; 10x10 grids; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos














3.4D determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10 3.4E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts 3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties 3.4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally 3.4I determine if a number is even or odd using divisibility rules 3.4J determine a quotient using the relationship between multiplication and division 3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

Multiplication is a shortcut for repeated addition and involves joining equal sized groups.

In multiplication, the whole is unknown.

An array is a way of modeling or representing multiplication in repeated equal sized columns and rows.

In multiplication, the numbers multiplied are called factors.

When two factors are multiplied, the answer is called the product.

The product(s) of any two factors is called a multiple(s).

Multiplication expressions can be stated as a comparison.

An expression only includes the two factors that are being multiplied. It should not have an equal sign or solution, but can have an expression of equal value on the opposite side of the equal side.

An equal sign or solution changes an expression to an equation. It shows that both sides of the equal sign are equal.

An equation is a mathematical statement that says or shows that this is equal to that.

Some ways to represent multiplication are by repeated addition, combining equal-sized groups or objects, arrays, area models (partial products), equal jumps on a number line, and skip counting.

Arrays reflect the combination of equally-sized groups of objects.

Division of the product and known factor or repeated addition/subtraction of the known factors can be used to determine the unknown/missing factor or product.

Unknown factors or products can be determined by finding the number that makes the unknown when multiplied by the given factor.

Decomposing a two-digit number into tens and ones (partial

Relate multiplication and division.

Use (Origo) numerical fluency strategies to remember basic facts to 10 x 10.

Identify the number of groups and how many are in each group in a multiplication problem.

Write an equation (number sentences) to match multiplication models.

Record and solve multiplication problems up to a two digit number times a one digit number.

Use various number based

strategies to solve multiplication

and division problems and

situations.

Represent multiplication situations through the use of repeated addition, combining equal-sized groups or objects, arrays, equal jumps on a number line, and skip counting.

Determine the total number of objects when equally-sized groups of objects are combined or arranged.

Represent and describe arrays up to 10 by 10.

Represent multiplication facts by using repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting.

Use arrays to reflect the combination of equally-sized groups of objects.

Recall the division facts up to 10 by 10.

Use place value strategies, algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number.

Use mental math, partial products, and the commutative, associative, and distributive properties to solve problems.

Determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally.


products or area models) helps to multiply.

In division, the number of equal-sized groups or the total number in each group is unknown.

The commutative, associative, and distributive properties can be used to multiply a two digit number by a one digit number.

Even numbers can be divided into two equal groups.

Numbers that end in 0, 2, 4, 6, or 8 are even.

Even numbers are sums of two equal numbers.

Numbers that end in 1, 3, 5, 7, or 9 are odd.

There will always be a remainder when an odd number is placed into 2 groups.

The sum of any two odd numbers is even.

The sum of any two even numbers is even.

Use pairings of objects to represent even and odd numbers.

Use divisibility rules to determine if a number is even or odd.

Determine a quotient using the relationship between multiplication and division.

Use strategies based on objects; pictorial models, arrays, area models, equal groups, properties of operations, and recall of facts to solve one-step and two-step problems involving multiplication and division problems within 100.

Identify and describe the commutative, associative, and distributive properties.


3.5B represent and solve one- and two-

step multiplication and division problems

within 100 using arrays, strip diagrams,

and equations

3.5C describe a multiplication expression

as a comparison such as 3 x 24 represents

3 times as much as 24

3.5D determine the unknown whole

number in a multiplication or division

equation relating three whole numbers

when the unknown is either a missing

factor or product

It can take more than one step to find the solution to a multiplication or division situation.

A multiplication expression can be describes as 2, 3, 4, 5, 6, etc. times as much as__.

The unknown factor is what you are solving for.

Arrays, strip diagrams, and equations can be used to find unknowns.

Connections can be made between arrays and strip diagrams.

The relationship between multiplication and division can be used to find unknowns.

Represent and solve one- and two-step multiplication and division problems within 100.

Use arrays, strip diagrams, and equations to solve multiplication and division problems.

Use the phrase _ times as much as _ to describe a multiplication expression as a comparison.

Determine the unknown whole number in a multiplication equation relating three whole numbers when the unknown is either a missing factor or product.

Determine the unknown whole number in a division equation relating three whole numbers when the unknown is either a missing factor or product/quotient.

Connect arrays to strip diagrams.

ASSESSMENT EVIDENCE





Task: Activity : Hands On Standards 3-4, Multiplying With Arrays pp 24-25.

Place students in pairs and post the following problem.

Mr. Booth asked a police officer to speak to his class and another fourth grade class about summer safety. To make room for the other students, Mr. Booth arranged the chairs in his classroom into 8 rows and put 4 chairs in each row. How many chairs were there in all?

o Paired activity:

Introduce the problem by reading it aloud with students.

Distribute color tile (or other manipulatives), paper and pencil to students.

Explain that students will use arrays, strip diagrams, and equations to represent and solve the problem.

Explain that once students have solved the problem, they are to rewrite the equation and represent it by using the commutative, associative, and distributive properties and label the property that was used.













Webquest




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title:



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 5: Multiplication and Division Concepts In this unit on multiplication and division, students will use knowledge of place value relationships, recall of multiplication facts up to 10 X 10, and properties of operations to multiply, divide, and estimate to determine solutions to mathematical and real‐world problems involving multiplication and division of whole numbers within 100. The learning of facts related to 11s and 12s is not included in the Revised TEKS. As you are teaching this unit, you should focus on the student’s ability to determine how and when it is appropriate to use multiplication or division and strategies that support the learning of multiplication facts such as repeated addition, equal‐sized groups, arrays, area models, equal jumps on a number line, skip counting, mental math, partial products, the commutative, associative, and distributive properties, and the standard algorithm. Arrays should reflect the combination of equally‐sized groups of objects. As you teach this unit, students should use manipulatives and concrete models and objects. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of multiplication and division concepts through real world experiences. This unit was strategically placed so that students are able to use their knowledge of addition and subtraction to solve problems involving the four operations. Multiplication and division concepts should be spiraled throughout the school year.













