WORK IN PROGRESS Grade 1 Elsinore Unified School District Instructional Module To Enhance the Teaching of Envision Math – CA Edition WORK IN PROGRESS Grade 1 Module 12 ... Envision

Lake Elsinore Unified School District

Instructional Module To Enhance the Teaching of Envision Math – CA Edition

WORK IN PROGRESS

Grade 1

Module 12

Revised June 2015

1st Grade Mathematics Sequence 2015-2016

Trimester Module/Topic Envision Lessons Approximate Days

1st Trimester

Five and Ten Relationship Topic 3 8 days

Understanding Addition Topic 1 12 days

Understanding Subtraction Topic 2 12 days

Length Topic 12 6 days

Counting and Number Patterns

to 120 Topic 7 8 days

Tens and Ones Topic 8 8 days

2nd Trimester

Time Topic 13 10 days

Addition and Subtraction to 12 Topic 4 10 days

Geometry Topic 15 10 days

Comparing and Ordering to 100 Topic 9 10 days

Addition & Subtraction to 20 Topic 5 10 days

Compare Problems* Topic 6 10 days

3rd Trimester

Adding with Tens and Ones Topic 10 10 days

Subtracting with Tens and Ones Topic 11 10 days

Using Data to Answer Questions Topic 14 5 days

Fractions of Shapes Topic 16 5 days

Applying Properties of Operations

Topic 6 10 days

1st Grade Module 12 at a Glance

“Grade one students should have an opportunity to solve and discuss such problems [compare

problems], but proficiency with these most difficult subtypes should wait until grade two.” - Framework

Some lessons may take more than one day.

Lesson Number Lesson Focus

Materials

Optional Binder

Materials

Technology Integration

1 Comparing numbers with difference unknown

Chart paper, markers, math tools

Explain Everything

Doceri

Braingenie.com Visnos.com App: Equalo

2 Comparing numbers with difference unknown

Math tools, chart paper, markers

Explain Everything

Doceri


3 Comparing numbers with bigger unknown – more

Math tools, whiteboards, whiteboard markers, chart paper, markers

Explain Everything

Doceri


4 Comparing numbers with smaller unknown - fewer

Chart paper, markers

Explain Everything

Doceri

Braingenie.com

App: Equalo Visnos.com

5 Comparing numbers with bigger unknown – fewer

Whiteboards, whiteboard markers, chart paper, markers

Explain Everything

Doceri


6 Comparing numbers with smaller unknown – more

Math tools, chart paper, markers

Explain Everything

Doceri


*Some lessons were supported with the following resources: CCSS Math Framework for 1st Grade, Georgia Department of Education, San Diego Math Modules and Teaching Student Centered Mathematics

Connecting Mathematical Practices and Content Grade 1

The Standards for Mathematical Practice (MP) are developed throughout each grade and, together with the content standards, prescribe that students experience mathematics as a rigorous, coherent, useful, and logical subject that makes use of their ability to make sense of mathematics. The MP standards represent a picture of what it looks like for students to understand and do mathematics in the classroom and should be integrated into every mathematics lesson for all students.

Although the description of the MP standards remains the same at all grades, the way these standards look as students engage with and master new and more advanced mathematical ideas does change. Below are some examples of how the MP standards may be integrated into tasks appropriate for grade one students. Standards for Mathematical Practice

Explanation and Examples from Mathematics Framework

MP.1 Make sense of problems and persevere in solving them.

In first grade, students realize that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Younger students may use concrete objects or math drawings to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They are willing to try other approaches.

MP.2 Reason abstractly and quantitatively.

Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities. In first grade students make sense of quantities and relationships while solving tasks. They represent situations by decontextualizing tasks into numbers and symbols. For example, “There are 14 children on the playground and some children go line up. If there are 8 children still playing, how many children lined up?” Students translate the situation into the situation equation: 14 − ? = 8, and then into the related equation 8 + ? = 14 and solve the task. Students also contextualize situations during the problem solving process. For example, students refer to the context of the task to determine they need to subtract 8 from 14 because the total number of children on the playground is the total number less the 8 that are still playing. Teachers might ask, “How do you know” or “What is the relationship of the quantities?” to reinforce students’ reasoning and understanding. Students might also reason about ways to partition two-dimensional geometric figures into halves and fourths.

MP.3 Construct viable arguments and critique the reasoning of others.

