Mathematics · Kindergarten

Active learning ideas

Decomposing Numbers to 10

Active learning works because decomposing numbers to 10 requires students to experience quantity in multiple ways. When students manipulate objects, build with models, and explain their thinking, they internalize the abstract idea that numbers can be split apart and recombined. This hands-on approach builds the mental flexibility needed for place value and mental math.

• Common Core State Standards
• CCSS.Math.Content.K.OA.A.3

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Stations Rotation: Ten-Frame Fun

Set up stations with giant floor ten-frames. Students use beanbags to fill the frames, practicing seeing '5 and 5' or '8 and 2' to make a full ten, then recording their combinations.

How many different ways can we break apart the number 5?

Facilitation Tip

During How Many More to Ten?, pause after each pair shares to ask the class to restate their partner’s idea in their own words.

What to look for

Give each student a card with a number from 1 to 10. Ask them to draw two different ways to make that number using dots or simple shapes, and write the number sentence for each way. For example, for 6, they might draw 3 dots and 3 dots, writing '3 + 3 = 6', and then 4 dots and 2 dots, writing '4 + 2 = 6'.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Inquiry Circle
• 20 min · Pairs

Inquiry Circle: Teen Number Builders

Pairs are given a 'full' ten-frame and a handful of extra counters. They must build numbers like 13 or 17 and explain to each other that 13 is 'one ten and three more.'

Construct a visual model to show two parts that make up the number 8.

What to look for

Present students with a ten-frame partially filled with counters. Ask: 'How many more counters do we need to fill the ten-frame?' Then ask: 'What two numbers make up the total number of counters in the ten-frame?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: How Many More to Ten?

Flash a partially filled ten-frame for three seconds. Students think about how many empty spots they saw, then share with a partner how they knew how many more were needed to reach ten.

Analyze why some numbers have more ways to be decomposed than others.

What to look for

Show students two different ways to decompose the number 7, for example, 5 + 2 and 4 + 3. Ask: 'Which way is easier for you to see? Why do you think some numbers have more ways to be broken apart than others?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers approach this by letting students explore combinations without rushing to memorization. Avoid telling students there’s only one correct way to decompose a number. Instead, model curiosity about different strategies and invite students to compare them. Research shows that when students justify their own methods, they develop stronger number sense than when they memorize facts alone.

Successful learning looks like students confidently breaking numbers into two parts with ease. They should explain their strategies using ten-frames, counters, or number sentences without hesitation. You’ll notice students recognizing ten as a unit and adding on, not just counting on one by one.

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Watch Out for These Misconceptions

• During Ten-Frame Fun, watch for students who count each dot one by one across the entire frame without recognizing the ten as a unit.

  Prompt them to look at the full ten-frame and say, ‘This frame shows ten. How many dots do you see in the top row? How many more are in the bottom row? That means 5 and 5 make 10.’

• During Teen Number Builders, watch for students who build 14 as one tower of 1 and one tower of 4 instead of one tower of 10 and one tower of 4.

  Use overlapping numeral cards where the digit 4 is placed over the 0 in 10, then ask, ‘What number is still under the 4? How many is that?’

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Methods used in this brief

• Stations Rotation
• Inquiry Circle
• Think-Pair-Share