CRM 6 Patterns In a Table Pacing

9 days

December 8 – December 18 DESIRED RESULTS


Making Meaning


Patterns can be recognized, extended, and generalized with both words and symbols.

Number patterns are found in the real world.

Essential Questions

What are some ways you can describe patterns in a table?

How can you describe a rule in a table?

How can you use real world relationships to generate patterns in a table?

Vocabulary Vocabulary Cards, repeating pattern, growing pattern, increasing, decreasing, multiples, relationship, paired numbers, process, rule, generalization, equation, expression, table, list, chart, extend, generate, predict, horizontal, vertical

Student pre-requisite knowledge Identify and extend simple repeating and growing patterns; recognize multiples of a number

Resources: Pattern Blocks; Color Tiles; Chart Paper; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos







3.5E represent real-world relationships using number pairs in a table and verbal descriptions

Patterns can be represented in a table.

There is a relationship between the pairs of numbers in a table.

Multiples can be seen as patterns.

In mathematics, the rule helps us determine the next number in a sequence.

A multiplication expression can be described as a comparison such as 3 x 24 represents 3 times as much as 24.

Real-world relationships can be represented using number pairs in a table and verbal descriptions.

Expressions and equations can be

Generate a table of paired numbers.

Use real life situations to generate both horizontal and vertical tables.

Use lists, charts, and tables to recognize patterns and relationships between numbers.

Identify and describe patterns in a table of related number pairs.

Extend the pattern in a table using multiples of a given number.

Extend the relationship in the table to explore and communicate the verbal description of the relationship.








written to show the relationship between numbers in a table.

The pattern must work for all numbers in the table.

Make generalizations about patterns and express the rule in words, expressions, and equations.

Write and describe expressions and equations to show the relationship between numbers in a table.

Represent real-world relationships using number pairs in a table.

ASSESSMENT EVIDENCE




Task: Hands On Standards 3-4, pp. 124-125 Input/Output Tables

Present the following problem to the class: Every day, Mrs. Barr has “secret numbers of the day”.” She gives her class clues. Today’s clue is an input/output table, and the “secret numbers of the day” are the two missing numbers in the table.

Explain that students will work independently to determine how to find the missing numbers and write a description to explain the table rule.

Input Output

2 4

5

4 6

5

Review the interactive math journal to determine:

o What strategy the student uses to determine the relationship between the numbers in the table?

o Can the student use words to explain the pattern/number relationship (rule) in the table and explain how he/she got to the solution?

o Is the student is able to describe a multiplication expression as a comparison?













Webquest







learning, physical activity, creative learning, and wellness. Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Relationships in Number Pairs



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 7: Fraction Concepts In this unit on fraction concepts, students will compose and decompose fractions; represent fractions of halves, fourths, and eighths as distances from zero on a number line; and model fractions that are greater than zero and less than or equal to one and compare two fractions having the same numerator or denominator. As you are teaching this unit, you should focus on fractions with denominators of 2, 3, 4, 6, or 8 and understand that equivalent fractions must be describing the same whole. Students are expected to represent fractions using concrete objects and pictorial models, including strip diagrams and number lines and justify conclusions about their comparisons using symbols, words, and pictorial models. Concrete models should be linear in nature to build to the use of strip diagrams and number lines. As you teach this unit, students should use manipulatives to develop the understanding of the concept and a number line to determine the length of the portion of a number between 0 and the location of the point. The process TEKS should be partnered with concepts throughout this unit. This unit was strategically placed to build upon fraction concepts learned in 2nd grade. Problems involving fraction concepts should be spiraled throughout the school year.












© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 3rd Nine Weeks

CRM 7 Fraction Concepts (24 days)

Pacing

24 days

January 5 – February 6 DESIRED RESULTS


Making Meaning


Fractional parts have special names that tell how many parts of that size are needed to make the whole.

Fractional parts are equal shares or equal-sized portions of a whole or unit.

A unit can be an object or a collection of things.

Fractions can be composed and decomposed by unit parts.

Objects, pictorial models, strip diagrams, and number lines can be used to represent and compare fractions.

Essential Questions

Why do you need to know how to make an equal share?

What do the top and bottom numbers of a fraction tell?

How does a fraction name part of a whole?

How can you represent and locate fractions on a number line?

How can you use objects, pictorial models, and strip diagrams to represent fractions?

How can you write a fraction as a sum of unit fractions with the same denominator?

Vocabulary Vocabulary Cards, fraction, numerator, denominator, part, whole, equal parts, equal shares, number line, compare, equivalent, benchmark number/fraction, half, halves, third(s), fourth(s), sixth(s), eighth(s), compose, decompose, partition, construct, model, unit fraction Student pre-requisite knowledge represent and name fractional parts (with denominators of 8 or less) using concrete models; locate and name whole numbers on a number line

Resources: Objects; Pictorial Models; Strip Diagrams ; Counters; Number Lines; Fraction Circles; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos






3.3 Number and operations: The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

Fractions are equal sized parts of a whole or a set of objects.

Fractions are related to division.

In a fraction, when an object or set is partitioned/divided into fractional parts, the parts are the same size or represent equal

Use concrete objects and pictorial models, strip diagrams, and number lines to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8.