First graders construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They practice mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” or “Explain your thinking,” and “Why is that true?” They explain their own thinking and listen to the explanations of others. For example, “There are 9 books on the shelf. If you put some more books on the shelf and there are now 15 books on the shelf, how many books did you put on the shelf?” Students might use a variety of strategies to solve the task and then share and discuss their problem solving strategies with their classmates.

MP.4 Model with mathematics.

In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, and creating equations. Students need opportunities to connect the different representations and explain the connections. They should be able to use any of these representations as needed. First grade students model real-life mathematical situations with an equation and check to make sure equations accurately match the problem context. Students use concrete models and pictorial representations while solving tasks and also write an equation to model problem situations. For example to solve the problem, “There are 11 bananas on the counter. If you eat 4 bananas, how many are left?” students could

Connecting Mathematical Practices and Content – Grade 1

Connecting Mathematical Practices and Content Grade 1

write the equation 11 – 4 = 7. Students should be encouraged to answer questions, such as “What math drawing or diagram could you make and label to represent the problem?” or “What are some ways to represent the quantities?”

MP.5 Use appropriate tools strategically.

Students begin to consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, first graders decide it might be best to use colored chips to model an addition problem. Students use tools such as counters, place value (base ten) blocks, hundreds number boards, concrete geometric shapes (e.g., pattern blocks, 3-dimensional solids), and virtual representations to support conceptual understanding and mathematical thinking. Students determine which tools are appropriate to use. For example, when solving 12 + 8 = __, students might explain why place value blocks are appropriate to use to solve the problem. Students should be encouraged to answer questions such as, “Why was it helpful to use…?”

MP.6 Attend to precision.

As young children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and when they explain their own reasoning. In grade one, students use precise communication, calculation, and measurement skills. Students are able to describe their solutions strategies to mathematical tasks using grade-level appropriate vocabulary, precise explanations, and mathematical reasoning. When students measure objects iteratively (repetitively), they check to make sure there are no gaps or overlaps. Students regularly check their work to ensure the accuracy and reasonableness of solutions.

MP.7 Look for and make use of structure.

First grade students look for patterns and structures in the number system and other areas of mathematics. While solving addition problems, students begin to recognize the commutative property, for example 7 + 4 = 11, and 4 + 7 = 11. While decomposing two-digit numbers, students realize that any two-digit number can be broken up into tens and ones, e.g. 35 = 30 + 5, 76 = 70 + 6. Grade one students make use of structure when they work with subtraction as an unknown addend problem, such as 13 – 7 = __ can be written as 7+ __ = 13 and can be thought of as how much more do I need to add to 7 to get to 13?

MP.8 Look for and express regularity in repeated reasoning.

In the early grades, students notice repetitive actions in counting and computation. When children have multiple opportunities to add and subtract “ten” and multiples of “ten” they notice the pattern and gain a better understanding of place value. Students continually check their work by asking themselves, “Does this make sense?” Grade one students begin to look for regularity in problem structures when solving mathematical tasks. For example, students add three one-digit numbers by using strategies such as “make a ten” or doubles. Students recognize when and how to use strategies to solve similar problems. For example, when evaluating 8 + 7 + 2, a student may say, “I know that 8 and 2 equals 10, then I add 7 to get to 17. It helps if I can make a 10 out of two numbers when I start.” Students use repeated reasoning while solving a task with multiple correct answers. For example, solve the problem, “There are 12 crayons in the box. Some are red and some are blue. How many of each could there be?” Students use repeated reasoning to find pairs of numbers that add up to 12 (e.g., the 12 crayons could include 6 of each color (6 + 6 = 12), 7 of one color and 5 of another (7 + 5 = 12), etc.) Students should be encouraged to answer questions, such as “What is happening in this situation?” or “What predictions or generalizations can this pattern support?”

Connecting Mathematical Practices and Content – Grade 1

Technology at a glance The use of technology can be a tool for students to model mathematical relationships in real-‐world situations. Technology can enhance student understanding of mathematical concepts, bolster student engagement and strengthen problem solving skills.

Icon Description Possible Uses

Explain Everything This is a free app that allows the user to animate their thinking and explain anything using a variety of tools. The user can import and export documents, images, videos and explain everything creations. Explain Everything is a unique screencasting whiteboard explaineverything.com has a video of the variety of ways to use this app.

Teacher driven as a part of the lesson.

