Kindergarten - MATH
1: Letters
Unit 1: A - A Is for Musk Ox
Lesson 5
Day 5
In Activity 1 students handle apple die-cut objects, count them aloud, and match the quantity to number cards (1–3, with an optional extension to 10), showing representation of number with objects. Students are asked to choose a number of objects while the adult picks a number card and the student checks the match, which has students represent quantities and compare them. The teacher asks verbal prompts, e.g., "What number is one more than 1?" and "What number is one more than 2?", prompting students to think about adding one using objects and verbal explanation.
Unit 2: H - Hondo and Fabian
Lesson 3
Day 3
In Activity 3 students are given two piles of die-cut animals (one with 3 and one with 5) and are asked to lay each pile in a line, count each line left to right, and identify which line has more or fewer animals. The activity directs students to assign one number to each cat or dog as they count, explicitly using objects to represent quantity. An Optional Extension asks students to determine how many animals there are altogether and shows how to write the matching equation 3 + 5 = 8.
Lesson 5
Day 5
Students lay out a row of 3 toy animals, match a number card to the set, then add one more animal and count again to determine how many they have. Students are asked to find the number that matches the new total and respond to questions such as what number is one more than 4 and one more than 5. Students also trace and write the numerals 4, 5, and 6 and form those numerals with pipe cleaners, linking object counts to written number symbols.
Unit 3: I - The Little Island
Lesson 3
Day 3
Students count 7 die-cut cats and slide-count each animal from left to right, using physical objects to represent quantities. Students match each counted cat with a number card and are asked verbally, "What number is one more than 7?" and "What number is one more than 8?", prompting verbal and mental representation of adding one. Students trace the number with a finger and form numerals with playdough, providing physical and tactile number representation.
Unit 5: L - We're Going on a Leaf Hunt
Lesson 4
Day 4
Activity 2 has students divide leaves into two groups, count each group, and match each count to a number card before deciding which group has more. The optional extension asks students to determine how many more leaves the smaller group would need to make it equal to the larger group, which prompts students to use leaves as objects to reason about the difference (a subtraction/missing-addend idea).
Unit 6: F - Fireflies
Lesson 3
Day 3
Activity 2 asks students to count out 10 "fireflies," practice counting by 10s to 100, and to count out a number of "fireflies" that matches a given number card. The activity then asks students what the number of fireflies would be if they added one more, using objects and verbal counting to represent the change in quantity.
Lesson 5
Day 5
In Activity 1, students use pennies as concrete objects to represent fireflies, adding 2 pennies to 1, then 3, then 4 and counting the total each time (e.g., 1 + 2 = 3; totals 3, 6, 10). Students act out catching fireflies and tell stories about adding groups of fireflies, providing verbal explanations and counting. The optional extension invites students to record an equation (1 + 2 = 3), linking the concrete action to symbolic representation.
Unit 7: E - But No Elephants
Lesson 3
Day 3
Students sort animal picture cards by number of legs using number cards labeled 0, 2, 4, and 6. Students count the number of animals in each leg-count category. An optional extension directs students to count the number of legs altogether in each category and to count the number of legs by 2s.
Unit 8: C - Millions of Cats
Lesson 1
Day 1
The Skills section explicitly directs students to decompose numbers less than or equal to 10 into pairs using objects or drawing and to record each decomposition by drawing an equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). Activity 1 asks students to sort die-cut cat objects by features and count the number of cats in each group, providing practice using objects to represent and count quantities.
Lesson 2
Day 2
During Review, students are asked to close their eyes, choose 5 cats, and divide them into two groups based on one characteristic, which has students manipulate objects and create groups. That activity has students physically partition a set of five items, using concrete objects to show a numeric grouping.
Lesson 3
Day 3
In Activity 2 students count 10 die-cut cats, divide them into two groups (for example 9 and 1), count each group, place number cards above each group, and a teacher writes the equation 9 + 1 = 10. Students then move cats to make new groupings (8 and 2, 7 and 3, etc.), count each group, and write corresponding equations such as 8 + 2 = 10. The optional extension asks students to determine how many more cats are needed to make 10 when given a certain number from 1–9.