Given a specified point on a








3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number 3.3D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8 3.3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects, pictorial models, including number lines 3.3G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model 3.3H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

shares.

A simple fraction represents an amount less than one.

Names of fractional parts relate to how many pieces are needed to create the whole or the entire set.

The denominator in a fraction represents the number of parts that the whole is broken into. It tells how many parts are needed to make the whole.

The numerator in a fraction represents the number of parts that are under consideration.

The more fractional parts used to make the whole, the smaller the parts.

The less fractional parts used to make the whole, the larger the parts.

Fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 can be modeled and compared using concrete objects, pictorial models, strip diagrams, and number lines.

Objects, pictorial models, and

number lines to can be used to

represent equivalent fractions

with denominators of 2, 3, 4, 6,

and 8.

A unit fraction represents the amount formed by one part of a whole that has been partitioned into equal parts where the denominator is a non-zero whole number.

To decompose fractions is to break apart fractions into their unit parts such as 3/4 = ¼ + ¼ + ¼.

To compose fractions is to put together/represent fractions as a sum of their unit parts such as ¼ + ¼ + ¼ = 3/4 Note: Students are not using the addition symbol to add fractions but are recognizing how fractions are composed and decomposed.

Two fractions are equivalent if and only if they are both represented by the same portion

number line, determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8.

Explain that the unit fraction, such as one over 2, 3, 4, 6, or 8, represents the quantity formed by one part of a whole that has been partitioned into 2, 3, 4, 6, or 8 equal parts where the denominator is a whole number that is not zero.

Compose and decompose a fraction with a numerator that is greater than zero and less than or equal to its denominator as a sum of its unit parts.

Use pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8 to solve problems by partitioning an object or a set of objects between two or more recipients.

Use different objects, pictorial models, and number lines to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8.

Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line.

Use an area model to explain that two fractions are equivalent if and only if they both represent the same portion of a same size whole.

Use symbols, words, objects, and pictorial models to compare two fractions having the same numerator or denominator in problems.

Reason and justify conclusions

about the size of two fractions

having the same numerator or

denominator.


of a same size whole of an area model.

Comparison symbols, words, objects, and pictorial models can be used to compare fractions.


3.7A represent fractions of halves,

fourths, and eighths as distances from

zero on a number line

• Points on a number line represent whole numbers and fractions.

• When a fraction is plotted on a number line, it is shown as a point that is between whole numbers.

Fractions greater than zero and less than or equal to one with denominators of 2, 4, and 8 can be represented using number lines.

Number lines can be used to show the distance a fraction is from zero such as ¼ is half the distance from zero as ½ or ½ is twice the distance from zero as ¼.

Use a number line to represent fractions of halves, fourths, and eighths as distances from zero.

ASSESSMENT EVIDENCE




Tasks: Allow students to work in pairs to complete the following tasks in the math journal.

Identify and Write Fractions (parts of a set) James had 9 cookies. Three of the cookies were peanut butter. The rest were chocolate chip. What fraction of James’s cookies were peanut butter? What fraction were chocolate chip?

Comparing and Ordering Fractions Use the Try It activity on page 51 of Hands On Standards but use this different problem if you have already used the problem in the lesson. Three friends shared a candy bar. Lisa ate ¼ of the candy bar, Thomas ate 3/8, and Ana ate the same amount as Thomas. Did Lisa eat more or less than her friends? Equivalent Fractions Focus on the Try It section on page 49 of Hands On Standards but use this different problem if you have already used the problem in the lesson.

Keisha had a pizza cut into 8 equal slices. She ate 3 slices, and her brother ate 1 slice. What fraction of the pizza was left over?













Webquest




learning, physical activity, creative learning, and wellness. Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Representing and Comparing Fractions



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 8: Measurement Concepts and Attributes of Two‐dimensional Figures/Three‐dimensional Solids In this unit on measurement concepts and attributes of two‐dimensional figures and three‐dimensional solids, students will explore attributes of shapes and solids and use the relationships between their side lengths to determine and use formal vocabulary to express the area and perimeter of rectangles and volume of 3‐dimensional shapes. In measurement, students should be able to distinguish between liquid ounces and ounces that measure weight. For attributes, students are expected to determine a missing side length of a polygon when given the perimeter of the polygon and the remaining side lengths; separate two congruent squares in half in two different ways; and know that composite figures should be comprised of no more than three rectangles, including squares as special cases of rectangles. As you teach this unit, students should use manipulatives such as geometric shapes and solids to identify attributes and measure to connect concrete and pictorial models with their respective formula. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of geometry and measurement through real world experiences. This unit was strategically placed after units involving the four operations so that students are able to use their knowledge of operations, expressions, and equations when exploring geometry and measurement relationships, conversions, and formulas found in this unit. The concepts learned in this unit should be spiraled throughout the school year.












© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 3rd Nine Weeks

CRM 8 Measurement Concepts and Attributes of Two-dimensional Figures/Three-dimensional Solids

Pacing

19 days

February 9 – March 6 DESIRED RESULTS


Making Meaning


Geometric figures can be defined by their attributes.

Geometric properties or attributes can be used to sort and classify figures and solids.

There is a relationship between two and three-dimensional shapes.

Liquid ounces measure capacity and ounces measure weight.

Essential Questions

How can you draw and classify quadrilaterals?

How can you classify plane figures?

How can you identify, describe and classify 2-dimensional and 3-dimensional shapes and solids?

How can you find the area of a plane figure?

How can you divide figures into parts with equal areas and write the area as a unit fraction of the whole?

How can you break apart a figure to find the area?

How can you find and measure perimeter?

How can you find the unknown length of a side in a polygon when you know its perimeter?