Student driven to use as an interactive activity, discovery, or as a part of

a math blog.

Optional practice As an assessment piece.

Doceri This is a free app that you can create hand drawn lessons, presentations and graphics and shre them as still images, PDF’s or audio/video screencasts or mirror anything you’ve created to Apple TV via AirPlay. doceri.com has ideas for classroom presentations in the solution selection.



a math blog.

Optional practice As an assessment piece

Buncee for Edu This is an app and also a website for designing interactive lessons. Design interactive lessons, flip your class, and easily manage students and assignments with the classroom organizer tool. edu.buncee.com Takes you to the website for this program.



a math blog.


Interactive telling time – Learning to tell time is fun. This is a free app that allows students to practice telling time in a variety of ways.


a math blog.

Optional practice

http://catalog.mathlearningcenter.org/apps This website is a great resource for all sorts of math apps.

Teacher Resource


a math blog.


Early Learning Abacus App Counting tool for understanding number relationships.

Teacher Resource


a math blog.


Rekenrek by Mathies App Another counting tool that builds a deeper understanding of number relationships.

Teacher Resource


a math blog.


Kidblog.org Kidblog provides teachers with the tools to help students publish writing safely online. Students exercise digital citizenship within a secure classroom blogging space. Teachers can monitor all activity within their blogging community. There is a free version and a paid version of this site.



a math blog.


Visnos.com This website provides interactive teaching resources to use whole class or as an individual practice.



a math blog.


Braingenie https://braingenie.ck12.org This website helps build deep understanding and sharpen problem solving skills. It is broken up by grade level and standards. Free Sign up for teachers and students.

Teacher Resource

Optional skill practice

Mr. Wolfe’s interactive whiteboard Games This website provides math resources broken up by grade level.

Teacher Resource Optional skill practice

Fuel the Brain This is a website that provides grade level skill practice.


http://illuminations.nctm.org This website provides resources and lessons for teachers and links to interactive apps.


http://www.ictgames.com This website provides games for math and literacy.


Instructional Strategies Used in K-7 Instructional Modules

Taken from the CA Mathematics Framework and 5 Practices for Orchestrating

Productive Mathematics Discussions by Peg Smith and Kay Stein POSE THE PROBLEM

Simply pose the problem, without suggesting or allowing other students to suggest any particular mathematical strategy to solve the problem.

INDEPENDENT Students work independently and quietly, often for the purpose of letting students think about their own reasoning and informal assessment.

THINK-PAIR-SHARE Students get time to think quietly, then share their thoughts with a partner and listen to their partners’

TABLE TALK THINK-PAIR-SHARE with more than 2 students

WHOLE GROUP Focus is on pulling the whole class together. CONSENSUS Students share their individual ideas and

come to an agreement within the group to share with the whole class.

MONITOR Teacher pays close attention to students’ mathematical thinking and solution strategies as they work on a task, for the purpose of using their observations to decide what and whom to focus on during the class discussion that follows.

SELECT The teacher, through monitoring, selects student work samples or strategies to display or have students present.

SEQUENCE The teacher purposefully chooses the order in which student strategies are displayed and/or discussed, often beginning with the more concrete strategies moving to more abstract.

CONNECT The teacher helps students draw connections between their solutions/strategies and others’ solutions/strategies for the purpose of connecting their thinking to the mathematics we want them to learn

DISPLAY The teachers shows student work to the rest of the class for the purpose of allowing students to analyze the students’ strategies.

Grade 1 Module 12, Lesson 1

Lesson Focus Comparing numbers with difference unknown.

PLC Notes

Lesson Purpose

Students will solve comparison problems with difference unknown. Data from graphs will be used to solve the problem.

Content Standards

Operations & Algebraic Thinking 1.0A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns. In all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Measurement and Data 1.MD.4 Organize, represent, and interpret data with up to three categories, ask and answer questions about the total number of data points, how many in each category, and how many more or how many less are in one category than in the another.

Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☐Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically.

☒ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

POSE THE PROBLEM Display the following:

Number

Of Pennies WHOLE GROUP Read/display this story(template 12.1.1) On Monday Jose has 12 pennies and Samantha has 8 pennies. How many more pennies does Jose have than Samantha? THINK-PAIR-SHARE Using this bar graph how can we solve this problem? What strategies can help us? WHOLE GROUP Share student responses on t chart on whiteboard. Write “John says . . . “ for student responses.

