Math Grade 1: Operations

Concept 4: Addition Foundations (Sums to 10)

• Tools

  Two-Color Counters (200 count): Children combine red and yellow counters to see how two groups make a whole.
  CRA Focus & Purpose: Concrete. Builds hands-on understanding of addition as joining two quantities.
  How to Use It: Make small combinations—3 red, 2 yellow. Push together and count: “3 + 2 = 5.” Ask “Do we get the same total if we switch colors?”
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  Connecting Cubes (100–200 pieces): Snap cubes visually and physically show how numbers combine.
  CRA Focus & Purpose: Concrete. Helps children see addition as connecting separate parts into one longer whole.
  How to Use It: Build two towers and connect: “4 + 3 = 7.”
  Ask: “How many different color combinations can make 10?”
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  Ten Frame Set (4-pack with counters): Frames show numbers as parts of 10, helping children visualize combinations.
  CRA Focus & Purpose: Concrete to Representational. Connects physical counters to visual patterns that support mental strategies.
  How to Use It: Fill frames to show sums like 6 + 3 = 9. Slide counters together and observe when the frame is full.
  Ask: “How many more do you need to make 10?”
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  Rekenrek (20 Beads): Combines movement and visual structure for quick addition within 10.
  CRA Focus & Purpose: Concrete to Representational. Encourages five- and ten-based reasoning with visual grouping.
  How to Use It: Slide 4 red and 3 white beads—count together to find 7. Ask “What do you notice about the colors when you make 10?”
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  Montessori Addition & Subtraction Learning Board: Wooden tiles show addition and subtraction facts with self-check visuals.
  CRA Focus & Purpose: Representational to Abstract. Connects counting dots to symbolic equations, building fluency through matching.
  How to Use It: Match addition tiles to correct sums. Use dots to check.
  Ask: “Which number pairs make 9? How do you know?”
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• Games

  Sum Swamp by Learning Resources: Players travel across a swamp, solving addition facts each turn. Engaging and self-correcting through gameplay.
  CRA Focus & Purpose: Representational to Abstract. Children roll dice, add numbers, and move spaces, building fluency through repetition and play.
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  Hasbro Gaming Sorry! Kids Board Game: Classic movement game where players count and add spaces to advance.
  CRA Focus & Purpose: Concrete to Representational. Reinforces counting on, adding movement, and turn-taking as an intuitive form of early addition.
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  Learning Resources Pop For Addition & Subtraction Math Game: Pop-and-play game using spinner-style “gumball” poppers to reveal and solve addition facts.
  CRA Focus & Purpose: Representational to Abstract. Builds quick recall and fluency through repetition and immediate feedback in a playful setting.
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  Learning Resources tri-FACTa Addition and Subtraction Game: Triangle-shaped game board where players create true number sentences using cards and math fact triangles.
  CRA Focus & Purpose: Representational to Abstract. Reinforces relationships between numbers in equations and helps solidify part–part–whole thinking.
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  eeBoo Simple Math Bingo Game: Classic bingo format using addition and subtraction facts up to 10. Children match equations to correct answers on their boards.
  CRA Focus & Purpose: Representational to Abstract. Encourages recognition and recall of number combinations while reinforcing equality.
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  Melon Rind Clumsy Thief Math Game (Adding to 20): Fast-paced card game where players “steal” cards that add up to 20.
  CRA Focus & Purpose: Abstract. Strengthens mental addition, complements to 10 and 20, and rapid recall through play.
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  Suntex 24 Game Add/Subtract (96 Cards): Mental math card game where players use addition or subtraction to make 24 from four numbers.
  CRA Focus & Purpose: Abstract. Encourages flexible, strategic thinking and number manipulation once single-digit addition is fluent.
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• Activities

  Story Problems with Objects
  CRA Focus & Purpose: Concrete. Builds real-world understanding of addition through physical combining and storytelling.

  • Materials: Toys, snacks, or household items

  • Steps: Create simple stories: “You have 3 toy cars, and you get 2 more—how many now?” Let your child act it out and count aloud.

  • Ask: “What happens when we add more?” “How can we show what’s happening?”