How can you measure liquid volume/capacity?

When is it appropriate to measure weight?

How are ounces and pounds related? Vocabulary Vocabulary Cards, attribute, dimension, two-dimensional, three-dimensional, figure, identify, classify, sort, describe, cones, cylinders, spheres, triangular and rectangular prisms, cubes, edge, vertex (vertices), rhombuses, parallelograms, trapezoids, rectangles, squares, unit square, square unit, side, congruent, prism, composite, compose, decompose, face, base, polygon, quadrilateral, area, additive property of area, perimeter, equal share, liquid volume, capacity, weight, liter, milliliter, ounces, pounds, cups, gallons, pints, quarts, gallons,

Student pre-requisite knowledge Name 2-D and 3-D geometric figures; describe attributes of 2-D and 3-D figures (vertices, edges, sides, faces) and use attributes to describe how 2-D and 3-D figures are alike or different.

Resources: MathBoard; 2-Dimensional and 3-Dimensional solids and figures; Real World Examples; Measuring tools for liquid Capacity and Weight; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos






3.6 Geometry and measurement: The student applies mathematical process standards to analyze attributes of two-








dimensional geometric figures to develop generalizations about their properties. The student is expected to:

3.6A classify and sort two- and three-dimensional (figures) solids, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language 3.6B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories 3.6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row 3.6D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area 3.6E decompose two congruent two-dimensional figures into parts with equal area and express the areas of each part a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape.

An attribute is the characteristic of an object or geometric shape.

Geometric attributes refer to the shape, size, number and type of faces, edges, vertices, lines, and angles of a figure.

You can use attributes to recognize and describe rhombuses, parallelograms, trapezoids, rectangles, and squares.

You can use attributes to draw and draw examples of quadrilaterals.

Three-dimensional figures are identified and classified according to their attributes.

A three-dimensional figure is also called a solid figure.

Solid figures take up space and have length, width, and height.

Two figures can be classified the same if they share all of the same attributes.

Faces are the flat surfaces of a three-dimensional figure.

Cylinders and cones have some curved surfaces.

A cylinder and a prism each have two bases.

A sphere has no flat faces.

A triangular prism has some triangular faces.

A cube has all square faces.

A cone and a pyramid each have one base.

The apex, or point, of a cone is not a vertex.

A vertex is the point or corner where two edges (rays) meet.

An edge is the line or border of a figure.

Area is a measure of the number of square units it takes to cover an object completely.

Area can be found by multiplying the number of rows times the number of unit squares in each row.

Units of area may be in square inches or square centimeters.

A composite figure is made up of

Use attributes to classify and sort two- and three-dimensional (figures) solids, cones, cylinders, spheres, triangular and rectangular prisms, and cubes.

Use formal geometric language to such as vertex, edges, faces to describe attributes of two- and three-dimensional (figures) solids.

Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals.

Draw examples of quadrilaterals that are not listed above.

Use concrete or pictorial models of square units to represent the number of rows and the number of unit squares in each row.

Use multiplication of whole numbers related to the number of rows times the number of unit squares in each row to determine the area of rectangles.

Use the additive property of area to decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure.

Decompose two congruent two-dimensional figures into parts with equal area.

Express the areas of each of the two congruent two-dimensional figures as a unit fraction of the whole.

Recognize that equal shares of identical wholes need not have the same shape.

Find the perimeter of an object when given the lengths of the sides.

Find the area of a figure by covering it with square units and counting.

Count the squares in a pictorial model to determine the area.

Relate area to arrays in multiplication.

Determine the area of rectangles


two or more shapes.

You can decompose composite figures that have been formed by rectangles into non-overlapping rectangles.

Squares are a special type of rectangle where all side lengths are equal.

Two congruent two-dimensional figures can be decomposed into parts with equal area so that you can express the area of each part as a unit fraction of the whole.

Equal shares of identical wholes do not need to have the same shape.

You can use the additive property of area to determine the area of the original figure.

To find the area of a composite figure, decompose (break apart) the figure into shapes with areas you know. Then find the sum of these areas.

with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row instead of counting squares.

Decompose composite figures formed by rectangles (no more than 3 rectangles) into non-overlapping rectangles to determine the area of the original figure using the additive property of area.

Recognize squares as a special type of rectangle.

Separate two congruent squares in half in two different ways.

Identify that the two smaller parts represent one-half of each of the original squares even though the halves from one square are not congruent to the halves in the other square.

Determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problem situations.


3.7B determine the perimeter of a

polygon or a missing length when given

perimeter and remaining side lengths in

problems

3.7D determine when it is appropriate to

use measurements of liquid volume

(capacity) or weight.

3.7E determine liquid volume (capacity)

or weight using approximate units and

tools

Perimeter is the distance around the sides or edges of an object.

Perimeter can be found by measuring each side of a figure and adding the length measurements together.

A missing length, when given the perimeter and remaining side lengths can be found by adding together the known measurements for each side length and subtracting the total from the given perimeter. The difference represents the measurement of the missing side length.

Capacity is the maximum amount of liquid a container can hold.

Volume is the amount of cubic units it takes to fill a container or 3-D figure. It involves measuring the room inside the container or figure.

Volume is expressed in cubic

Choose the appropriate tool to measure weight and liquid capacity.

Measure the (whole number) side lengths of the polygon to determine its perimeter using inches or centimeters.

Determine a missing side length of a polygon when given the perimeter of the polygon and the remaining side lengths.

Measure weight but should not determine mass.

Use appropriate tools to determine weight in the standard system.

Determine when it is appropriate to use measurements of liquid volume (capacity) or weight.