Monday

Jose Samantha

Investigate

Materials Tools in toolkit

INDEPENDENT POSE THE PROBLEM Now let’s look at another bar graph another way. Display the following.

Number

of Pennies Read story below. On Friday Samantha has 6 pennies and Jose has 13 pennies. How many fewer pennies does Samantha have than Jose? THINK-PAIR-SHARE What is the story about? What information do we know? What information is missing? What tools can you use to solve this problem? What do you notice? MONITOR/SELECT/SEQUENCE Students work independently to solve the problem and record thinking on whiteboards. Students use math tools, draw a picture, & write a number sentence to show their thinking. Teacher pays close attention to students’ mathematical thinking and counting strategies the students utilize. Teacher chooses 2-3 student samples to display for other students to explain. DISPLAY The teacher shows a few student samples that show students using the counting on strategy. Ask students to analyze other students’ work. A teacher can display student work with errors so students can disprove the math.

Summarize Chart paper,

markers

WHOLE GROUP What strategy was most efficient in solving this problem? Why? What math tool was most efficient in solving this problem? Why? What did we learn about math today? What did we learn about ten today? Did we notice any relationships? What patterns did we see? Chart student responses on butcher paper and cite who said them.

Friday

Jose Samantha

Optional Practice

Doceri Braingenie.com

Visnos.com App: Equalo

“Coolest Robot” (template 12.1.2)

Homework Envision 14-2 (template 12.2.3)


Lesson Focus Comparing numbers with difference unknown.

P

Lesson Purpose

Students will solve comparison problems with difference unknown. Data from graphs will be used to solve the problem.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.



Introduce

Materials


Food Tally Marks

burger l l l l

hot dog l l l l l

pizza l l l l l l l

WHOLE GROUP Read/display this story(template 12.2.1) How many fewer kids voted for burger than pizza? THINK-PAIR-SHARE Using this bar graph how can we solve this problem? What strategies can help us? WHOLE GROUP How can we ask another question about “how many fewer” using this tally graph? Share student responses.

Favorite School Lunch

Investigate

Materials Tools in toolkit;

Template 12.2.1; Template 12.2.4

Document camera to

display

INDEPENDENT POSE THE PROBLEM Now let’s look at another bar graph another way. Display the following.

WHOLE GROUP Read story below(template 12.2.1) How many fewer kids eat peanut butter & jelly than yogurts for school lunch? THINK-PAIR-SHARE #1 What is the story about? What information do we know? What information is missing? What tools can you use to solve this problem? #2 What is another “fewer” question we can ask about this graph? MONITOR/SELECT/SEQUENCE Students work independently to solve the posed question AND to write their own “fewer” question and solve it. Student record thinking on template 11.11.4. Students use math tools, draw a picture, & write a number sentence to show their thinking. Teacher pays close attention to students’ mathematical thinking and counting strategies the students utilize. Teacher chooses 2-3 student samples to display for other students to explain. DISPLAY The teacher shows a few student samples that show students using the counting on strategy. Ask students to analyze other students’ work. A teacher can display student work with errors so students can disprove the math.

Yogurt

PB & J

Lunchable

Summarize



Optional Practice



“Favorite Zoo Animal ” with spinner(template 12.2.2)

Favorite Packed Lunch

Homework “Favorite Zoo Animal” (template 12.2.3) Have students write their own question on the back.


Lesson Focus Comparing numbers with bigger unknown – more PLC Notes

Lesson Purpose

Students will solve word problems by using various strategies: counting on, graphing, etc.

Content Standards

Operations & Algebraic Thinking 1.0A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns. In all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Practice Standards

☒ Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☒ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically. ☒ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials Template 12.3-

1 Tools

Whiteboards markers

INDEPENDENT POSE THE PROBLEM Template 12.3-1 Katie has 5 more erasers than Amy. Amy has 6 erasers. How many erasers does Katie have? Use your math tools and whiteboards to solve. MONITOR/SELECT/SEQUENCE student work Mix up samples that are correct and incorrect. Call on students to prove or disprove other students’ work. Be sure to ask a 2nd question. (How do you know that? Will that always work?)