Lesson 4
Day 4
The Getting Started review asks the child to "divide the 10 cats into two groups and count how many are in each group," which has students manipulate and count objects. This task has students physically partition a set of 10 items and report the number in each part.
Unit 10: O - Owl Babies
Lesson 1
Day 1
The lesson's Skills list explicitly names representing addition and subtraction with objects, fingers, drawings, sounds, acting out, verbal explanations, expressions, or equations. In Activity 1 students sort shapes, order them by size, and count each category of shapes. In the cookie activity students use two balls of dough to form each owl cookie, providing an instance of combining two items.
Lesson 5
Day 5
Students manipulate ten bean 'owls' on a tree mat, count them, and solve join problems by physically moving owls (e.g., "Three baby owls flew to the tree. Then two more came.") to show addition. Students model subtraction by moving owls away (e.g., "Six owls were sitting in the tree. Three owls flew away.") and by transferring owls between the tree and sky to show how quantities change. The activity asks students to act out stories and to create and explain their own stories, supporting verbal explanations and acting-out representations.
Unit 11: S - Seasons of Arnold's Apple Tree
Lesson 1
Day 1
Students use red pom-poms as "apples" and move them from the tree into baskets to model adding quantities (objects). Students act out shakes of the tree and move apples, count how many fell, and read and write equations such as 2 + 1 = 3, with teacher explanation of the plus and equals symbols (acting out, verbal explanations, expressions/equations). Students are encouraged to create their own addition stories and, if able, write the numbers or draw representations (drawings/writing).
Lesson 3
Day 3
Students are asked to identify the sum of 2 + 1 during the Getting Started review, showing exposure to an equation form. In Activity 2 (Ten Little Apples) students count 10 red pom-poms, move apples between two tree diagrams (using objects and drawings), and write equations such as 10 + 0 = 10, 9 + 1 = 10, 8 + 2 = 10, etc. Students are also prompted to choose a number for one tree and determine how many apples belong in the other tree when the total is 10, supporting use of objects and equations to represent combinations.
Lesson 4
Day 4
Students are shown the equation 2 + 1 and are asked to state the answer (3), so they practice reading and responding to an addition expression. Students are also asked to think of two numbers that go together to make 10, which has them mentally represent and combine numbers to form a sum.
Unit 12: D - Dinosaurs Big and Small
Lesson 1
Day 1
The Skills section explicitly asks students to "For any number from 1 to 9, find the number that makes 10 when added to the given number (e.g., using objects or drawings) and record the answer with a drawing or equation." This statement directs students to use objects or drawings and to record solutions with a drawing or equation, which are forms of representing addition.
Lesson 3
Day 3
Students build and use a simple balance to compare two objects, choosing items, predicting which is heavier, and placing them in the bowls to see which side lowers. They observe which bowl is lower and which side the bead hangs on to determine the heavier object. Students are challenged to add another object to the bowl with the lighter object to make the bowls hold equal weight, which has them combine concrete objects to achieve equality.
Lesson 5
Day 5
Students are given 10 dinosaur die-cuts, lay them out, and match each with number cards 1–10. Students count a chosen number of dinosaurs, move that group aside, count how many more are needed to make 10, and write the corresponding equation (for example, 4 + 6 = 10). Students repeat the activity with different numbers and optionally practice recalling the partner to make 10 and writing the equation without manipulatives.
Unit 14: B - Blueberries for Sal
Lesson 1
Day 1
In Activity 1 students draw two number cards, place the corresponding number of blue pom-poms in two foil "pails," count the total, write the equation, and record the answer, which represents addition with objects and equations. Students also count to 10 and divide blueberries between the two pails in many ways, recording matching equations (e.g., 9 + 1 = 10), which practices composing numbers and representing sums with drawings/expressions. The skills list explicitly asks students to compose and decompose numbers and to record compositions or decompositions by drawings or equations.
