In this section, students interact with the tools that they will use in math activities and centers throughout the year. They have the opportunity to freely explore the tools and think of their mathematical purposes before choosing a tool for use in structured activities later in the section and in centers. Students also build a shared understanding of what it means to do math and to be a part of a mathematical community, where everyone’s contributions are valued. They are also encouraged to share their ideas and listen to others’, make connections between their work and their home life, and to see themselves as productive mathematical thinkers.

• This section is organized to take 5 lessons with TK students.

• The lessons in this section are intentionally designed to be shorter to allow time for students to learn the structures and routines for the activities and centers.

Building towards:

PLF.NS-1.0

• Children begin to understand numbers and quantities in their everyday environment. (around 48 months)

• Children expand their understanding of numbers and quantities in their everyday environment. (around 60 months)

PLF.AF-1.0

• Children begin to sort and classify objects in their everyday environment. (around 48 months)

• Children expand their understanding of sorting and classifying objects in their everyday environment. (around 60 months)

PLF.M-1.0

• Children begin to compare and order objects. (around 48 months)

• Children expand their understanding of comparing, ordering, and measuring objects. (around 60 months)

PLF.G-1.0

• Children begin to identify and use common shapes in their everyday environment. (around 48 months)

• Children identify and use a variety of shapes in their everyday environment. (around 60 months)

In this section, students continue to explore numbers and quantities in their classroom, focusing on small groups of objects or images they can quantify without counting (subitize). They match groups that have the same number of things.

Students are sometimes asked to show quantities up to 5 on their fingers. This is a chance to formatively observe if students are comfortable showing quantities on their fingers (any way is acceptable). For example, they may put up 4 fingers to show how many objects there are before saying the number word “four.”

• This section is organized to take 4 lessons with TK students.

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

Addressing:

PLF.NS-1.3

• Identify, without counting, the number of objects in a collection of up to three objects (i.e., subitize). (around 48 months)

• Identify, without counting, the number of objects in a collection of up to four objects (i.e., subitize). (around 60 months)

In this section, students work on the concept of one-to-one correspondence. They match one object to one person or image to answer “are there enough” questions and to get enough objects. This matching skill will be useful in future lessons when students match one number word to one object and when students match to compare groups of objects.

“Are there enough” and “can you get enough” questions encourage students to mathematize situations. Look for ways to incorporate these prompts into other parts of the school day, for example, when classroom supplies are being distributed.

• This section is organized to take 2 lessons with TK students. 

• Notes for Centers:

  • In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

Addressing:

PLF.NS-2.1

• Compare visually (with or without counting) two groups of objects that are obviously equal or unequal and communicate “more” or “same.” (around 48 months)

• Compare, by counting or matching, two groups of up to five objects and communicate “more,” “same as,” or “fewer” (or “less”). (around 60 months)

PLF.NS-1.4

• Count up to 5 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 48 months)

• Count up to 10 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 60 months)

In this section, students focus on counting up to 10 objects and answering “how many of _____ are there” questions. Students count collections of objects from the classroom or from home. Students may use counting mats, 5-frames, or other tools to help them count.

To initiate counting, ask “how many of _____ are there?” instead of saying “count the objects.” This helps to reinforce counting as a way to quantify a collection and the idea of cardinality—that the last number counted tells us how many there are.

• This section is organized to take 6 lessons with TK students.

• Most students should be given collections with up to 5 objects. Based on formative assessment data collected in previous sections, adjust the number of objects in collections for individual students.

• Each lesson in this section includes an optional activity to support students in certain aspects of counting. All of these optional activities should be completed in a TK classroom. The optional activity may be completed as a separate lesson.

Addressing:

PLF.NS-1.4

• Count up to 5 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 48 months)

• Count up to 10 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 60 months)

PLF.NS-1.5

• Use the number name of the last object counted to answer the question, “How many . . . ?” (around 48 months)

• Understand, when counting, that the number name of the last object counted represents the total number of objects in the group (i.e., cardinality). (around 60 months)

In this section, students count to answer “how many” questions and develop their understanding of the connection between quantities and spoken number words. Display and write the number associated with a quantity whenever possible. As students count and rearrange objects, students notice that the arrangement of objects does not affect the number of objects (conservation of number). They will continue to build this understanding over time.