Investigate

Materials Template

12.3-2, 12.3-3 &

12.3-4

INDEPENDENT POSE THE PROBLEM Template 12.3-2 Cooper has 8 more surfboards than Cliff. Cliff has 8 surfboards. How many surfboards does Cooper have? Use template 12.3-3 to have students demonstrate all the different ways they can represent the problem. CAROUSEL MUSEUM WALK When students are done, ask them to leave their work on top of their desk and walk around and look at other students’ work. When finished ask students to go back to their seats. Tell them to go ahead and add on to their own work if they got some great ideas from their peers. WHOLE GROUP What tools worked best for solving a problem like this? What makes this problem tricky? What is a problem like this really asking us to do? POSE THE PROBLEM THINK-PAIR-SHARE Template 12.3-4 Morgan has 3 more candies than Sammi. Sammi has 17 candies. How many candies does Morgan have? How can we solve this? What equation(s) can we write? What tools can we use?

Summarize


WHOLE GROUP What strategy was most efficient in solving this problem? Why? What math tool was most efficient in solving this problem? Why?

Optional Practice Template

12.3-5

Doceri Visnos.com

Braingenie.com App: Equalo

Ask students to create their own word problems using the bigger unknown more version. Template 12.3-5

Homework Template 12.3-6

Compare: Bigger Unknown: More

Katie has 5 more erasers than Amy. Amy

has 6 erasers. How many erasers does Katie have?

12.3-1


Cooper has 8 more surfboards than Cliff. Cliff has 8 surfboards. How many surfboards does Cooper have?

12.3-2

Name_____________________ Draw all the different ways you can represent the problem.

12.3-3


Morgan has 3 more candies than Sammi. Sammi has 17 candies. How many candies does Morgan have?

12.3-4

Name:_____________________ Directions: Write your own “more” word problem using addition.

_______________________________________________________________________________________________________________________________________

Solve your problem. Write the equation.

___ ___ ___

12.3-5

Name _________________ Directions: Solve the word problems. Draw a picture and write an equation for each problem.

1. Noah has 7 more cats than Aiden. Aiden has 5 cats. How many cats does Noah have?

_____ _____ _____ Write another equation you can use to help solve.

_____ _____ _____

What do you notice about the two equations that you wrote above? _________

_________________________________________

12.3-6

2. Jenna has 2 more balls than Bria. Bria has 6 more balls than Crystal. Crystal has 9 balls. How many balls do Jenna and Bria have?

Jenna:

Bria:

How did you get your answers?

________________________________________________________________________________________________________________________________________________


Lesson Focus Comparing numbers with smaller unknown – fewer PLC Notes

Lesson Purpose

Students will use various subtraction and/or addition strategies to solve. They will also strengthen their understanding of the connection between addition and subtraction.

Content Standards


Practice Standards



Introduce


1 Tools

Projector Document

camera

INDEPENDENT POSE THE PROBLEM Give students a copy of template 12.4-1 CRA* (Concrete, Representation, Abstract) Cole has 3 fewer skateboards than Luke. Luke has 9 skateboards. How many skateboards does Cole have? Use tools of your choice to build a representation of this problem, then draw a picture of it and write two equations to support your work. MONITOR/SELECT/SEQUENCE student work Mix up samples that are correct and incorrect and DISPLAY the student work over the projector. Call on students to prove or disprove other students’ work. Be sure to ask a 2nd question.

Investigate

Materials Template

12.4-2,

THINK-PAIR-SHARE POSE THE PROBLEM Display and give students template 12.4-2 Work with your neighbor or group to solve. Colin has 6 fewer caterpillars than Kaylin. Kaylin has 13 caterpillars. How many caterpillars does Colin have? Use strategies and tools of your choice to solve. POSE THE PROBLEM THINK-PAIR-SHARE Is it possible to take the problem we just did and rewrite it as a more problem like the ones we worked on yesterday? (*If needed read this sample problem: Julie had three more apples than Lucy. Lucy has two apples. How many apples does Julie have?) Why does this work or why doesn’t it work? How can we solve this? What equation(s) can we write? What tools can we use? Is there a relationship here? With your group, write how you would rewrite the problem. If it is not possible to rewrite this problem, write a sentence or two telling me why. Teacher MONITORS/SELECTS student samples to share in the summary.

Summarize


WHOLE GROUP DISPLAY student work that you selected. Ask probing questions. Chart questions and student responses. Draw illustrations if needed.

Optional Practice



Template 12.4-3


Name: ________________ Cole has 3 fewer skateboards than Luke.

