MAXIMIZING MATH MENTALITYmath.sarasotacountyschools.net/wp-content/uploads/2020/05/K-Unit-1-GPS.pdf• Preview and review skills throughout the year using mental math. *Number talks

Grade K: Unit 1

MAXIMIZING MATHMENTALITY

SARASOTA COUNTY SCHOOLS

Guide to Plan for Success

Unit 1: Exploring Quantity, Number, Shape, and Space

Grade K: Unit 1Number and Operations Geometry Measurement

MAFS.K.CC.1.1

16 days

MAFS.K.G.1.1

5 days

MAFS.K.MD.1.2

5 days MAFS.K.CC.1.3 MAFS.K.G.1.2 MAFS.K.MD.2.3 MAFS.K.CC.2.4 MAFS.K.G.2.5 MAFS.K.CC.2.5

K Unit 1 Assessment

Instructional Routines for the Kindergarten Math Block

Number Talk: 5-15 Minutes Every Day Overarching Goals:

• Develop computational fluency (flexibility, accuracy, and efficiency) with numbers. • Developing number sense. • Preview and review skills throughout the year using mental math.

*Number talks do not always align with the instructional skills sequence used for problem of the day. Teaching Format:

• Teacher: poses problem • Students: mentally solve the problem and uses hand signals to communicate the message • Teacher: calls on students to get answers and records them on the board (for questions with one

answer only) • Students: Justify their answers and strategies with purposefully picked partners. • Teacher: Calls on students, records students’ strategies, and connects strategies with the learning

goal. • Class agrees on the answer.

Number of the Day: 15-20 Minutes Every Day

Overarching Goals: Building conceptual understanding with place value of numbers.

• Develop a strong sense of numbers based on comprehension, rather than rules and procedures.

• Connect different representations for the same quantity or number. • Exploration with materials to build models that represent numbers.

Teaching Format (Upside-Down Teaching):

You Do: • Students grapple independently and record their thinking. • Teacher monitors: circulates, listens to student thinking, encourage,

ask questions, observe, and assess. We Do:

• Students work in partners or teams to share answers, justify thinking, clarify understanding, explain their thinking, question each other. Teacher continues to monitor and mentally selects students who s/he would like to share with whole group.

I Do: • Teacher purposefully selects and sequences students to share

strategies with the whole class. • Teacher poses questions for students to make connections across

strategies, and with the learning intentions and success criteria for that day.

Unit 1 Number Talk Goals (after the “First 10 Days of Math”)

• Setting up Expectations • Subitizing Practice • Developing Number Sense (more or less) • Developing Fluency with Numbers to 4

Resources:

• Unit 1 Number Talks Digital • Unit 1 Number Talks PDF

Problem of the Day: 15-20 Minutes Every Day *Overarching Goals:

• Making sense of problems and persevering • Promote student discourse and reasoning. • Collaborating and constructing mathematical ideas with peers.

*It is important to understand that mathematics is to be taught through problem solving. Problem-based tasks or activities are the vehicle through which the standards are taught. (Van de Walle and Lovin, Teaching Student-Centered Mathematics: 3-5 pg. 11 and 12) *For additional support, reference “The 5 Practices In Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom” book (Margaret Peg S. Smith, Victoria bill, and Miriam Gamoran Sherin) for best practices in facilitating productive mathematical conversations in your classroom.

**Teaching Format (Upside-Down Teaching): Whole group or partners: Problem is posed and “Three Reads Method” is utilized

You Do: • Students grapple independently and record their thinking. • Teacher monitors: circulates, listens to student thinking, encourage,

ask questions, observe, and assess. We Do:

• Students work in partners or teams to share answers, justify thinking, clarify understanding, explain their thinking, question each other. Teacher continues to monitor and mentally selects students who s/he would like to share with whole group.

I Do: • Teacher purposefully selects and sequences students to share

strategies with the whole class. • Teacher poses questions for students to make connections across

strategies, and with the learning intentions and success criteria for that day.

Similar question is posed for students to work together while teacher works with a small group or students go to centers while teacher works with a small group.