Lesson 2
Day 2
In Getting Started, the child is asked to name some number pairs that add up to equal 10, which asks the student to produce verbal representations of addition. The lesson provides 20 blue pom-poms (called blueberries) that the child handles when forming the letter B, offering countable objects in the activity even though they are used for letter formation rather than explicit arithmetic.
Lesson 3
Day 3
Students count and place 10 pom‑pom "blueberries" into a pail and match the number 10 card. They then add one blueberry to a second pail while the instructor shows the number 11 card and states that 11 means 10 plus 1 more, and they repeat this by adding a second blueberry and showing 12 means 10 plus 2 more, continuing through 19. Students are also asked to read a number card from 11–19 and count out that many blueberries using the pails, using objects and verbal explanations to represent quantity and addition.
Lesson 4
Day 4
The Getting Started review asks the child to name number pairs that add up to 10, which requires students to generate representations of addition (e.g., verbally or mentally). The review also asks the child to read the number 13 and explain what it means (10 plus 3 more), prompting students to express a number as an addition expression. These prompts require students to represent addition through verbal explanation and numeric expression.
Lesson 5
Day 5
Activity 1 instructs students to use 10 blueberries in one pail and the remaining blueberries in a second pail for numbers 11–19. Students are shown how to write the matching equation (for example, 10 + 5 = 15) and practice these representations in random order. An optional extension asks students to practice writing the equation that goes with each number.
Unit 15: R - Rain
Lesson 3
Day 3
Activity 2 asks students to read written addition equations (totals 5 or less), say the answers, and check answers by showing the equation using raindrop objects. The activity has students lay out 5 raindrops, physically remove one to find how many remain, and count the result while labeling the action as "subtracting." The optional extension shows written subtraction equations (e.g., 5 - 1 = 4), has students read those equations aloud, and use raindrops to find the solution.
Unit 16: N - Night in the Country
Lesson 1
Day 1
The Skills list explicitly includes representing addition and subtraction with objects, drawings, verbal explanations, expressions, or equations. In Activity 1, students place 10 pom-pom apples in a tree, remove a given number to a basket, count how many remain, and write and read the matching subtraction equation (e.g., 10 - 1 = 9). Students practice several subtraction problems using the objects and are guided to say and read the corresponding equations.
Lesson 2
Day 2
The Review section explicitly asks the child to figure out the answer to 10 - 5 using fingers or small objects, so students practice representing a subtraction problem with concrete objects and fingers. The lesson also includes repeated prompts to use manipulatives (paper dolls and craft sticks) and role play, which provide materials students could use for concrete representations of situations.
Lesson 3
Day 3
The Review section asks the child what "5 minus 1" would equal, prompting a verbal subtraction response. Activity 2 (War) has students turn over number cards and keep the higher-numbered cards, engaging students with number comparison and card collection.
Lesson 5
Day 5
In Activity 1, students put 10 "apples" in a tree, decide how many apples fall, and physically move those apples to baskets, providing an object-based and acted-out representation of subtraction. Students say the matching number sentence aloud (for example, "10 minus 3 equals 7") and then write or copy the corresponding equation, practicing verbal and written representations. Students generate several falling-apple scenarios and write matching equations independently or by tracing, reinforcing representation of subtraction with objects, actions, verbal explanations, and equations.
Unit 17: M - Marshmallow
Lesson 1
Day 1
In Activity 1 students use twenty mini marshmallows to cover numbers on a hundred chart, first covering 1–10 and then adding marshmallows to reach 15, and they count the remaining marshmallows to find 5. They are prompted to record the situation with an equation (10+5=15) and to complete missing-addend equations such as 10+__=12. These tasks require students to represent addition with concrete objects and with written equations.
Lesson 3
Day 3
The Review prompt explicitly asks the child to "break the number 16 into two parts," which requires students to think of a number as two addends. Activity 2 has students form a line of marshmallows next to a toy and count the marshmallows, so students represent a quantity with physical objects and record numeric values. Activity 3 has students assemble a marshmallow bunny from multiple marshmallows, which involves counting and combining discrete objects.