Luke has 9 skateboards. How many skateboards does Cole have?

After you build the problem with your math tools, draw a picture of how you would represent this problem here.

Write two different equations that support your representation above.

_____ _____ = _____

_____ = _____ _____ What do you notice about the two equations that you wrote

above? ___________________________

_______________________________

12.4-1

Name: ________________ Colin has 6 fewer caterpillars than Kaylin.

Kaylin has 13 caterpillars.

How many caterpillars does Colin have?

After you build the problem with your math tools, draw a picture of how you would represent this problem here.

What are two ways we can write the equation?

_____ _____ = _____

_____ = _____ _____

12.4-2

Is it possible to take the problem we just did and rewrite it as a “more problem” like the ones we worked on yesterday?

Yes No If you circled yes, then tell me how you would rewrite the problem. If you said no, tell me why it doesn’t work.

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Name: ________________ Directions: Complete the graph and answer the questions.

Number Of Video Games

1 2 3 4 5 6 7 8 9 10 Talan

Ryder

1. Talan has 4 fewer video games than Ryder. Ryder has 9 video games. How many video games does Talan have?

__________________________________________________________

2. How do you know how many video games Talan has?

__________________________________________________________

12.4-3

Name: ________________ Directions: Complete the graph and answer the questions.

Number Of Dolls

1 2 3 4 5 6 7 8 9 10 Summer

Sophia

1. Sophia has 3 fewer dolls than Summer. Summer has 10 dolls. How many dolls does Sophia have?

__________________________________________________________

2. How do you know how many dolls Sophia has? What do you have to do to get the answer?

__________________________________________________________

12.4-4

3. How do you know that Sophia does not have 3 dolls?

__________________________________________________________

4. Can you rewrite this “fewer” problem as a “more” problem? If yes, write the new problem and tell me what relationship you see, if not then justify your answer. * See example below if you need help.

_________________________________________________________________________________________________________________________________________________ * Example of a “more” problem:

Julie has three more apples than Lucy.

Lucy has two apples.

How many apples does Julie have?


Lesson Focus Comparing numbers with bigger unknown – fewer PLC Notes

Lesson Purpose

Students will use various subtraction and/or addition strategies to solve comparison problems. They will also strengthen their understanding of the connection between addition and subtraction.

Content Standards


Practice Standards



Introduce


1 Tools

Whiteboards markers

THINK-PAIR-SHARE POSE THE PROBLEM Display template 12.5-1 Have students write on whiteboards Kinsley has 8 fewer pieces of gum than Addilyn. Kinsley has 2 pieces of gum. What question can you write about this? What information are we missing?

Investigate

Materials Template

12.5-2

POSE THE PROBLEM Display and give students template 12.5-2 There are 2 fewer star stickers than happy face stickers. There are 4 star stickers. What question can you ask? Let students work in pairs or groups to solve. Teacher MONITORS/SELECTS student samples to share in the summary.

Summarize


WHOLE GROUP DISPLAY student work that you selected. Ask probing questions. Chart questions and student responses. Draw illustrations if needed.

Optional Practice

Doceri Visnos.com

Braingenie.com App: Equalo

Have students either solve or write more “bigger unknown – fewer version problems.”


Compare: Bigger Unknown: Fewer

Kinsley has 8 fewer pieces of gum than Addilyn. Kinsley has 2 pieces of gum. What question can you write about this? What information are we missing?

12.5-1

Name: ________________ Directions: Use the graph to write a problem

Number Of Stickers

1 2 3 4 5 6 7 8 9 10

happy

1. There are 2 fewer star stickers than happy face stickers. There are 4 star stickers. What question can you ask?

__________________________________________________________

2. Solve your question and write the answer.

__________________________________________________________

12.5-2

3. Use the data above to create a pie chart. Use for the stars and for the happy .

4. What do you notice about the pie chart?

__________________________________________________________

5. How can using a pie chart help you?

_______________________________________________________________________________________

Name: ________________ Directions: Use the graph to write a problem

Favorite Toys 1. There are 5 fewer Mr. Potato Heads

than Legos. There are 9 Mr. Potato Heads. How many Legos are there? Solve and graph.

________________________________________________ Tell me the steps you used to solve the problem.

_____________________________________________________________________________________________

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Legos

Mr. Potato

Head

12.5-3

2. Create your own problem or question like the one you just did. Then, create some sort of graph or chart of the information in your problem. When finished, ask your parents to solve the problem you created and check to make sure they did it correctly. Have fun!