The next section within this guide, Instructional Sequence, will support the Problem of the Day by connecting standards, Success Criteria, and aligned resources.

Grade K: Unit 1

Unpacking the Standards: Counting and Cardinality

MAFS.K.CC.1.1: Count to 100 by ones and by tens.

MAFS.K.CC.1.3: Read and write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Comments about the Standards: Students come in to Kindergarten with wide range of counting skills. It is easily assumed that if a child can orally count the sequence, that they can “count.” It will be critical to identify any misconceptions about counting as early as possible, as these misconceptions will continue to adversely affect future math learning. Teachers must carefully observe counting behaviors, ask questions such as “how do you know?” and note mastery of these counting concepts for each student. Follow up with explicit modeling for students who are unable to count, as described in the standard, to 10. Time has been given to attend to writing, recognizing, and representing numbers

in August so that students are better equipped to communicate their thinking and representations in problem solving later. Future Learning:

• Reading, writing and recognizing numbers to 20 • Understanding that each number in the counting sequence adds 1 each

time. • Comparing quantities to 10 using more/less equal/same • Telling what comes before or after numbers to 10. • Verbally counting to 50 by 1’s • Word Problems: Joining and Separating within 5

Manipulatives/Tools:

• counters • five and/or ten frames • rekenreks • 100 Chart • dominoes/dice • digit card sets 0-9, 0-20

Notes:

→ Although the standard MAFS.K.CC.1. (Count to 100 by ones and by tens) is included throughout this unit, students should be given ample time to count and really focus on numbers through 20.

→ This standard is seen as a progression that is to be met by the end of the year, however, Unit 1 allows ample time for this skill to be practiced with the intent of continual follow up until mastery hereafter.

→ Although the standard states “to 100”, this unit (in particular the tasks), focus on numbers and number relationships through 10. It is because of the aforementioned reasons that skip counting is not specifically addressed in this unit.

Grade K: Unit 1

MAFS.K.CC.2.4: a. When counting objects, say the number names in

the standard order, pairing each object with one and only one number name and each number name with one and only one object.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that is one larger.

MAFS.K.CC.2.5: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. *within 10

Comments about the Standards: For a Kindergarten student, understanding how to count objects with precision and accuracy is a multifaceted task. As students come to understand what numerals are and what each represents, they must first use those numbers and counting concepts in their daily living situations with meaning and purpose. Through these situations and contexts, students naturally begin to internalize several key concepts that can be brought to light by the teacher in a classroom setting:

• In order to find out “how many” of something, I need to count.

• When I count, I can only touch each thing 1 time, I must say a number for each touch/object.

• The last number I say tells “how many.”

• I can organize the things I want to count (put them in a line or move them from one side to the other) to help keep track of what I have counted.

• If I count a set of objects one time, those objects can be rearranged, and the quantity does not change.

• Numbers are nested inside of each other. If I have 5 of something, then I also have 4, 3, 2 and 1.

Notes:

→ Object counting, verbal counting, reading and writing of numbers will be developed over time.

→ The Counting and Cardinality standards in K are major standards that will be revisited several times throughout the year with an emphasis on building strong foundations for future place value concepts.

Grade K: Unit 1

Pre-Assessments

Kindergarten Math Screener w/ Teacher Guide Number Writing Grid

Skill: FL. Pre-K Standards Require Students to be able to:

• Subitize to 5 • Identify the number sequence

to 31 • Demonstrate 1-1

Correspondence to 15+ when objects are placed in a row

• Demonstrate cardinality up to 10

• Produce sets of objects to 10 • Finds more/less/equal within

10 • Read and write numbers to 10

Pacing:

Within the first 10 days

of Unit 1

Success Criteria: *Time has been considered within this unit to introduce and/or review these skills to allow for the range of skill levels students demonstrate upon entering Kindergarten. * Students who may be struggling with these skills after they have been introduced and practiced in the classroom may benefit from repetition of and extended time using the activities within the resources during Build and Explore or sent home for extra practice.

Resources: LearningTrajectories.org will have additional high-quality activities with videos, should additional remediation (or enrichment) be required. Florida Pre-K Math Standards includes videos of students demonstrating skills within each standard and may be helpful for teachers and families.

