Anchor Chart · Chunking for Division
Roots of Reason
What Is Chunking?
A quantity can be broken into pieces without changing its value.
75
50
+
20
+
5
still 75. nothing gained, nothing lost.
more honest ways to chunk 75
75 = 70 + 5
tens and ones
75 = 25 + 25 + 25
equal pieces
75 = 80 − 5
overshoot, then back off
Many ways to chunk. The question is which pieces make your problem easier.
Anchor Chart · Chunking for Division
Roots of Reason
How Many Groups?
How many groups of 5 make 75?
amounts
50
20
5
= 75
↕
↕
↕
groups
10 groups
of 5
of 5
4 groups
of 5
of 5
1 group
of 5
= 15 groups
of 5
Every chunk of amount has a matching chunk of groups.
1Make groups you know
10 groups of 5 = 50
4 groups of 5 = 20
1 group of 5 = 5
2Check the amount
50 + 20 + 5 = 75 ✓
3Count the groups
10 + 4 + 1 = 15
So, 75 ÷ 5 = 15.
division asks: how many fit?
Anchor Chart · Chunking for Division
Roots of Reason
Choose Useful Chunks
175 ÷ 7
valid, but slow
100 + 70 + 5
100 ÷ 7 = 14 and change
70 ÷ 7 = 10 ✓
5 ÷ 7 = less than 1
the pieces don't fit groups of 7
70 ÷ 7 = 10 ✓
5 ÷ 7 = less than 1
The chunks equal 175, so nothing is wrong. They are just inconvenient.
useful
140 + 35
140 is 20 groups of 7 ✓
35 is 5 groups of 7 ✓
every piece divides evenly
35 is 5 groups of 7 ✓
Both chunks are multiples of 7. That is what "useful" means in division.
Before you cut, ask: what multiples of the divisor do I already know?
Anchor Chart · Chunking for Division
Roots of Reason
Division in Chunks
The group reasoning from chart 2, written as equations.
groups, in words
140 holds 20 groups of 7
35 holds 5 groups of 7
↓ same thinking, shorter to write ↓
groups, as equations
140 ÷ 7 = 20
35 ÷ 7 = 5
↓
175 ÷ 7 = 20 + 5 = 25
the answers add because the groups add
140 ÷ 7 = 20 is not a trick. It means 140 contains 20 groups of 7.
Anchor Chart · Chunking for Division
Roots of Reason
Partial Quotients
partial quotient: one chunk of the total number of groups
252 ÷ 7, subtracting groups
252start
− 21030 groups of 7
42
− 426 groups of 7
030 + 6 = 36
Pull out easy groups until nothing is left. The quotient is the groups removed.
It is the same chart as before
Each subtraction line is one amount chunk leaving, and each note on the right is its matching groups chunk. The stack is just charts 2 and 4 written vertically.
Any honest chunks work
70 + 70 + 70 + 42 takes more steps and still lands on 36. Fewer chunks is faster, not more correct.
Choose chunks that are easy multiples of the divisor. Any size chunk is allowed.