  • Variation: Let your child create their own addition stories for you to solve.

  Nature Addition
  CRA Focus & Purpose: Concrete. Encourages hands-on exploration by adding and counting natural objects.

  • Materials: Leaves, rocks, sticks, pinecones

  • Steps: Collect items outdoors. Combine two groups: “3 rocks and 4 rocks make how many?” Count to find the total.

  • Ask: “How many altogether?” “How many more would make 10?”

  • Variation: Create outdoor number stories or patterns that show sums.

  Snack Time Addition
  CRA Focus & Purpose: Concrete. Makes math part of daily routines while reinforcing one-to-one counting.

  • Materials: Small snacks (crackers, grapes, cereal pieces)

  • Steps: Serve 3 crackers first, then add 4 more. Have your child count and say, “3 plus 4 equals 7!”

  • Ask: “How many did you start with?” “What happens when we add more?”

  • Variation: Use mealtime to compare and add family members’ portions.

  Part–Part–Whole Mat
  CRA Focus & Purpose: Concrete to Representational. Shows how two smaller groups combine into a whole through tactile play and visual structure.
  

  • Materials: Paper mat with two “part” boxes and one “whole” box, counters

  • Steps: Place counters in each part box (3 and 4). Move them to the whole box and count total (7).

  • Ask: “What two parts make this whole?” “Can we find another way to make the same number?”

  • Variation: Start with the whole filled and split it into two parts.

  Domino Addition
  CRA Focus & Purpose: Representational. Helps children see number relationships visually and connect to equations.
  

  • Materials: Set of dominoes

  • Steps: Flip a domino and count the dots on both sides. Add them together to find the total.

  • Ask: “How many dots in all?” “How many ways can you make 8?”

  • Variation: Group dominoes by total and look for patterns (5+3 and 4+4 both make 8).

  Ten Frame Flash
  CRA Focus & Purpose: Representational to Abstract. Strengthens quick recognition of quantities and complements of 10.
  

  • Materials: Ten frames and counters

  • Steps: Fill a ten frame, flash for 2–3 seconds, then hide. Ask, “How many?” and “How many more to make 10?”

  • Ask: “What did you see quickly without counting?” “What happens when the frame is full?”

  • Variation: Use two ten frames for larger sums or to visualize doubles.

  Roll and Add
  CRA Focus & Purpose: Abstract. Encourages mental calculation and fluency within 10 using play and repetition.
  

  • Materials: Two dice, paper with numbers 2–12, counters or coins

  • Steps: Roll two dice, add them, and cover that number on your board. First to cover all wins.

  • Ask: “Which numbers come up most often?” “Can you predict your next sum?”

  • Variation: Use three dice for sums up to 18 or fix one die for “adding on.”

  Number Bond Practice
  CRA Focus & Purpose: Abstract. Deepens understanding of number pairs and flexible reasoning with sums.

  • Materials: Counters, paper, pencil

  • Steps: Choose a target number (like 8). Find all pairs that make it (7+1, 6+2, 5+3, 4+4). Write or draw each.

  • Ask: “How many ways can we make 8?” “Which pair is easiest for you to remember?”

  • Variation: Make it a timed challenge to build fluency.

• Books

  Ten Apples Up On Top! by Dr. Seuss Classic Dr. Seuss counting story where animals balance apples on their heads, wonderful for counting and adding to 10.
  CRA Focus & Purpose: Concrete to Representational. Uses rhythmic counting and movement to help children experience combining quantities physically.
  How to use it: Count apples with each character, then combine: "Lion has 3, dog has 2—that's 5 apples up on top!" Act it out with blocks or stuffed animals balancing objects.
  View on Amazon | Read Aloud on YouTube

  Jack the Builder by Stuart J. Murphy Shows counting on strategy through building context. CRA Focus & Purpose: Concrete to Representational. Connects physical construction to number growth—children learn to start with a known amount and add on.
  How to use it: Practice "counting on" like Jack does—start with the bigger number and count up. Use blocks to build like Jack. Start with 5 blocks, add 3 more by counting "6, 7, 8."
  View on Amazon | Read Aloud on YouTube