Instructional Skill Sequence: Counting and Cardinality and Writing and Recognizing Numbers Skill: Introduction to Counting and Number

• What is counting? • Why is important to count? • What are some things I

count in my life, classroom and school?

• What does it mean when someone asks, “How many?”

Pacing: 5 days

Success Criteria:

• I can tell why we count. • I can give examples of things I can count

in my life, classroom and school. • I can give examples of things we can count

in my classroom or school. • When I am asked, “how many?” I can

count to find out.

Resources:

Ready MAFS Teacher Resource Book • Lesson 1: p. 3 • Dot Cards p. AS1-2 • Cards for 2, 3 and 4 p. AS30

LearningTrajectories.org Activity: • Counting All Around You

Skill: Introduce Numbers

Success Criteria:

• I can tell what a number is.

Resources:

Ready MAFS Teacher Resource Book

Grade K: Unit 1

• What are numbers? • Why do we use numbers? • What are some numbers I

know?

• I can tell why we use numbers. • I can give some examples of numbers I

know.

• Lesson 2: p. 7, 9 • Lesson 3: p. 13-15 • Lesson 4: p. 19, 20, 21

Skill: Number Recognition

• How can I tell the names of each number 0-5?

Success Criteria:

• I can use digit cards to learn number names.

• I can use _____ (classroom resource: number poster, number line, number chart, calendar, number line) to help me learn number names.

Resources:

Ready MAFS Teacher Resource Book • Number Cards p. AS6a-b

LearningTrajectories.org Activity: • Order Dot Cards to 5

Skill: Counting and Cardinality *within 10

• What does it mean when someone asks, “how many?”

• How can I arrange objects to count them?

• How can I keep track of objects I already counted?

• How can I count with accuracy?

Pacing: 5 days

Success Criteria:

• When I am asked, “how many?” I can count to find out.

• I can line up objects before I begin counting them. *reinforce left to right directionality when counting.

• I can keep track of objects I already counted by moving them over at each count.

• I can count with accuracy by using the number sequence to name each object only 1 time.

• I can count up to 10 objects accurately.

Resources:

Ready MAFS Teacher Resource Book • Lesson 1: p. 1-2, 4 • Differentiated Instruction

Activities p. 6b • Lesson 6: p. 31-33 • Lesson 7: p. 37-39 • Lesson 8: p. 44, 45

*The standards require students to count physical objects that can be moved.

Ready MAFS Teacher Resource Book • Number Cards 0 to 9 p. AS6a • 10-frame Cards p. AS15a-b

Teacher Toolbox: • Lesson 4 Tools for Instruction

o Making a Set Up to 10 Objects

o Counting Backward: 10 to 0

Grade K: Unit 1

o Identifying Numerals to 10

LearningTrajectories.org Activity:

• Cardinality with Hidden Counters

Skill: Read and Write Numbers 0-10

• How can I remember ways to write numbers?

• How can I use numbers to represent “how many?”

Success Criteria:

• I can use (classroom resource: number writing poster; anchor chart; poem/song) to help me write numbers 0-9.

• I can count up to 10 objects and use a number to represent how many there are. *Match sets of objects with numeral cards and move towards writing numbers for sets of objects.

Resources:

Ready MAFS Teacher Resource Book • Lesson 2: p. 10, 11 • Lesson 3: p. 16, 17 • Lesson 4: p. 22, 23 • Write Numbers 0-10 p. AS7-10

Teacher Toolbox: • Lesson 4 Tools for Instruction

o Counting Backward: 10 to 0

Skill: Counting and Cardinality up to 10

• Which number tells “how many” after you have counted?

• What happens to the number of objects after they have been rearranged?

• How can I show an amount of objects to match a number?

Pacing: 5 days

Success Criteria:

• I can tell how many there by the last number I say after I counted.

• I can tell that the amount does not change even if it was rearranged.

• I can count out up to 10 objects with accuracy.