Lesson 4
Day 4
The Getting Started prompt asks the child to explain the number 14 in his own words and encourages explaining 14 in terms of ten and four, which asks the child to express a number as a sum (10 + 4). This prompt requires a verbal or mental decomposition of a number, which is a form of representing addition.
Unit 18: U - Umbrella
Lesson 1
Day 1
Activity 1 directs students to use umbrellas to act out addition and subtraction story problems and then write the matching equations with sidewalk chalk (examples: 3+4=7, 5-1=4, 5+5=10). The Skills section explicitly lists solving addition and subtraction within 10 using objects or drawings and recording decompositions with drawings or equations. Students are asked to create their own math story problems, show them with the umbrellas, tell the story, and write the matching equation.
Lesson 2
Day 2
In the Getting Started review students are asked to solve the problem "2 + 3 = ___" using fingers, small objects, or mental math. The lesson also presents the equation format "2 + 3 = ___," prompting students to use concrete materials and mental images to find the sum. These directions explicitly have students represent an addition problem with objects, fingers, and mental strategies.
Lesson 3
Day 3
Students name all pairs of numbers that add up to 10 and record equations such as 9 + 1 = 10 on the sidewalk or paper. Students use ten die-cut umbrellas as concrete objects to model the addition combinations and check for any equations they missed. Students may also respond verbally to the optional extension when given a number and asked what number pairs with it to make 10.
Lesson 4
Day 4
In the Getting Started Review, students are asked to "name a pair of numbers that adds up to 10," which prompts them to produce an addition fact verbally. No other parts of the lesson explicitly require students to represent addition or subtraction with objects, fingers, drawings, sounds, acting, or equations.
Lesson 5
Day 5
In Activity 1, students turn over two umbrellas with written numbers and keep them if the two numbers add up to ten, so they use physical objects to form and check addition pairs. Students manipulate concrete items (umbrellas) and make addition judgments as they take turns trying to collect pairs that equal ten. The game requires students to identify sums of two numbers using the objects as representations.
Unit 19: J - Jump Frog Jump
Lesson 1
Day 1
The Skills section directs students to "compose and decompose numbers from 11-19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18=10+8)." This explicitly asks students to use objects or drawings and to record compositions as equations, providing direct practice representing a number as a sum (10+8).
Lesson 2
Day 2
Students learn and sing the finger-play "Five Little Speckled Frogs," practicing counting backwards from five and bending down fingers as each frog jumps, which represents subtraction using fingers and sound. Students are prompted to create motions for the song and to "count down on his fingers as he sings," providing an acting-out and kinesthetic representation of taking away.
Lesson 3
Day 3
Activity 2 "Jumping to Ten" has students write numbers 1–9 on paper "lily pads," hear a chosen number, and physically jump to the numbered pad that, when paired with the called number, makes 10. The activity uses concrete objects (numbered pads) and acting out (the child as the frog jumping) to represent an addition situation. The Getting Started prompt also asks the child to count as high as she can, supporting number sense used in the activity.
Lesson 5
Day 5
In Activity 1 students count out frog counters (e.g., 16 frogs) and arrange them in a row of 10 plus the remainder. They are asked to determine how many more than 10 make the total (e.g., 16 → 10 + 6) and to write the corresponding addition equation (10+6=16). Students repeat this concrete counting and equation-writing with other numbers between 11 and 19 and with number cards/dot representations.
Unit 20: K - Kindness
Lesson 1
Day 1
The Skills section explicitly states that students will "Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawing to represent the problem." Activity 1 asks students to count and manipulate cut-out animal outlines (numbering, ordering, and pointing to numbers), providing concrete objects for number representation and practice with numerals 1–9. The Student Activity Page provides animal manipulatives that could be used as objects to model simple arithmetic situations.
Lesson 3
Day 3
In Activity 2 (Apple Giveaway) students use ten red pompoms as apples and a basket to model subtraction by physically giving away a chosen number of apples. The teacher asks the child what it means to subtract and prompts the child to perform the removal, count remaining apples, and write the corresponding equation (for example, 10-3=). Students are also asked to predict the number of apples remaining before they count, which engages mental representation and verbal explanation.