Distinguish between liquid ounces and ounces that measure weight.


units.

When determining volume, all cubic units may not be visible when looking at the container or 3-D figure.

Different tools are used to determine weight and liquid capacity.

Liquid ounces are different from ounces that determine weight.

Weight measures the amount of gravity that pushes down on an object.

ASSESSMENT EVIDENCE




Tasks

Geometric Figures Performance Assessment (English)

Length Performance Assessment (English)

Liquid Volume (Capacity) and Weight: Give small groups of students various containers of colored water to measure and compare the liquid volume and various objects weigh and compare the weights.

Ask students to write in the math journal to describe the comparisons.













Webquest




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Classifying and Sorting Shapes and Solids

http://www.escweb.net/tx_bm/math/docs/questions/P33.80E4.DOC

http://www.escweb.net/tx_bm/math/docs/questions/P33.11A0E1.DOC




3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 9: Data Analysis In this unit on data analysis, students will explore and interpret a variety of displays of data and solve one‐ and two‐step problems using categorical data. As you teach this unit, you should focus on students being able to summarize a set of data with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals. The process TEKS should be partnered with concepts throughout this unit to make connections between displays of data and real world experiences. Students begin work with pictographs in grade K and bar graphs in grade 1 with the Revised TEKS. This unit was strategically placed because it allows time for students to create, explore, and apply background knowledge of number lines to read and interpret data while still allowing time for engaging STAAR Review. The resources and activities for STAAR review can be accessed from the Engaging STAAR Review hyperlink found on the CRM. Data analysis and graphical representation concepts should be spiraled throughout the school year.












© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 3rd- 4th Nine Weeks

CRM 9 Data Analysis and STAAR Review Pacing

26 days

March 9 – April 21 DESIRED RESULTS


Making Meaning


Data can be represented and organized in various graphical forms to visually convey information.

Data can be interpreted.

Essential Questions

How can you use the strategy make a table to organize data and solve problems?

How can you display and interpret data?

How can you read and interpret data?

How can you solve problems using a graph?

How can you use a frequency table?

How can you display data in a dot plot? Vocabulary Vocabulary Cards, data, survey, tally mark, pictograph, bar graph, scale, labels, title, key, frequency table, dot plot

Student pre-requisite knowledge Construct, draw conclusions, and answer questions based on picture graphs and bar-type graphs.

Resources: Chart Paper; Graph Paper; Snap Cubes; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos






3.8 Data analysis: The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to:

3.8A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals 3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

Graphs represent data and convey information that can be used to solve problems.

Data can be collected in various ways, including surveys and frequency tables.

Different graphs can represent the same data.

Pictures or cells in graphs might represent more than one piece of data.

Data can be interpreted and suggest trends.

A frequency table is a table that

• Collect and organize data. • Use tally marks in data collection. • Record and display data using

pictographs and bar graphs. • Use results from a survey to

display in graphs. • Create and read graph titles,

labels, and keys. • Create and read graphs where

each picture or cell might represent more than one piece of data.

Represent and summarize a data set with multiple categories using a frequency table, dot plot,








lists particular items and uses tally marks to record and show the number of times they occur.

The data collected in a frequency table is represented in a graph.

A pictograph shows/ represents data using images/pictures.

Pictures in the graph may represent whole or ½ portions of data.

A bar graph represents data using bars of different heights.

A dot plot shows each item of numerical data above a number line, or horizontal axis.

Dot plots make it easy to see gaps and clusters in a data set, as well as how the data spreads along the axis.

A dot plot includes a dot for each value in a data set.

If a data set contains a large number of values, a dot plot might not be practical.

pictograph, or bar graph with scaled intervals.

STAAR Review

Students should use the remaining time to engage in hands-on, interactive activities to review Readiness and Supporting Standards.

Grade 3 Mathematics Assessment Eligible Texas Essential Knowledge and Skills

See CRMs 1-8 • See CRMs 1-8

ASSESSMENT EVIDENCE




Tasks: Mr. Smith the Dairy Farmer Place students in pairs and present the problem below:

Mr. Smith is a dairy farmer. On Monday he delivered 12

gallons of milk to the general store. Tuesday he delivered

16 gallons. On both Wednesday and Thursday, Mr. Smith

had good deliveries and doubled the amount he delivered

on Tuesday. Friday was a slow day because he only

delivered half of the amount that he delivered on Monday.

How many gallons of milk were delivered on Friday?

Complete the graph. Explain your process.

Ask these questions about the milk delivery graph

created in the above task:









1. On which days did Mr. Smith deliver the most milk?

2. On which days did he deliver the least amount of

milk?

3. How much milk did he deliver for the whole week?

4. If he delivers 26 gallons next Wednesday, what will

be the difference in the number of gallons he

delivered this Wednesday and will deliver next

Wednesday?

The dotplot below shows the number of pets owned by

children in an Austin neighborhood.

*

* * *

* * * * *

* * * *

* * *

* * * * *

0 1 2 3 4 5 6 7 8

1. Based on the data represented, what do know about the pets in the Austin neighborhood?

2. What information is not represented by the data?

Observations:

1. How does the student decide to set up the graph?

2. Can the student explain what each picture or cell

represents?

3. Does the student accurately label the graph?

4. Can the student locate information on the graph?

5. Does the student’s explanation represent the

written work?