_______________________________________________________________________________________

Parents solve here:________________________ __________________________________


Lesson Focus Comparing numbers with smaller unknown

PLC Notes Lesson

Purpose Students will solve comparison problems with smaller unknown. Data from graphs will be used to solve the problem.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.



Introduce

Materials

Template 12.6-1


Number of Pencils

Cole l l

Luke l l l l

Allison l l l l l l l

WHOLE GROUP Read/display this story(template 12.6-1) Cole has 3 fewer pencils than Luke. Luke has 5 pencils. How many pencils does Cole have? THINK-PAIR-SHARE Using this bar graph how can we solve this problem? What strategies can help us? What information do we know? What information is missing? Is there any information that is not important? Why or why not. WHOLE GROUP Share student responses on t chart on whiteboard. Write “John says . . . “ for student responses.

Investigate

Materials Tools in toolkit; template 12.6-1; Template 12.6-2

INDEPENDENT POSE THE PROBLEM Now let’s look at another tally chart another way. Display the following.

Number of Erasers

Cole

Luke

Allison l l l l l l l l l l l l l l l

Read story below.(template 12.6-1) #1 - Allison has 9 more erasers than Luke. Allison has 18 erasers. Luke has 9 fewer erasers than Allison. How many erasers does Luke have? #2 – Luke has ________(insert solution from part #1) Cole has 2 fewer erasers than Luke. How many erasers does Cole have? THINK-PAIR-SHARE What is the story about? What information do we know? What information is missing? What tools can you use to solve this problem? What do you notice? MONITOR/SELECT/SEQUENCE Students work independently to solve the problem and record thinking on template 12.6-2. Students use math tools to solve their problem as needed. Students then write their own question about the tally chart. Teacher pays close attention to students’ mathematical thinking and counting strategies the students utilize. Teacher chooses 2-3 student samples to display for other students to explain. DISPLAY The teacher shows a few student samples that show students using the counting on strategy. Ask students to analyze other students’ work. A teacher can display student work with errors so students can disprove the math.

Summarize



Optional Practice Doceri

Visnos.com Braingenie.com

App: Equalo


“Comparison Problems with Smaller Unknown”

Read story problem below. INTRODUCE

Number of Pencils

Cole has 3 fewer pencils than Luke. Luke has 5 pencils. How many pencils does Cole have?

INVESTIGATE

Number of Erasers #1 – Allison has 9 more erasers than Luke. Allison has 18 erasers. How many erasers does Luke have?_________. Cole has 2 fewer erasers than Luke. How many erasers does Cole have? #2 – Now we know that Luke has ________ erasers. Cole has 2 fewer erasers than Luke. How many erasers does Cole have?

Cole

Luke l l l l

Allison l l l l l l l

Cole

Luke


12.6-1

Name: _________________

Directions: Use the graph to solve your problem. Fill in the graph as

you solve the problems.

Number of Erasers

1. Allison has 9 more erasers than Luke. Allison has 18 erasers. Luke has 9 fewer erasers than Allison. How many erasers does Cole have?

__________________________________

________________________________________________

_________________________________________________

Cole

Luke


12.6-2

2. Luke has erasers. Cole has 2

fewer erasers than Luke. How many erasers

does Cole have? How do you know and why?

_________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

3. Using this tally chart write another question using

“fewer”.

_________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

Name: _________________

Directions: Use the graph to solve your problem. Fill in the graph as

you solve the problems.

Number of Cookies

1. Matt has 7 fewer erasers than Nathan. Matt has 15

erasers. How many erasers does Nathan have?

2. Nathan has erasers. Erin has 2 fewer

erasers than Nathan. How many erasers does Erin have?

How do you know and why?

___________________________________________

_________________________________________________

_________________________________________________

Matt

l l l l l l l l l l l l

Nathan

Erin

12.6-3

3. Create your own problem or question like the one you

just did. Then, create some sort of tally chart of

the information in your problem. When finished, ask

your parents to solve the problem you created and

check to make sure they did it correctly. Have fun!!