  Ten Friends by Bruce Goldstone explores all the ways to make 10 through vibrant photography and clear visual models. Each page shows a different combination with real objects.
  CRA Focus & Purpose: Representational. Deepens understanding of combinations that form 10—the foundation for all addition within 20.
  How to use it: Study each page to find the two groups that make 10. Use household objects to recreate each combination. Play "make 10" games: "I have 7 buttons, how many more do I need to make 10?"
  View on Amazon | Read Aloud on YouTube

  Mission: Addition by Loreen Leedy Engaging story that introduces addition basics through relatable scenarios. Clear visual models support understanding.
  CRA Focus & Purpose: Representational to Abstract. Bridges from pictorial to symbolic understanding using clear visual models.
  How to use it: Read and discuss the different addition situations in the story. Act out similar scenarios with household objects. Create your own addition missions: "Mission: find out how many shoes are by the door!"
  View on Amazon |Read Aloud on YouTube

  
  Gus the Plus by Emily Barnes personifies the plus sign, helping children understand what addition means and when to use it.
  CRA Focus & Purpose: Abstract. Connects real-world combining to the symbolic operation of addition.
  How to use it: Look for "Gus situations" in daily life—anytime things are combined or joined. Practice writing the plus sign. Create addition stories: "When do we need Gus? When we put things together!"
  View on Amazon | Read Aloud on YouTube

Concept 5: Subtraction Foundations (Numbers within 10)

• Books

  Five Little Monkeys Jumping on the Bed by Eileen Christelow: Classic counting-down story where monkeys fall off the bed one by one. Perfect introduction to subtraction as "taking away."
  How to use it: Act out the story with stuffed animals or toys. Start with 5, take away 1 each time. Count how many are left. Create your own countdown stories: "5 cookies on the plate, I ate 1, now there are 4!" Write subtraction equations for each page: 5-1=4, 4-1=3.
  View on Amazon | Read Aloud on YouTube

  Ten Little Fish by Audrey Wood: Ten fish swim away one by one in this beautifully illustrated countdown book. Shows subtraction in an engaging ocean setting.
  How to use it: Count down from 10 as each fish leaves. Discuss where each fish goes and why. Use toys or drawings to recreate: start with 10, take away 1 at a time. Practice writing equations: 10-1=9, 9-1=8. Ask: "How many fish left? How many swam away?"
  View on Amazon | Read Aloud on YouTube
  

  Monster Musical Chairs by Stuart J. Murphy: Monsters play musical chairs, creating different addition combinations as they sit down. Shows addition in action through a familiar game.
  How to use it: Act out the story with stuffed animals and chairs. Count monsters in different groups: "3 on chairs plus 4 standing equals 7 monsters!" Play your own musical chairs and create addition sentences for each round.
  View on Amazon| Read Aloud on YouTube

  Subtraction Action by Loreen Leedy: Engaging animal characters explore subtraction through relatable scenarios. Clear visual models support understanding of taking away and comparing.
  How to use it: Read and discuss the different subtraction situations. Act out similar scenarios with household objects. Notice the different types of subtraction: taking away, comparing, finding what's missing. Create your own "subtraction action" stories throughout the day.
  View on Amazon | Read Aloud on YouTube

  Elevator Magic by Stuart J. Murphy: Children ride an elevator down, subtracting floors as they go. Makes counting backwards and subtraction concrete through a familiar experience.
  How to use it: Practice counting backwards like the elevator going down. Start at floor 10, subtract 3—which floor are you on? Use building blocks to create floors and physically move down. Connect to real elevator rides: "We're on floor 5, going down 2 floors. Where will we be?"
  View on Amazon | Read Aloud on YouTube

  
  Teeth, Tails, & Tentacles: An Animal Counting Book by Christopher Wormell Counts up to 10 then back down, showing both addition and subtraction. Beautiful woodcut illustrations make numbers memorable.
  How to use it: Count up to 10 with the animals, then count back down. Practice both directions: adding and subtracting. Use the pattern to create your own counting up and down stories. Notice how subtraction is the opposite of addition.
  View on Amazon | Read Aloud on YouTube

