Kindergarten · Operations · MAT-K-OPS-004
Subtraction as Taking Apart
Model subtraction by starting with a whole and removing part within 10.
Learning objectives
What you should be able to do
- Model subtraction by starting with a whole and removing part within 10.
- Write or interpret simple subtraction equations from take-away situations.
- Explain that the difference tells how many remain after a part is removed.
Prerequisite check
Make sure the foundation is ready.
Checks whole-to-parts reasoning.
Checks starting totals and remaining quantities.
Learn
Build the idea from meaning, not memorization.
Subtraction can describe taking away
Begin with a whole group, remove some objects, and count what remains. If five blocks are present and two are taken away, three remain.
The equation records start, removal, and remainder
The story '5 blocks, take away 2, 3 remain' is written 5 − 2 = 3. The minus sign marks the amount being removed; the equals sign states that the subtraction expression has the same value as the remainder.
Subtraction reveals a part of the whole
If the whole is five and two are removed, the remaining three is the other part. This connects subtraction to decomposition and later to addition as an inverse relationship.
Use objects and count what remains
For young learners, physically crossing out or moving removed objects makes the action visible. Later, number-line backward hops can represent the same subtraction.
Interactive math lab
Change it. See what stays true.
Ten-Frame Lab
Fill the frame from left to right and connect the visible amount to the numeral.
5 filled; 5 empty; 10 spaces altogether.
- build whole
- cross out removed part
- count remainder
- check with addition
Worked examples
Twenty different ways to see the concept work.
Start with 2; remove 1.
2 − 1 = 1One object remains.
Start with 3; remove 1.
3 − 1 = 2Taking one makes one less.
Start with 4; remove 2.
4 − 2 = 2Two of four remain.
Start with 5; remove 2.
5 − 2 = 3Three remain.
Start with 5; remove 5.
5 − 5 = 0Removing the whole leaves none.
Start with 5; remove 0.
5 − 0 = 5Removing nothing changes nothing.
Start with 6; remove 1.
6 − 1 = 5One less than six is five.
Start with 7; remove 3.
7 − 3 = 4Remove three and count four remaining.
Start with 8; remove 2.
8 − 2 = 6Two objects are taken away.
Start with 10; remove 4.
10 − 4 = 6Six remain.
Five balloons; two float away.
5 − 2 = 3The story removes part of the starting group.
Seven crackers; one is eaten.
7 − 1 = 6One fewer remains.
Eight blocks; three are put away.
8 − 3 = 5Five remain visible.
Ten pencils; all ten are removed.
10 − 10 = 0No pencils remain.
Which operation matches 'take away': + or −?
−The minus sign represents subtraction.
What does the first number in 6−2 describe?
The starting whole of 6Subtraction begins with the whole in this model.
What does the 2 in 6−2 describe?
The part removedTwo are taken away.
What does the 4 in 6−2=4 describe?
The amount remainingFour is the difference.
Check 6−2=4 by recomposing.
4 + 2 = 6Remaining part plus removed part returns the whole.
Explain why 5−1 is 4 without recounting from 1.
Removing one makes the quantity one less.The number before five is four.
Practice
Guided practice with hints
01Model 4−1 with counters.
Hint: Build four, move one away.
Answer: 3
02Model 5−3.
Hint: Cross out three of five.
Answer: 2
03Complete 7−2=__.
Hint: Remove two and count the remainder.
Answer: 5
04Complete 6−0=__.
Hint: Nothing is removed.
Answer: 6
05Complete 3−3=__.
Hint: All objects are removed.
Answer: 0
06Tell a take-away story for 5−2.
Hint: Start with five and remove two.
Answer: Any valid story leaving 3.
Practice
Independent practice
013−1
Answer: 2
024−2
Answer: 2
035−1
Answer: 4
046−2
Answer: 4
057−3
Answer: 4
068−1
Answer: 7
0710−5
Answer: 5
08What operation means taking away?
Answer: Subtraction
Common mistakes
Learn to catch the error, not just the answer.
Build the first number as the complete starting group before taking anything away.
Separate removed objects visually from the remaining set.
Removing no objects leaves the starting quantity unchanged.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Model snacks being eaten from a small starting group.
- Put away some toys and calculate how many remain.
Challenge problems
Create two different take-away stories for 7−2.
Any two contexts starting with seven, removing two, leaving five.
Why is 5−5 equal to zero?
The entire starting group is removed.
How can addition check 8−3=5?
5+3=8 returns the starting whole.
Explain subtraction using whole and parts.
Subtraction starts with a whole and finds a remaining part after another part is removed.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Take-Away Trail
Start with the shown group, remove the requested amount, and choose the correct remainder and equation.
Practice
Mastery check
01Model 4−2.
Answer: 2 remain
02Solve 5−1.
Answer: 4
03Solve 7−3.
Answer: 4
04Solve 10−4.
Answer: 6
05What does − mean?
Answer: Subtract or take away.
06What happens in 6−0?
Answer: Nothing is removed, so 6 remains.
07How can addition check 6−2=4?
Answer: 4+2=6.
08Explain why a take-away story uses subtraction.
Answer: A part is removed from a starting whole.
Terminology
Words to know
- subtraction
- Removing a part or finding how much remains.
- minus sign
- The symbol − showing subtraction.
- difference
- The result of a subtraction.
- remain
- The quantity left after a part is removed.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Kindergarten Operations & Algebraic Thinking
Standards progression for composing, decomposing, adding, and subtracting within 10.