Resources:

Ready MAFS Teacher Resource Book • Lesson 6: p. 34, 35 • Lesson 7: p. 40, 41 • Lesson 8: p. 46, 47

Teacher Toolbox: • Lesson 4: Tools for Instruction

o Making a Set of Objects to 10”

LearningTrajectories.org Activity:

• Memory Dots to 10

Grade K: Unit 1

Skill: Compare sets as “more/less” within 5 and explore the concept of combining sets using the word “and” to join.

• How can I tell which set has more or less?

• How can I find the total of 2 sets?

Success Criteria:

• I can count the number of objects in a set to tell which has more or less than the other set.

• I can count one set and another set to find out how many there are all together.

*Pose problems such as: “3 bugs and 2 bugs, how many bugs?” “2 red candies and 3 pink candies, how many candies?”The goal here is to introduce joining sets by using the word “and.” Students should be modeling and drawing to show their thinking of how they determined the total. Equations and use of the + or = sign are not an expectation for Unit 1.

Resources:

Ready MAFS Teacher Resource Book • Lesson 5 p. 28, 29

Skill: Recognizing, Writing and Representing with Numbers 0-20

• What is a digit? What is a one-digit number/2-digit number?

• What patterns do I notice with numbers 0-19? *present numbers 0-9 next to 10-19, vertically.

• How can I order numbers to 20? *using number cards.

• How can I write numbers 0-20?

• How can I show what a number 0-20 means?

Success Criteria:

• I can identify a one digit and two-digit number.

• I can tell the patterns I see with the numbers 0-19 and how the pattern repeats with the digits 0-9.

• I can use the patterns I see with the digits 0-9 to help me order numbers 0-19.

• I can use ____ (classroom resource) to help me write numbers.

• I can use drawings and models to show the meaning of a number.

Resources:

Ready MAFS Teacher Resource Book • Write Numbers p. AS11a • Number Cards p. AS16-17c • Numbered 10-Frames p. AS22

Formative Assessment: Counting Observation Checklist and Number Writing Grid

Grade K: Unit 1

Unpacking the Standards: Positional Words, Shapes, and Attributes MAFS.K.G.1.1: DOK 2

Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, besides, in front of, behind, and next to.

Comments about the Standard: When students are asked to describe objects in their environment using positional words, they are using spatial thinking, an important awareness to develop as they begin formally learning about shape and space. Students should understand directions using these words as well as use these words when describing the relationship of an object in the space. For example, if a child can determine “the ball is close to/next to/further from the table”, they are likely to have an easier time understanding the relationship of numbers, “8 is close to 10 and 2 is further from 10 than it is from 8.”

Notes: → Due to the increase in vocabulary required to understand

geometric concepts, class discussions around shapes, the relationship to the space around them, and their attributes, will be key to developing students who understand and use the language of shapes.

MAFS.K.G.1.2:

Correctly name shapes regardless of their orientations or overall size.

Comments about the Standard: When students are presented with shapes of various orientations and sizes they come to understand that shapes are named for their attributes and that their size and position do not change the name of the shape. Young students tend to have “all or nothing” thinking and this standard challenges this thinking to allow for consideration of “if/then” thinking. Instead of “all tringles have a point at the top” they move to, “If it has 3 sides and 3 corners, then it is a triangle.”

Notes: → Present students with situations that challenge their

beliefs about shapes. Shapes should be presented in various sizes, turns, colors. and with side lengths of different sizes.

→ Refer to the following documents to reference mathematical accuracies when referring to geometric concepts when teaching:

The Language of Shapes for Teachers Tips for Introducing Shapes

Grade K: Unit 1

MAFS.K.G.2.5: (DOK 2)

Model shapes in the world by building shapes from components (e.g., sticks and clay balls) drawing shapes.

Comments about the Standard: Standards require students to engage in geometry experiences that are unable to be assessed on a pencil/paper assessment. Modeling of shapes is an experience that will be required of students as the year progresses. As students make shapes with materials they are making connections about shape concepts while developing spatial thinking and problem-solving skills. To meet this standard, students must apply their knowledge of shape attributes to hands on experiences of modeling shapes. Future Learning:

• Describing objects in the environment 3D • Identifying shapes as 2D or 3D • Comparing 2D shapes

Notes: → Students mastery of geometric concepts relies heavily

on spatial experiences and time must be built into the math block for students to develop their sense of shape over time and through various experiences.