Webquest

Create a Graph




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: Analyzing Data

http://nces.ed.gov/NCESKIDS/createagraph/default.aspx




3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 10: Place Value Concepts In this unit on place value, students will use knowledge of place value relationships and concepts to represent, order, compare, and round whole numbers. As you are teaching this unit, you should focus on the relationship between the value of digits and numbers as a whole. Students are expected to represent whole numbers to 100,000 with objects and pictorial models and compare and order whole numbers between 9,999 and 100,000. As you teach this unit, students should use manipulatives to develop the understanding of place value position as 10 times the position to the right and as one‐tenth of the value of the place to its left and use phrases such as “closer to,” “is about,” or “is nearly,” when representing numbers on a number line. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of place value concepts through real world experiences. This unit was strategically placed first because the concept is fundamental for understanding the value of numbers and how numbers are composed and decomposed as it relates to the four operations. Place value concepts and relationships should be spiraled throughout the school year.












© Austin Independent School District, 2014 Math Grade 3 Curriculum Road Map (CRM) 4th Nine Weeks

CRM 10 Place Value Concepts

Pacing

8 days

April 22 – May 1 DESIRED RESULTS


Making Meaning


Patterns in our number system and relationships between numbers are helpful in determining the value of a number.

Each decade of numbers has a symbolic pattern that is reflective of the 1-9 sequence.

The groupings of hundreds, tens, and ones can be taken apart in different ways based on patterns.

Patterns created by the base 10 system provide a framework for building number sense.

Essential Questions

How can you represent whole numbers using expanded notation?

How can you use base-tens, objects and pictures to compose and decompose whole numbers?

What are some ways that you can read and write numbers to 999,999?

What relationship can you find in the place value system?

How can you represent whole numbers through ten thousands on a number line to round?

What are some ways you can compare and order whole numbers?

Vocabulary Vocabulary Cards, word form, expanded form/notation, standard form, hundred thousands, ten thousands, thousands, hundreds, tens, ones, round, compose, decompose, place value, place, sum, nearest number, close to, about Student pre-requisite knowledge Reading, writing, composing/decomposing, and representing place Value to the thousands

Resources: MathBoard; Base-ten Blocks; Centimeter Grid Paper; Place Value chart to the Hundred Thousands; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos

Pre-AP and AP: Advanced Placement Vertical Teams Guide and Pre-AP Resource Bank Gifted and Talented: Exemplar Lessons, GT Scope and Sequence, GT Performance Reports ELPS: Mandated by Texas Administrative Code (19 TAC §74.4), click on the link for English Language Proficiency Standards (ELPS) to support English Language Learners.




3.2 Number and operations: The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

A number is composed of one or more periods.

A number is composed of one or more digits.

Each digit in a number holds a “place.” (ie. place value)

Each place in a number represents ten times the value of the place to

Read, write, and describe numbers up to the hundred thousands place.

Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so








3.2B describe the mathematical relationships found in the base-10 place value system through the hundred thousands place 3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

its right.

The place of a digit represents its value.

The symbol for zero allows us to represent symbolically the absence of value in a digit.

There are different representations for the same whole number value.

Numbers are composed and decomposed by the sum of the digit value.

Composing is to create a number based on the value of the digit(s).

Decomposing is to break a number apart based on the value of its digit(s).

Objects, pictorial models,

numbers, and expanded notation

can be used to compose and

decompose numbers.

When you round a number you

find a number that tells you about

how much or about how many.

You can use a number line to

round numbers.

You can round by finding the

closest or nearest 10, 100, 1000,

10,000, 0r 100,000.

Numbers can be compared using symbols to represent greater than, less than, and equal to.

Whole numbers can be ordered from least to greatest on a number line.

Whole numbers become greater on a number line as you move from left to right.

Whole numbers become less on a number line as you move from right to left.

The closer a number is to “zero” the smaller the number.

The farther a number is from “zero” the larger the number.

The symbol > represents greater than.

The symbol < represents less than.

The symbol = represents equal to.

many ones using objects, pictorial models, and numbers.

Compose and decompose numbers using expanded notation.

Describe the mathematical relationships found in place value system through the hundred thousands place as 10 times the position to the right.

Represent numbers up to 999,999 using objects and pictorial models.

Represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000.

Use words such as “closer to, is about, and is nearly” to describe the relative size of numbers in order to round whole numbers.

Compare and order all whole numbers up to 9,999 and between 9,999 and 100,000.

Represent comparisons using the symbols greater than, less than, and equal to.


ASSESSMENT EVIDENCE




Task: Comparing and ordering numbers to 999,999

Write the number 986,391 on the board. Ask students to record on white boards the number that is 1,000 less than your number (985,391). Repeat this activity with other numbers up to 999,999 using 10, 100, 1,000, and 10,000 more and less than your number.

Put students in groups of 6. Give each student a number card 0-9 or a playing card (take out face cards, aces are 1, jokers are 0.)

Have the groups arrange the cards to create the largest number possible and record it using numbers and words, then find the smallest number possible and record it. Use symbols to write a comparison of the two. Ask the group to write a statement to justify that the number is the largest possible or smallest possible.

Then, in the math journal, ask each student to represent one of their numbers as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects and pictures, numbers, and expanded notation.

Use the link below to create a grading rubric. http://rubistar.4teachers.org/













Webquest




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: More With Representing and Comparing Numbers to 100,000

http://rubistar.4teachers.org/



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 11: Fraction Concepts In this unit on fraction concepts, students will compose and decompose fractions; represent fractions of halves, fourths, and eighths as distances from zero on a number line; and model fractions that are greater than zero and less than or equal to one and compare two fractions having the same numerator or denominator. As you are teaching this unit, you should focus on fractions with denominators of 2, 3, 4, 6, or 8 and understand that equivalent fractions must be describing the same whole. Students are expected to represent fractions using concrete objects and pictorial models, including strip diagrams and number lines and justify conclusions about their comparisons using symbols, words, and pictorial models. Concrete models should be linear in nature to build to the use of strip diagrams and number lines. As you teach this unit, students should use manipulatives to develop the understanding of the concept and a number line to determine the length of the portion of a number between 0 and the location of the point. The process TEKS should be partnered with concepts throughout this unit. This unit was strategically placed to build upon fraction concepts learned in 2nd grade. Problems involving fraction concepts should be spiraled throughout the school year.