Students also compare groups of objects. They start with quantities that are very different and can be compared visually, such as 5 and 2, and relate the comparisons to the terms “more” and “fewer,” which may be new. Then students compare groups with similar numbers of objects, which requires them to match or count to compare.

• This section is currently organized to take 6 days. In a TK class, it may be appropriate to cover this content over 12 or more days.

• Throughout the section, when students are asked to compare groups of objects, adjust the quantities so that there are 5 or fewer objects in each group. If students are comparing groups with very different quantities (as in K.2.A.3), each group can contain up to 10 objects. For example, students can compare a group of 7 objects and a group of 2 objects.

• Notes for Centers:

  • In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole lass or in small groups.

  • When introducing stage 2 of the Shake and Spill center (K.2.A.4 Activity 2), give each group of students 7–8 counters instead of 10 counters.

  • In Activity 3 of K.2.A.3, do not introduce the Number Race center. Instead, students can choose to work on any centers that have been previously introduced. Number Race should not be given as a choice in future lessons.

Addressing:

PLF.NS-2.1

• Compare visually (with or without counting) two groups of objects that are obviously equal or unequal and communicate “more” or “same.” (around 48 months)

• Compare, by counting or matching, two groups of up to five objects and communicate “more,” “same as,” or “fewer” (or “less”). (around 60 months)

PLF.NS-1.4

• Count up to 5 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 48 months)

• Count up to 10 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 60 months)

PLF.NS-1.5

• Use the number name of the last object counted to answer the question, “How many . . . ?” (around 48 months)

• Understand, when counting, that the number name of the last object counted represents the total number of objects in the group (i.e., cardinality). (around 60 months)

In this section, students connect quantities to spoken and written number words. Students also count out a given number of objects. Counting out objects requires students to remember which number they need to stop at while also matching each object with one number. As students develop their ability to recognize and name written numbers, consider providing a resource with the corresponding number of dots under each written number. If needed, students can count the dots to determine what number is shown.

• This section is organized to take 2 lessons with TK students.

• With TK students, complete Lessons K.2.C.12 and K.2.C.14. Do not complete Lessons K.2.C.13, K.2.C.15, or K.2.C.16.

• To support students in number recognition throughout these lessons, consider drawing the corresponding number of dots under each written number. If needed, students can count the dots to determine what number is shown.

Notes for Centers:

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

• In Activity 3 of K.2.C.12, do not introduce the Number Race center. Instead, students can choose to work on any centers that have been previously introduced. Number Race should not be given as a choice in future lessons.

• In Activity 3 of K.2.C.14, do not introduce the Bingo center. Instead, students choose to work on any centers that have been previously introduced. Bingo should not be given as a choice in future lessons.

Addressing:

PLF.NS-1.2

• Begin to recognize and name a few written numerals. (around 48 months)

• Recognize and know the name of some written numerals. (around 60 months)

PLF.NS-1.4

• Count up to 5 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 48 months)

• Count up to 10 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 60 months)

PLF.NS-1.5

• Use the number name of the last object counted to answer the question, “How many . . . ?” (48 months)

• Understand, when counting, that the number name of the  last object counted represents the total number of objects in the group (i.e., cardinality). (60 months)

In this section, students work to name, describe, and compare shapes in their environment. They focus on identifying circles, rectangles, squares, and triangles. To help expand students’ mental image of shape categories, the shapes seen here vary in size, type, and orientation. When comparing shapes, students use their own language to describe attributes of shapes and how shapes are the same and different.

• This section is currently organized to take 9 days. In a TK class, it may be appropriate to cover this content over 12–15 or more days.

• During the Choral Count warm-up (K.3.A.4 and K.4.3.A.7), focus on counting to 20 instead of counting to 30.

• Some activities (K.3.A.4 Activity 2, K.3.A.5 Activities 1 and 2, K.3.A.6 Activity 1, K.3.A.7 Activity 1, K.3.A.9 Activity 1) ask students to write a number to record how many shapes are in each group. TK students should not be required to write numbers, but can record in a way that makes sense to them if they choose to.

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

• When introducing the Counting Collections center (K.3.A.5 Activity 3), most students should be given collections with 6–10 objects. Based on formative assessment data collected in previous sections, adjust the number of objects in collections for individual students. TK students should not be required to record their count, but can choose to record in a way that makes sense to them.