→ Students will benefit from direct modeling from the

teacher of how to use clay or other materials to make shapes. Instruct on how to pinch, roll, flatten, etc…so that students can apply these techniques to make shapes.

Pre-Assessment

Geometry Skills Checklist

Prerequisite Instruction Skill: FL PreK Standards Require students to be able to:

• Recognize circle, square, triangle, rectangle of different size/orientation

• Sort based on attribute • Make 2D shapes by

combining • Construct 3D shapes through

play • Describe objects using

positional word

Pacing:

Within Unit 1

Success Criteria: *Time has been considered within this unit to introduce and/or review these skills to allow for the range of skill levels students demonstrate upon entering Kindergarten. * Students who may be struggling with these skills after they have been introduced and practiced in the classroom may benefit from repetition of and extended time using the activities within the resources during Build and Explore or sent home for extra practice.

Resources: LearningTrajectories.org will have additional high-quality activities with videos, should additional remediation (or enrichment) be required. Florida Pre-K Math Standards includes videos of students demonstrating skills within each standard and may be helpful for teachers and families.

Manipulatives/Tools:

• pattern blocks • materials to model shapes • shape cards • pattern block puzzle card

Grade K: Unit 1

Instructional Skill Sequence: Positional Words, Shapes, and Attributes Skill: Positional words, shapes and attributes

• How can I tell where an object is in its space?

• Which shapes can I see in objects around me?

• What is a square, circle, rectangle or triangle.

Pacing:

1 day

Success Criteria:

• I can use the words “above” and “below” to describe objects around me.

• I can describe objects around me and tell which ones are shaped like a square, circle, or triangle.

• I can identify a square, circle, rectangle or triangle in different sizes.

Resources:

Ready MAFS Teacher Resource Book • Lesson 28: p. 163, 164 • Flat Shapes p. AS25 • Flat Shape Cards p. AS28

LearningTrajectories.org Activity: • Find the Twin • True or False Shape ID • Shape Descriptors and Tips for

Teachers •

Skill: Positional words, shapes and attributes

• How can I tell where an object is in its space?

• Which shapes can I see in objects around me?

• Does the name of a shape change if the size changes?

Pacing: 1 day

Success Criteria:

• I can use the words “below, beside, behind, or above” to describe objects around me.

• I can describe objects around me and tell which ones are shaped like a square, circle, triangle or rectangle

• I can identify a square, circle rectangle or triangle in different sizes or if they are turned different ways.

Resources:

Ready MAFS Teacher Resource Book • Lesson 28: p. 166, 168, 168b • Lesson 30: p. 178

Skill: Positional words, attributes and representing shapes

• How can use the number of sides to determine the name of a shape?

• How can I represent shapes by drawing?

Pacing: 1 day

Success Criteria:

• I can use the words “on, in and under” to describe objects around me.

• I can tell how many sides are on a rectangle, triangle, circle or rectangle.

• I can draw a circle, square and triangle.

Resources:

Ready MAFS Teacher Resource Book • Lesson 28: p. 168

*Can change directions to include on, in and under.

LearningTrajectories.org Activity:

• Exploring Shape Sides • Feely Bag

Grade K: Unit 1

Skill: Positional words, shapes, attributes and representing shapes

• How can I use the number of corners to determine the name of a shape?

• How can I represent a shape with a model?

Pacing: 1 day

Success Criteria:

• I can use the words “between and next to” to describe the objects around me.

• I can tell how many corners are on a rectangle, triangle, circle or rectangle.

• I can draw a circle, square and triangle. • I can model a circle, square, triangle and

rectangle.

Resources:

Ready MAFS Teacher Resource Book • Lesson 31 p. 181, 184

LearningTrajectories.org Activity: • Explore Shapes and Corners

Formative Assessment: Unit 1 Shape Attributes Formative Assessment

Grade K: Unit 1

Unpacking the Standards: Describe Objects and Sort by Attributes

MAFS.K.MD.2.3: (DOK 2)

Classify objects (shapes) into given categories, count the numbers of objects in each category and sort the categories by count.