CRM 11 Fraction Concepts (14 days)

Pacing

14 days

May 4 – May 21 DESIRED RESULTS


Making Meaning


Fractional parts have special names that tell how many parts of that size are needed to make the whole.

Fractional parts are equal shares or equal-sized portions of a whole or unit.

A unit can be an object or a collection of things.

Fractions can be composed and decomposed by unit parts.

Objects, pictorial models, strip diagrams, and number lines can be used to represent and compare fractions.

Essential Questions

Why do you need to know how to make an equal share?

What do the top and bottom numbers of a fraction tell?

How does a fraction name part of a whole?

How can you represent and locate fractions on a number line?

How can you use objects, pictorial models, and strip diagrams to represent fractions?

How can you write a fraction as a sum of unit fractions with the same denominator?

Vocabulary Vocabulary Cards, fraction, numerator, denominator, part, whole, equal parts, equal shares, number line, compare, equivalent, benchmark number/fraction, half, halves, third(s), fourth(s), sixth(s), eighth(s), compose, decompose, partition, construct, model, unit fraction Student pre-requisite knowledge represent and name fractional parts (with denominators of 8 or less) using concrete models; locate and name whole numbers on a number line

Resources: Objects; Pictorial Models; Strip Diagrams ; Counters; Number Lines; Fraction Circles; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos






3.3 Number and operations: The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

3.3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects, pictorial models, including number lines 3.3G explain that two fractions are equivalent if and only if they are both

The denominator in a fraction represents the number of parts that the whole is broken into. It tells how many parts are needed to make the whole.

The numerator in a fraction represents the number of parts

Use concrete objects and pictorial models, strip diagrams, and number lines to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8.

Given a specified point on a








represented by the same point on the number line or represent the same portion of a same size whole for an area model 3.3H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

that are under consideration.

The more fractional parts used to make the whole, the smaller the parts.

The less fractional parts used to make the whole, the larger the parts.

Fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 can be modeled and compared using concrete objects, pictorial models, strip diagrams, and number lines.

Objects, pictorial models, and

number lines to can be used to

represent equivalent fractions

with denominators of 2, 3, 4, 6,

and 8.

Two fractions are equivalent if and only if they are both represented by the same portion of a same size whole of an area model.

Comparison symbols, words, objects, and pictorial models can be used to compare fractions.

number line, determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8.

Use pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8 to solve problems by partitioning an object or a set of objects between two or more recipients.

Use different objects, pictorial models, and number lines to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8.

Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line.

Use an area model to explain that two fractions are equivalent if and only if they both represent the same portion of a same size whole.

Use symbols, words, objects, and pictorial models to compare two fractions having the same numerator or denominator in problems.

Reason and justify conclusions

about the size of two fractions

having the same numerator or

denominator.


3.7A represent fractions of halves,

fourths, and eighths as distances from

zero on a number line

• Points on a number line represent whole numbers and fractions.

• When a fraction is plotted on a number line, it is shown as a point that is between whole numbers.

Fractions greater than zero and less than or equal to one with denominators of 2, 4, and 8 can be represented using number lines.

Number lines can be used to show the distance a fraction is from zero such as ¼ is half the distance from zero as ½ or ½ is twice the distance from zero as ¼.

Use a number line to represent fractions of halves, fourths, and eighths as distances from zero.


ASSESSMENT EVIDENCE




Task: Fractions as a Distance From Zero

Present the following problem to the class: Marlana rode her bike to a friend’s house. She stopped for a water break when she was 1/2 way there and 5/8 of the way there. How can she represent those distances on a number line?

Ask pairs of students to complete the following task in their math journals:

o Draw a number line and represent the distances on the number line.

o Count each fraction from zero to 1 to label the distances from zero.

o Draw a point at 1/2 and 5/8 to label the distance from zero.

o Is there an eighth that is equivalent to 1/2? If so, label its point to show its distance from zero.

o Draw a fraction strip diagram to show the length of each equal point on your number line.

o What is the length of each equal point on your number line?

o Which is a greater fraction, 1/2 or 5/8? Write an entry in your journal that explains how you know.













Webquest




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: More With Fraction Concepts



3rd Grade Math

The following summaries are intended to give an overview and rationale behind curriculum decisions. The Curriculum Road Maps (CRMs) will provide clarification of specific TEKS and what students should know and be able to do at the conclusion of each unit. To access the instructional resources, exemplar lessons and additional teacher tools, you must reference the CRMs. CRM 12: Multiplication and Division Concepts In this unit on multiplication and division, students will use knowledge of place value relationships, recall of multiplication facts up to 10 X 10, and properties of operations to multiply, divide, and estimate to determine solutions to mathematical and real‐world problems involving multiplication and division of whole numbers within 100. The learning of facts related to 11s and 12s is not included in the Revised TEKS. As you are teaching this unit, you should focus on the student’s ability to determine how and when it is appropriate to use multiplication or division and strategies that support the learning of multiplication facts such as repeated addition, equal‐sized groups, arrays, area models, equal jumps on a number line, skip counting, mental math, partial products, the commutative, associative, and distributive properties, and the standard algorithm. Arrays should reflect the combination of equally‐sized groups of objects. As you teach this unit, students should use manipulatives and concrete models and objects. The process TEKS should be partnered with concepts throughout this unit lending itself to the application of multiplication and division concepts through real world experiences. This unit was strategically placed so that students are able to use their knowledge of place value to solve problems involving the four operations. Multiplication and division concepts should be spiraled throughout the school year.