  
  Mouse Count by Ellen Stoll Walsh Mice are captured one by one, then escape—shows both adding and taking away. Simple, engaging story perfect for acting out.
  How to use it: Use toy mice or counters to follow along. Count as mice are added to the jar, then count as they escape. Write both addition and subtraction equations. Discuss: "When mice went in, we added. When they escaped, we subtracted. These are opposite actions!"
  View on Amazon | Read Aloud on YouTube

  
  12 Ways to Get to 11 by Eve Merriam While focused on addition combinations, this book brilliantly shows how subtraction is the inverse: if these combinations make 11, you can subtract to break 11 apart.
  How to use it: After exploring how to make 11, reverse it: "If 7+4=11, then 11-7=? and 11-4=?" Use objects to show both operations. This builds deep understanding of the addition-subtraction relationship.
  View on Amazon | Read Aloud on YouTube

• Tools

  Melon Rind Jump 1 by Melon Rind focused specifically on adding and subtracting 1—the foundational skill for counting forward and backward.
  How to use it: Players practice the essential skill of adding 1 (counting on) and subtracting 1 (counting back). These "plus or minus 1" facts are the building blocks for all other addition and subtraction. The game format makes this critical practice fun and memorable. Master these facts first, and all other facts become easier!
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  Pop for Addition and Subtraction! Game by Learning Resources Fast-paced game where children pop bubbles while solving subtraction problems. Builds fluency through engaging play.
  How to use it: Roll the dice to create a subtraction problem, then race to pop the correct answer bubble. The popping action adds excitement and keeps children motivated to practice. Multiple players can compete, or play solo against the clock. Perfect for making subtraction fact practice fun and memorable.
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  Cloud Hoppers Addition and Subtraction Game Sky-themed board game where players hop across clouds while solving addition and subtraction problems. Makes practice playful and engaging.
  How to use it: Draw a card with an addition or subtraction problem, solve it, then move that many spaces along the cloud path. The whimsical theme keeps children engaged while building fluency with both operations. Practice switching between adding and subtracting—an important skill for mental flexibility.
  View on Amazon

• Activities

  1. Countdown Stories

  • Materials: 5-10 small toys or objects

  • Start with a group of objects and create a countdown story: "5 birds on a branch, 2 fly away..."

  • Remove objects one at a time as you tell the story.

  • Count what remains after each subtraction. Write the equation: 5-2=3.

  • Variation: Let your child create countdown stories for you to act out and solve.

  2. Take Away Game

  • Materials: 10 small objects (blocks, crackers, coins), cup or container

  • Place objects in a group. Count them together.

  • Cover some with the cup: "I'm hiding 3. How many can you still see?"

  • Child counts visible objects, then figures out how many are hidden.

  • Variation: Start with the total covered, reveal some, ask how many are still hidden.

  3. Crossing Out Subtraction

  • Materials: Paper, markers, stickers or stamps

  • Draw or stamp a group of objects (like 7 stars).

  • Cross out some (cross out 4 stars).

  • Count what's NOT crossed out: 3 stars remain! Write the equation: 7-4=3.

  • Variation: Create a subtraction picture book with different scenarios on each page.

  4. Roll and Subtract

  • Materials: Two dice, paper and pencil

  • Roll both dice. Subtract the smaller number from the larger.

  • Write the equation and solve: "I rolled 6 and 2, so 6-2=4!"

  • Keep playing, tracking all subtraction problems you create.

  • Variation: Roll one die and always subtract from 10 to practice "subtract from 10" facts.

  5. Subtraction War

  • Materials: Deck of cards (remove face cards)

  • Each player flips two cards and subtracts the smaller from the larger.

  • Largest difference wins all four cards.

  • Simple, repetitive practice that builds fact fluency. Aces = 1.

  • Variation: Smallest difference wins, or exact match of differences wins all cards on table.

  6. Number Line Hop Back

  • Materials: Number line (floor mat, tape on floor, or drawn with chalk)

  • Start at a number, call out a subtraction: "Start at 9, subtract 4!"

  • Child hops backwards 4 spaces and announces the answer: "5!"

  • Take turns creating subtraction problems for each other.

  • Variation: Time how fast child can solve 5 subtraction problems by hopping.