Comments about the Standards:

Kindergarten students may not come to us with the vocabulary to explain what an object looks like using describing words that include color, texture, size or shape, when asked. Teachers can help students become more aware of attributes by describing everyday objects and connecting new learning, e.g., “Those square tiles on the floor are white and shiny.” Students can become more aware of objects and their various attributes through sorting tasks. Only then can we can expect them to understand measurable attributes such as longer or shorter, heavier/ lighter etc...

Future Learning:

• Compare the attribute of length using long, longer, longest, short, shorter, shortest.

• Measuring length by number of units end to end. • Sorting objects as awareness of attributes increases.

Manipulatives/Tools: Objects for describing, sorting or comparing color, size, texture, shape and length.

Notes:

→ When students have worked with shapes and shown the understanding of their attributes, they can sort shapes into categories based on the attribute that is being studied.

→ If learning about corners, sort by corners to demonstrate understanding of the attribute.

MAFS.K.MD.1.2: (DOK 2)

Directly compare two objects with a measurable attribute in common to see which object has “more of”/” less of” the attribute and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Notes:

→ Direct comparison refers to the act of lining up objects at one of their endpoints and then comparing the other end points.

→ Comparing heights is sufficient initially, but then it will be necessary to move toward being able to determine the end points if 2 objects are lying down.

Grade K: Unit 1

Prerequisite Instruction Skill: FL PreK Standards Require students to be able to:

• Measure object attributes using standard and non- standard units.

• Identify measurable attributes such as length and weight and make comparisons.

• Seriates objects in sequence of up to 6 in height order.

• Begins to predict results of data collections

Pacing: Within Unit 1

Success Criteria: *Students must be able to determine attributes of an object such as color, size, texture or shape. *Considering those attributes, they must be able to compare how two objects are alike or different.

Resources: LearningTrajectories.org will have additional high-quality activities with videos, should additional remediation (or enrichment) be required. Florida Pre-K Math Standards includes videos of students demonstrating skills within each standard and may be helpful for teachers and families.

Instructional Skill Sequence: Describe Objects and Sort by Attributes Skill: Describe objects and sort by attributes.

• How can I describe an object?

• How can I sort objects?

Pacing: 1 day

Success Criteria:

• I can tell about an object by describing its color, size, texture, or shape.

• I can sort objects by grouping by color, size, texture, or shape.

Resources:

Ready MAFS Teacher Resource Book • Lesson 27: p. 159, 160, 161

Skill: Directly Compare lengths, describe length

• How can I compare the length of 2 objects?

• How can I describe the length of 2 objects?

Pacing: 1 day

Success Criteria:

• I can compare length of 2 objects by placing them next to each other.

• I can tell which object is long, longer or longest.

Resources:

Ready MAFS Teacher Resource Book Lesson 24: p. 139, 141 Teacher Toolbox:

• Practice and Problem Solving o Lesson 24 Family Letter

LearningTrajectories.org Activity:

• Encourage Length Comparisons

Grade K: Unit 1

Skill: Compare lengths, describe length

• How can I compare the length of 2 objects?

• How can I describe the length of 2 objects?

Pacing: 1 day

Success Criteria:

• I can compare 2 objects by placing them next to each other.

• I can tell which object is short, shorter, shortest.

Resources:

Ready MAFS Teacher Resource Book • Lesson 24: p. 140, 142, 143, 144

Skill: Compare and order lengths

• How can I model numbers 0-5 to show different lengths? *note the pattern of adding 1 each successive number.

Pacing:

1 day

Success Criteria:

• I can use connecting cubes and counters to model each number 0-5 and order them from shortest to longest.

• I can match models and numbers 0-5.

Resources:

Ready MAFS Teacher Resource Book • Number Cards AS6a-b

LearningTrajectories.org Activity: • Length Riddles with Cubes • Line Up by Height to 5

Kindergarten Unit 1 Assessment