CRM 12 Multiplication and Division Concepts

Pacing

8 days

May 26 – June 4 DESIRED RESULTS


Making Meaning


Multiplication and division are related.

Multiplication and division involve counting groups of like size.

Models can be used to solve problems for multiplication and division and give meaning to equations (number sentences).

Basic facts are conceptually related.

Essential Questions

How is multiplication like/different addition?

How is division related to subtraction?

How are multiplication and division related?

How can you model multiplication and division problems to find products and quotients?

What strategies can be used to solve one and two step problems?

How can you use the properties of operations to solve multiplication problems?

How can you use strip diagrams top solve problems?

Vocabulary Vocabulary Cards, operation, multiplication, factor, product, array, area model, partial product, repeated addition, equal groups, multiple, division, divisor, dividend, quotient, partial quotient, repeated subtraction, equation, decompose, tens, ones, algorithm, expression, rows, columns, addition, subtraction, divide, multiply, commutative, associative, and distributive properties , equal groups

Student pre-requisite knowledge Basic multiplication and division facts; counting groups and the number in each group; building models of multiplication and division situations

Resources: Color tiles; Strip Diagrams; Snap Cubes; Counters; Centimeter Graph Paper; Base-ten Blocks; Number Lines; 10x10 grids; Exemplar Lessons; Instructional Resource Portfolios; Zip files; TEA Side-by-Side; 1st 20 Days of Math; Differentiation Resources; Go Math Think Central www.thinkcentral.com, Math on the Spot Video and Tour, Online Assessment System, and UR Code Professional Development Videos







3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and

Multiplication is a shortcut for repeated addition and involves joining equal sized groups.

In multiplication, the whole is unknown.

An array is a way of modeling or

Relate multiplication and division.

Use (Origo) numerical fluency strategies to remember basic facts to 10 x 10.

Identify the number of groups and how many are in each group in a








distributive properties 3.4J determine a quotient using the relationship between multiplication and division 3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

representing multiplication in repeated equal sized columns and rows.

In multiplication, the numbers multiplied are called factors.

When two factors are multiplied, the answer is called the product.

The product(s) of any two factors is called a multiple(s).

Multiplication expressions can be stated as a comparison.

An expression only includes the two factors that are being multiplied. It should not have an equal sign or solution, but can have an expression of equal value on the opposite side of the equal side.

An equal sign or solution changes an expression to an equation. It shows that both sides of the equal sign are equal.

An equation is a mathematical statement that says or shows that this is equal to that.

Some ways to represent multiplication are by repeated addition, combining equal-sized groups or objects, arrays, area models (partial products), equal jumps on a number line, and skip counting.

Arrays reflect the combination of equally-sized groups of objects.

Division of the product and known factor or repeated addition/subtraction of the known factors can be used to determine the unknown/missing factor or product.

Unknown factors or products can be determined by finding the number that makes the unknown when multiplied by the given factor.

Decomposing a two-digit number into tens and ones (partial products or area models) helps to multiply.

In division, the number of equal-sized groups or the total number in each group is unknown.

The commutative, associative, and

multiplication problem.

Write an equation (number sentences) to match multiplication models.

Record and solve multiplication problems up to a two digit number times a one digit number.

Use various number based

strategies to solve multiplication

and division problems and

situations.

Represent multiplication situations through the use of repeated addition, combining equal-sized groups or objects, arrays, equal jumps on a number line, and skip counting.

Recall the division facts up to 10 by 10.

Use place value strategies, algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number.

Use mental math, partial products, and the commutative, associative, and distributive properties to solve problems.

Determine a quotient using the relationship between multiplication and division.

Use strategies based on objects; pictorial models, arrays, area models, equal groups, properties of operations, and recall of facts to solve one-step and two-step problems involving multiplication and division problems within 100.

Identify and describe the commutative, associative, and distributive properties.


distributive properties can be used to multiply a two digit number by a one digit number.


3.5B represent and solve one- and two-

step multiplication and division problems

within 100 using arrays, strip diagrams,

and equations

3.5D determine the unknown whole

number in a multiplication or division

equation relating three whole numbers

when the unknown is either a missing

factor or product

It can take more than one step to find the solution to a multiplication or division situation.

The unknown factor is what you are solving for.

Arrays, strip diagrams, and equations can be used to find unknowns.

Connections can be made between arrays and strip diagrams.

The relationship between multiplication and division can be used to find unknowns.

Represent and solve one- and two-step multiplication and division problems within 100.

Use arrays, strip diagrams, and equations to solve multiplication and division problems.

Determine the unknown whole number in a multiplication equation relating three whole numbers when the unknown is either a missing factor or product.

Determine the unknown whole number in a division equation relating three whole numbers when the unknown is either a missing factor or product/quotient.

Connect arrays to strip diagrams.

ASSESSMENT EVIDENCE




Tasks: Jerry’s DVDs

Give pairs of students base-ten blocks and present the following problem: Jerry bought 4 DVDs of his favorite movies. Each DVD costs $27. How much money did Jerry spend on DVDs?

Explain that students will create a model, write an equation, and determine a solution to the problem.













Webquest


Explain that students should use a strip diagram or an array to check their equation and solution.

Have students write to explain the steps they took to solve the problem.




Exemplar Lessons and Instructional Resources PDF Exemplar Lessons and Instructional Resources ZIP Files Exemplar Lesson- Title: More With Relating Multiplication and Division




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