Lesson 4
Day 4
During the review, the child is asked to figure out the answer to 10-6 using small objects or mental math, which asks the student to represent a subtraction situation with manipulatives or mental images. That prompt explicitly directs the student to use at least two representation methods (objects and mental math).
Unit 21: V - Zin! Zin! Zin! A Violin
Lesson 1
Day 1
Students use instrument pictures and number cards to show how many instruments are playing: they find the trombone, choose the number card 1 and the label "solo," then add the trumpet and change the number card to 2 and the label "duet." Students continue adding instruments from the book, laying out pictures, number cards, and ensemble labels up to 10, using physical objects and groupings to represent combined quantities.
Lesson 5
Day 5
In Activity 1 students lay out pictures of instruments to show some members present and some missing and are asked to tell how many are here and how many are missing, then write the matching equation (for example, 3 + 7 = 10). Students then lay out all ten pictures, remove a specified number (for example, 2), tell how many remain, and write the subtraction equation (10 - 2 = 8). The activity repeats for other numbers between 1 and 10, reinforcing both addition and subtraction representations with objects and equations and encouraging verbal explanation.
Unit 22: Y - Little Blue and Little Yellow
Lesson 1
Day 1
The Skills section explicitly tells students to "decompose numbers less than or equal to 10 into pairs in more than one way ... by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5=2+3 and 5=4+1)." It also directs students to "compose and decompose numbers from 11 to 19 into ten ones and some further ones ... and record each composition or decomposition by a drawing or equation (e.g., 18=10+8)." These statements require students to use objects or drawings and to record additive relationships with equations.
Lesson 3
Day 3
Activity 2: Making Up Numbers has the child read a number card (e.g., 14), build that number with two colors of stickers (two rows of 5 blue stickers = 10, then 4 yellow stickers), and then write the equation 14 = 10 + 4. The activity is repeated with other numbers (16 and 19), so students practice decomposing numbers with physical objects and recording an equation.
Lesson 4
Day 4
The lesson asks the child to "explain the number 19 to you (10 plus 9 more)," which prompts the student to state a number as a sum (a verbal representation of addition). There are no other explicit prompts that ask students to create addition or subtraction expressions, equations, or to use objects/fingers/drawings specifically for combining or separating quantities.
Lesson 5
Day 5
Students count out 10 stickers, place them in a line, and physically cross off stickers to model taking away. Students answer how many remain after each removal and write matching subtraction equations (for example, 10-1=9, 10-2=8, …, 10-10=0). Students track number crossed off and number remaining, connecting the concrete action with written expressions.
Unit 23: W - George Washington's Birthday
Lesson 1
Day 1
Students are given addition and subtraction problems on the Student Activity Page (e.g., 4+2, 3+2, 5-1) and asked to write answers. Students are directed to use pennies as counters to check George Washington's arithmetic (Activity 2). The skills list explicitly states solving addition and subtraction within 10, e.g., by using objects or drawings to represent the problem.
Lesson 3
Day 3
The Getting Started section asks the child to "create and solve an arithmetic problem," which prompts the student to generate and work through a numerical problem. Activity 2 (Tossing a Rock Across the River) has students act out a situation while verbally counting each catch (saying "one," "two," and continuing), and it suggests counting by 10s as they catch. The toss-and-count activity uses physical action and verbal sounds as part of number work.
Lesson 5
Day 5
In Activity 1, students count a pile of up to 20 craft sticks and count out a specific number shown on a number card (11–20) using the sticks. Students put the sticks in groups of 10 and identify how many extras are needed, which has them represent a two-part number (ten plus extras) with concrete objects. The activity repeats with different piles and number cards so students practice representing numbers physically.
Unit 26: Z - Greedy Zebra
Lesson 1
Day 1
Students use animal cards as physical objects to model addition and subtraction (e.g., laying animals in rows of 10, taking away 7 animals so 13 remain). Students write an equation to record a composition (10 + 3 = 13) and are asked to show all ways to split 10 into two groups (9+1, 8+2, etc.). Students solve an additive word problem (four animals, three more join) and are prompted to create and solve their own story problems using the animals.