• Bingo should not be offered as a choice for centers. Instead, TK students can be given choices from any centers that have been introduced so far.

Addressing:

PLF.G-1.1

• Identify simple two-dimensional shapes, such as a circle and square. (around 48 months)

• Identify, describe, and construct a variety of different shapes, including variations of a circle, triangle, rectangle, square, and other shapes. (around 60 months)

PLF.AF-1.1

• Sort and classify objects by one attribute into two or more groups with increasing accuracy. (around 48 months)

• Sort and classify objects by one or more attributes, into two or more groups, with increasing accuracy (e.g., may sort first by one attribute and then by another attribute). (around 60 months)

PLF.M-1.1

• Demonstrate awareness that objects can be compared by length, weight, or capacity, by noting gross differences, using words such as “bigger,” “longer,” “heavier,” or “taller,” or by placing objects side by side to compare length. (48 months)

• Compare two objects by length, weight, or capacity directly (e.g., putting objects side by side) or indirectly (e.g., using a third object). (60 months)

In this section, students develop spatial reasoning by manipulating shapes and solving geometric puzzles. Students use pattern blocks to compose geometric figures, explore shapes in different orientations, find shapes that match exactly, and complete puzzles that require reorienting shapes. Throughout the section, students use their own language to describe how the shapes they are working with are alike and different.

• This section is organized to take 6 lessons with TK students.

• Do not complete K.3.B.10 Activity 1 with TK students.

• Some activities (K.3.B.10 Activity 2, K.3.B.11 Activity 2, K.3.B.12 Activity 1) ask students to write a number to record how many pattern blocks there are. TK students should not be required to write numbers, but can record in a way that makes sense to them if they choose to.

Notes for Centers:

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

• Pattern Blocks, Stage 4 should not be offered as a choice for centers. Instead, TK students can choose from the other stages of the Pattern Blocks center or any other centers that have been introduced so far.

• Less, Same, More, Stages 2–4 should not be offered as choices for centers. Instead, TK students can choose from Less, Same, More, Stage 1 or any other centers that have been introduced so far.

Addressing:

PLF.G–1.2

• Use individual shapes to represent different elements of a picture or design. (around 48 months)

• Combine different shapes to create a picture or design. (around 60 months)

PLF.G–2.1

• Identify positions of objects and people in space, including in/on/under, up/down, and inside/outside. (around 48 months)

• Identify positions of objects and people in space, including in/on/under, up/down, inside/outside, beside/between, and in front/behind. (around 60 months)

PLF.G-1.1

• Identify simple two-dimensional shapes, such as a circle and square. (around 48 months)

• Identify, describe, and construct a variety of different shapes, including variations of a circle, triangle, rectangle, square, and other shapes. (around 60 months)

In this section, students see adding as putting together two groups and counting the total number of objects, and subtracting as taking away a number of objects from a group and counting what remains. They represent combining and removing with physical objects. No stories or contexts are used here so that students can focus on the actions of putting together, adding to, and taking from. The language “add,” “put together,” “subtract,” “take away,” and “total” is used by the teacher throughout the section to describe addition and subtraction. The word “total” is used here instead of “sum” to reduce potential confusion with the word “some” or part of a whole. No symbolic notation is used at this point.

• This section is currently organized to take 3 days. In a TK class, it may be appropriate to cover this content over 6 or more days.

• With TK students, complete lessons K.5.A.1, K.5.A.4, and K.5.A.5. Do not complete lessons K.5.A.2 and K.5.A.3.

• Some activities (K.4.A.1 Activity 1 and Activity 2, K.4.A.4 Activity 1 and Activity 2, K.5.A.5 Activity 1 and Activity 2) ask students to write a number to record how many objects there are. TK students should not be required to write numbers, but can record in a way that makes sense to them if they choose to.

Notes for Centers:

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

• When introducing the 5-frames center (K.4.A.4 Activity 2 and K.4.A.5 Activity 2), consider drawing the corresponding number of dots under each written number on the number mat to support students in number recognition.

• Math Libs and Roll and Add should not be offered as a choice for centers. Instead, TK students can be given choices from any centers that have been introduced so far.