  7. Hide and Seek Subtraction

  • Materials: 10 small objects, two containers

  • Count out 10 objects together.

  • Hide some in one container, the rest in another. Don't let child see how many are in each!

  • Show one container: "Here are 6. How many must be hiding?" (10-6=4)

  • Variation: Let child hide objects and quiz you.

  8. Eating Subtraction

  • Materials: 10 small snacks (goldfish, cheerios, grapes)

  • Count snacks together: "We have 8 crackers!"

  • Child eats some: "You ate 3. How many are left?"

  • Count remaining snacks. Write the subtraction equation: 8-3=5.

  • Variation: Start with more snacks, subtract in multiple rounds, track the equations.

  9. Part-Part-Whole Subtraction

  • Materials: Part-part-whole mat (drawn or printed), counters

  • Put 9 counters in the "whole" box.

  • Move 4 counters to one "part" box. How many are left for the other part?

  • This shows subtraction as finding the missing piece: 9-4=5.

  • Variation: Give only the total and one part—child finds the other part each time.

  10. Comparison Subtraction

  • Materials: Two groups of objects (like 7 blocks and 4 blocks)

  • Line up objects in two rows to compare.

  • "Which group has more? How many more?"

  • Count the difference: 7-4=3 more!

  • Variation: Create comparison scenarios: "You have 5 toys, I have 8. How many more do I have?"

  11. Domino Subtraction

  • Materials: Set of dominoes

  • Use dominoes as ready-made subtraction problems.

  • Find the difference between the two sides: if one side has 6 dots and the other has 2, the difference is 4.

  • Variation: Find all dominoes with a difference of exactly 3 (or any target number).

  12. Mystery Number Subtraction

  • Materials: Paper, pencil, small objects for solving

  • Give subtraction clues: "I started with 9. I took away some. Now I have 5. How many did I take away?"

  • Child uses objects to figure it out: 9-?=5, so ?=4

  • Variation: Let child create mystery subtraction problems for you.

  13. Backwards Counting Practice

  • Materials: Just your voices!

  • Practice counting backwards from different numbers: "10, 9, 8, 7..."

  • Make it fun: "Rocket countdown! 5, 4, 3, 2, 1, BLAST OFF!"

  • Connect to subtraction: "Counting back is what we do when we subtract!"

  • Variation: Count backwards by 2s, or start from different numbers each time.

• Big Challenges

  1. Subtraction Treasure Hunt
  Why it’s powerful:
  Turns subtraction into an active adventure. Children physically experience “taking away” as they collect and count. Builds memory, sequencing, and number sense.
  How to do it:
  Hide 10–20 small objects around a room or garden. Start with a visible total on a tray (say 15 shells). Each time your child finds one, take it away from the tray and say the equation: “15 - 1 = 14.” Continue until all are gone.
  Variation: Start with 20 and hide 5 at a time — subtract in chunks (“20 - 5 = 15”).
  
  2. Bowling Alley Builders
  Why it’s powerful:
  Incorporates gross motor skills and repeated subtraction practice through real action. Every roll is a math problem in disguise.
  How to do it:
  Set up 10 cups or empty bottles as bowling pins. Each turn, knock some down and count how many are left standing. Write or shout the equation after every roll (“10 - 4 = 6”).
  Variation: Play cooperative mode — how many turns until all pins are gone?
  
  3. Pop & Drop Balloon Subtraction
  Why it’s powerful:
  Adds excitement and anticipation to math! Children visually and physically experience “taking away” as balloons disappear.
  How to do it:
  Blow up 10 balloons. Label them 1–10. Pop one balloon at a time and count how many remain.
  Variation: For noise-sensitive environments, let the balloons drop or deflate instead of popping.
  
  4. Toy Rescue Mission
  Why it’s powerful:
  Makes subtraction meaningful through storytelling and sensory play — turning every equation into a mini-drama.
  How to do it:
  Line up 10 toy animals “stuck” in a paper jungle. Rescue a few each round (“We saved 3 tigers — 10 - 3 = 7 left!”). Continue until all are safe.
  Variation: Time each round and graph how many you rescued each turn.