_________________________________________________

_________________________________________________

_________________________________________________

Parents solve here: __________________________

_________________________________________________

Grade 1

Module 12

Assessment

Compare Problem

Types

Difference Unknown

“How many more?” version: Lucy has two apples. Julie has five apples. How many more apples does Julie have than

Lucy? “How many fewer?” version: Lucy has two

apples. Julie has five apples. How many fewer apples does Lucy have than Julie? 2 + ? =

5, 5 – 2 = ?

Bigger Unknown Version with “more”: Julie has three more apples than Lucy. Lucy has two apples.

How many apples does Julie have?

Version with “fewer”: Lucy has 3 fewer apples than

Julie. Lucy has two apples. How many apples does Julie

have? 2 + 3 = ?, 3 + 2 = ?

Smaller Unknown Version with “more”:

Julie has three more apples than Lucy. Julie has five

apples. How many apples does Lucy have?

Version with “fewer”: Lucy has 3 fewer apples than

Julie. Julie has five apples. How many apples does Lucy

have? 5 – 3 = ?, ? + 3 = 5

“Unshaded problems are the most difficult, grade one students work with these problems but do not master them until grade two. “ (CCSS Math Framework, pg. 13) – Unshaded problem types are represented in test item #5 and #6.

1

2

3

4

2

2

3

4

3

2

3

4

4

2

3

4

5

2

3

4

6

2

3

4

Name _____________________

1. Read the story problem below.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Felix Kevin

Felix has 7 horses and Kevin has 13 horses. How many more horses does Kevin have than Felix? Write an equation to represent the problem.

_________________________ Kevin has more horses than Felix.

Grade 1

Module 12

Assessment

Use tools to solve

2. Read the story problem below. Students’ Favorite Movie

Frozen How To Train Your Dragon

Sponge Bob Square Pants

llll llll

llll llll

llll l

How many fewer students chose Sponge Bob Square Pants than How To Train Your Dragon as their favorite movie?

Write an equation to represent the problem.

_________________________ fewer students chose Sponge Bob Square Pants than How To Train Your Dragon as their favorite movie.


Lea has 11 more stickers than Summer. Summer has 8 stickers. How many stickers does Lea have?

Choose and solve an equation that represents the story problem. Choose all that apply.

29 - 8 = ____

8 + 11 = ____

11 – 8 = ____

11 + 8 = ____

Create a graph displaying how many stickers Lea and Summer have.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Lea

Summer


Amy has 4 fewer books than Katie.

Katie has 10 books. How many books does Amy have?

Draw a picture of how you would solve this problem in the space below.

Write two different equations that support your representation above.

_____ _____ = _____

_____ = _____ _____ What do you notice about the two equations that you wrote above?

_______________________________

_______________________________


Janelle has 7 fewer lizards than Lori. Janelle has 6 lizards.

How many lizards does Lori have?

Graph and solve for how many lizards Janelle and Lori each have.

Write an equation to represent this

problem.

__________________

Lori has lizards.

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Number of lizards

Janelle Lori

*


Chase has 6 fewer games than Cole. Cole has 12 games.

How many games does Chase have?

Chase Cole

?

llll llll ll

Chase has games.

Graph the number of games Chase has.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Chase Cole

Write an equation to represent this problem.

_______________________________

*

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How to use the recording sheet:

The numbers on the recording sheet on the left correspond with the number of the test question. When you are grading the assessment and the student answers a question incorrectly put their initials on the recording sheet next to the number they got wrong on the assessment. So, for example if Maddison Andrews missed #1, #5, and #8 on the assessment you would put her initials in the boxes on the recording sheet next to #1, #5, and #8. (See below.)

The purpose of the recording sheet is that when you’re done recording who missed what on the assessment you can work with students based on their exact needs. So, in my class during their center time I call small groups based on which students need more support on a particular standard. This way you can also send home the assessment so student’s parents can work with them at the same time. You won’t have a huge pile of papers crowding your desk, just one sheet per assessment.

1 MA __ __ __

2

3

4

5 MA

6

7

8 MA

9

10

_________________________’s

Class Snapshot of Module 12 Assessment

1 Difference Unknown

More Version

2 Difference Unknown

Fewer Version

3 Bigger

Unknown More

4 Smaller

Unknown Fewer

5

Bigger Unknown

Fewer

6

Smaller Unknown

More

WORK IN PROGRESS Grade 1 Elsinore Unified School District Instructional Module To Enhance the Teaching of Envision Math – CA Edition WORK IN PROGRESS Grade 1 Module 12 ... Envision

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