Lesson 2
Day 2
The review section instructs: "Using the animal cards from the previous lesson, have your child create and solve a story problem," which directs students to construct and solve a problem using physical cards. The vocabulary list explicitly includes "arithmetic: math problems involving numbers," which names numerical problem solving. These items indicate students will work with number problems and may use manipulatives (animal cards) while creating and solving problems.
Lesson 3
Day 3
Students are asked to name three pairs of numbers that add up to equal 10, which requires verbal and mental representation of addition. In Activity 2, students use animal cards (objects) to sort groups, count how many animals are in each group, and count how many legs are in each group, engaging with quantities using objects and counting.
2: Holidays
Unit 27: Halloween
Lesson 1
Day 1
The lesson's Skills list explicitly states that students will "Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawing to represent the problem." It also says students will "For any number from 1 to 9, find the number that makes 10..., e.g., by using objects or drawings, and record the answer with a drawing or equation." These items directly ask students to represent addition and subtraction with objects, drawings, and equations.
Lesson 3
Day 3
Activity 1 has students make 10 ghost manipulatives, divide them into two unequal groups, count and compare which group has more, and use the ghosts to answer join and take-away story problems (e.g., "2 ghosts came out to play. 2 more joined them." and "8 ghosts were playing tag. 3 stopped..."). Students are prompted to remove ghosts and determine how many are needed to make 10 or how many remain after some are taken away, and to create and solve their own story problems using the ghosts.
Lesson 4
Day 4
Students are asked to name two pairs of numbers whose sum is 10, which requires them to identify addition combinations and state them verbally. Students are asked to count by 10s to 100, which involves repeated addition and mental number sequencing. These prompts require students to use mental images or verbal explanations to represent simple addition relationships.
Lesson 5
Day 5
Students line up and count 10 die-cut stars and are asked to divide the stars into two groups in many ways, providing practice with composing numbers. Students add by placing 2 stars on the mat, being told 3 more become visible, then physically add 3 more stars and count the total; similar addition scenarios are repeated (e.g., 4+5, 3+1, 6+2). Students also write the numbers 1 through 10 on the stars, reinforcing number-symbol correspondence while working with the objects.
Unit 29: Christmas
Lesson 1
Day 1
The Skills section directs students to "compose and decompose numbers from 11 to 19... by using objects or drawing, and record each composition or decomposition by a drawing or equation (e.g., 18=10+8)", which explicitly asks students to represent number compositions with drawings/equations. The Skills also state that students will "fluently add and subtract within 5," indicating practice with addition and subtraction. Activity 1 has students handle and stick foam shapes to the tree branches, giving students opportunities to use physical objects (manipulatives).
Lesson 3
Day 3
Students count out five bells and string them on a pipe cleaner, and then count each of the remaining bells as they add them to the original five, providing a concrete combining action with objects. Students perform the finger play "Five Little Bells," holding up one through five fingers to represent quantities while chanting, which uses fingers and gestures to represent numbers.
Unit 30: February Celebrations
Lesson 1
Day 1
The lesson's Skills list explicitly states that students will "Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem." This language directly identifies student work with addition and subtraction and mentions representing problems with objects or drawings.
Lesson 2
Day 2
The lesson has students handle and sort real coins (pennies, nickels, dimes, quarters) and asks them to determine how many pennies equal a nickel (5), how many pennies equal a dime (10), and how many pennies equal a quarter (25). It prompts challenge questions that require grouping coins (e.g., how many nickels equal a dime or 25 cents). Students also sort a mixed cup of change into piles and review the name and value of each coin.
Lesson 3
Day 3
Students cut out heart-shaped pieces that contain addition problems and separate the problem half from the answer half, physically manipulating pieces to match equations to sums. Students read each addition problem out loud and match written expressions (for example, 5 + 4 = 9) to corresponding answers. Students therefore represent addition using written equations, verbal reading, and physical objects (the cut-apart hearts) during the matching activity.