Mathematics · Kindergarten · Building and Breaking Numbers · Weeks 10-18

Taking Groups Apart (Subtraction Intro)

Exploring subtraction as taking apart sets and finding the difference between quantities.

• Common Core State Standards
• CCSS.Math.Content.K.OA.A.1
• CCSS.Math.Content.K.OA.A.3

About This Topic

Taking groups apart introduces subtraction as taking away from sets and finding differences between quantities. Kindergarten students use concrete objects, such as counters, blocks, or snacks, to model actions like removing some items from a group of five or eight. They act out stories, draw representations, and count remainders to see how totals decrease predictably. This builds on addition while highlighting the contrast between putting together and taking apart.

In the Building and Breaking Numbers unit, this topic strengthens decomposition of numbers into pairs summing to 10 or less, per CCSS.Math.Content.K.OA.A.1 and K.OA.A.3. Students answer key questions through exploration: how taking away differs from putting together, ways to show take-away stories with objects, and the consistent effect on totals. These experiences foster early fluency and flexible thinking about quantity.

Active learning benefits this topic greatly because kindergarteners need tactile experiences to distinguish subtraction from addition. When they physically manipulate objects in pairs or small groups to take away and recount, abstract ideas become concrete, errors surface for discussion, and joy in discovery cements understanding before symbolic work.

Key Questions

1. How is taking away different from putting together?
2. What are different ways we can show a taking-away story with objects?
3. When we take some objects away, what happens to the total? Is this always true?

Learning Objectives

• Demonstrate the process of taking apart a set of 5 or fewer objects into two smaller groups.
• Compare the result of taking away objects from a set to the result of adding objects to a set.
• Explain in words or drawings how a set changes when objects are removed.
• Identify the number of objects remaining after some are taken away from a small group.

Before You Start

Counting to 10

Why: Students need to be able to accurately count the initial group and the remaining group.

Number Recognition (0-10)

Why: Students must be able to recognize and name the numbers involved in the taking apart stories.

Putting Together (Addition Intro)

Why: Understanding addition as combining sets helps students contrast it with subtraction as separating sets.

Key Vocabulary

take away	To remove some items from a group. This is how we start thinking about subtraction.
left	The number of items that remain in a group after some have been taken away.
how many	Asking for the total number of items in a group, or the number of items remaining.
difference	What is left over after taking some away. It is the result of a taking apart story.

Watch Out for These Misconceptions

Common Misconception

Taking away means objects disappear forever.

What to Teach Instead

Subtraction finds the amount left after removal, not permanent loss. In hands-on play where students hide and reveal objects, they see conservation of the whole set. Pair discussions help them articulate remainders clearly.

Common Misconception

Subtraction only works starting from 10.

What to Teach Instead

Young learners anchor to familiar benchmarks. Active tasks with varied starts like 4, 6, or 9 show the pattern holds. Small group comparisons of multiple examples build flexible number sense.

Common Misconception

Taking away is the same as putting together.

What to Teach Instead

The actions oppose each other. Role-playing both in sequence during partner games clarifies the inverse relationship. Students recount totals to contrast growth versus decrease.

Active Learning Ideas

Partner Play: Snack Take-Away

Partners start with 6-8 shared snacks like raisins or cubes on a plate. One partner covers some with a cloth to 'eat' them, uncovers, and the other recounts the remainder. Switch roles twice, draw the before-and-after. Discuss total changes.

20 min·Pairs

Small Groups: Block Drop Story

Each group gets 5-10 blocks and a story card like 'Five birds fly away, two left.' They build the start amount, remove by dropping into a cup, count and record what's left. Rotate stories.

25 min·Small Groups

Whole Class: Counting Jar Subtract

Display a jar with 8-10 objects visible. Class chorally counts total. Teacher removes some behind screen, reveals new total. Students predict and thumbs-up differences, then try with personal counters.

30 min·Whole Class

Individual: Finger Story Draw

Students use fingers to show numbers 5-10, 'take away' by hiding some under table, draw the story with tallies or dots. Label 'took away 3, 4 left.' Share one with partner.

15 min·Individual

Real-World Connections

• When a baker takes cookies out of a jar to serve customers, they are using the concept of taking apart. The number of cookies left in the jar decreases.
• A child sharing their toys might give some to a friend. The number of toys the child has left is smaller than when they started.

Assessment Ideas

Exit Ticket

Give each student 5 counters. Ask them to show you 5 counters, then take away 2. On their paper, they should draw what they did and write how many are left.

Quick Check

Present a story problem: 'There were 4 birds on a branch. 1 bird flew away. How many birds are left?' Ask students to use their fingers or counters to show the story and hold up the number of birds remaining.

Discussion Prompt

Show a group of 6 blocks. Ask: 'What happens to the number of blocks if I take 2 away? How do you know?' Encourage students to explain their thinking using words like 'take away' and 'left'.

Frequently Asked Questions

What manipulatives work best for introducing subtraction in kindergarten?

Counters, linking cubes, snacks like goldfish crackers, or two-sided counters excel because they are easy to grasp and manipulate. Students physically take away handfuls, recount remainders, and see changes visually. These support CCSS standards by allowing concrete modeling before drawings or equations, with clean-up built into routines for smooth transitions.

How does taking groups apart align with kindergarten math standards?

CCSS.Math.Content.K.OA.A.1 requires representing addition and subtraction within 10 using objects or drawings. K.OA.A.3 asks decomposing numbers into pairs. This topic directly addresses both through take-away actions and difference-finding, building foundational operations via stories and sets, preparing for fluency.

How can active learning help students understand subtraction?

Active approaches like manipulating objects to take away make subtraction tangible for kindergarteners, countering confusion with addition. In pairs or groups, recounting remainders after physical removal reveals patterns through trial and error. Collaborative sharing corrects misconceptions on the spot, boosts engagement, and transitions naturally to symbolic notation with high retention.

What are simple ways to assess subtraction understanding?

Observe during object-based tasks: can students recount accurately after taking away? Use exit tickets with drawings of '6 take away 2.' Partner talks reveal reasoning. Track growth by noting if they predict remainders correctly, aligning with standards for representation and decomposition.