Addressing:

PLF.NS-2.4

• Solve simple addition and subtraction problems nonverbally (and often verbally) with a very small number of objects (sums up to 4 or 5). (around 48 months)

• Solve simple addition and subtraction problems with a small number of objects (sums up to 10), usually by counting. (60 months)

PLF.NS-2.3

• Understand that putting two groups of objects together will make a bigger group. (around 48 months)

• Understand that putting two groups of objects together will make a bigger group and that a group of objects can be taken apart into smaller groups. (60 months)

PLF.NS-1.4

• Count up to 5 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 48 months)

• Count up to 10 objects, using one-to-one correspondence (one object for each number word) with increasing accuracy. (around 60 months)

PLF.NS-1.5

• Use the number name of the last object counted to answer the question, “How many . . . ?” (48 months)

• Understand, when counting, that the number name of the last object counted represents the total number of objects in the group (i.e., cardinality). (60 months)

Here, students distinguish between flat and solid shapes before focusing on solid shapes. They consider the weight and capacity of solid objects and identify solid shapes around them. Geoblocks, connecting cubes, and everyday objects are used throughout the unit.

Throughout the section, students hear and use the terms “flat” and “solid” to describe two- and three-dimensional shapes. When comparing weights, the terms “heavy,” “light,” “heavier,” and “lighter” are used. While students are introduced to the names of solid shapes, they are not expected to use the formal terms for solid shapes or shape attributes. For example, they may say “ball” to refer to a sphere.

• This section is currently organized to take 9 days. In a TK class, it may be appropriate to cover this content over 12–15 or more days.

• With TK students, do not complete Lesson K.5.B.15.

• In lesson K.7.B.8, do not complete the cool-down at the end of the lesson. The TK checkpoint can be used instead.

• During the Choral Count warm-up (K.7.B.9 and K.7.B.16), focus on counting to 20 instead of counting by 10s.

• Do not complete the warm-ups in Lessons K.7.B.10 and K.7.B.14. An alternate warm-up can be chosen from the list of additional warm-ups below.

• Some activities (K.7.B.7 Activity 2, K.7.B.11 Activity 2) ask students to write a number to record how many shapes there are. TK students should not be required to write numbers, but can record in a way that makes sense to them if they choose to.

Notes for Centers:

• In Activity 3 of each lesson, students participate in centers. Centers can be completed as a whole class or in small groups.

• Students can choose to work on Counting Collections, Stage 1 during centers. Most students should be given collections of 6–10 objects. Based on formative assessment data collected in previous sections, adjust the number of objects in collections for individual students. TK students should not be required to record their count, but can choose to record in a way that makes sense to them.

• Shake and Spill, Stages 3–4 should not be offered as choices for centers. TK students can choose from Shake and Spill, Stages 1–2 or any other centers that have been introduced so far. When completing Shake and Spill, Stage 2, students should be given 7–8 counters instead of 10 counters.

Addressing:

PLF.G-1.1

• Identify simple two-dimensional shapes, such as a circle and square. (around 48 months)

• Identify, describe, and construct a variety of different shapes, including variations of a circle, triangle, rectangle, square, and other shapes. (around 60 months)

PLF.G–1.2

• Use individual shapes to represent different elements of a picture or design. (48 months)

• Combine different shapes to create a picture or design. (60 months)

PLF.G–2.1

• Identify positions of objects and people in space, including in/on/under, up/down, and inside/outside. (around 48 months)

• Identify positions of objects and people in space, including in/on/under, up/down, inside/outside, beside/between, and in front/behind. (around 60 months)

PLF.AF-1.1

• Sort and classify objects by one attribute into two or more groups, with increasing accuracy. (around 48 months)

• Sort and classify objects by one or more attributes, into two or more groups, with increasing accuracy (e.g., may sort first by one attribute and then by another attribute). (around 60 months)

PLF.M-1.1

• Demonstrate awareness that objects can be compared by length, weight, or capacity, by noting gross differences, using words such as “bigger,” “longer,” “heavier,” or “taller,” or by placing objects side by side to compare length. (around 48 months)

• Compare two objects by length, weight, or capacity directly (e.g., putting objects side by side) or indirectly (e.g., using a third object). (around 60 months)

Classroom-based