Roots of Reason
Roots of Reason

Chunking

Break a hard problem into easier parts without changing its value.
1
Break it
into useful chunks
175 140 + 35
2
Work with the chunks
140 ÷ 7 = 20 35 ÷ 7 = 5
3
Put them back together
20 + 5 = 25 so 175 ÷ 7 = 25
whole ⇄ chunks  ·  the pieces change, the value never does
Roots of Reason CA CCSS 4.NBT.B.6 rootsofreason.org
Anchor Chart · Chunking Series · 1 of 8
Anchor Chart · Chunking Series · 2 of 8
Roots of Reason
Roots of Reason

Choose Useful Chunks

Place value 347 → 300 + 40 + 7 break by hundreds, tens, ones
Reach a benchmark 58 + 27 → 58 + 2 + 25 get to 60 first, then it's easy
Use a fact you know 8 × 7 → 8 × 5 + 8 × 2 fives and twos are fast facts
Compatible multiple 175 ÷ 7 → 140 + 35 both pieces divide evenly by 7
Go past, compensate 6 × 39 → 6 × 40 - 6 borrow an easy number, pay it back
There is often more than one good choice.
Roots of Reason CA CCSS 4.NBT.B.6 rootsofreason.org
Anchor Chart · Chunking Series · 3 of 8
Roots of Reason
Roots of Reason

Chunking Addition and Subtraction

+Break an addend to reach a friendly number
57 + 26 57 + 3 + 20 + 3 +3+20+357608083 = 83
What number were you trying to reach? 60, then 80.
−Break the distance into manageable pieces
83 − 27 count up: 27 → 30 → 80 → 83 +3+50+327308083 3 + 50 + 3 = 56
The answer is the distance between 27 and 83, walked in easy steps.
Roots of Reason CA CCSS 3.NBT.A.2 rootsofreason.org
Anchor Chart · Chunking Series · 4 of 8
Roots of Reason
Roots of Reason

Multiply in Chunks

7 × 36
7
306
210
42
210 + 42 = 252
7 × 36 = 7 × (30 + 6) = 7×30 + 7×6 = 210 + 42 = 252
Every chunk of the rectangle gets multiplied. None may be skipped.
also works backward 6 × 39 = 6 × (40 − 1) = 240 − 6 = 234 go past to a friendly factor, then take the extra back out
Break one factor. Multiply every chunk. Recombine.
Roots of Reason CA CCSS 4.NBT.B.5 rootsofreason.org
Anchor Chart · Chunking Series · 5 of 8
Roots of Reason
Roots of Reason

Divide in Chunks

252 ÷ 7  ·  two honest ways to write the same thinking
ABreak the dividend
252 = 210 + 42 210 ÷ 7 = 30 42 ÷ 7 = 6 30 + 6 = 36
Each piece divides evenly by 7. That is what makes it a good chunk.
BSubtract groups away
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.
Choose chunks that are easy multiples of the divisor. Any size chunk is allowed.
Roots of Reason CA CCSS 4.NBT.B.6 rootsofreason.org
Anchor Chart · Chunking Series · 6 of 8
Roots of Reason
Roots of Reason

Fractions Can Chunk Too

114 = 84 + 34 = 2 34
Two whole bars of fourths, then 3 more fourths. Eleven fourths never changed.
more than one way
78 = 48 + 38 78 = 28 + 58
The pieces can change. The total cannot.
Roots of Reason CA CCSS 4.NF.B.3 rootsofreason.org
Anchor Chart · Chunking Series · 7 of 8
Roots of Reason
Roots of Reason

There Is More Than One Way

168 ÷ 6
120 + 48 20 + 8 groups 2 chunks
60 + 60 + 48 10 + 10 + 8 groups 3 chunks
180 − 12 30 − 2 groups go past, come back
all three land on 28
Which is easiest for you?
Roots of Reason CA CCSS 4.NBT.B.6 rootsofreason.org
Anchor Chart · Chunking Series · 8 of 8
Roots of Reason
Roots of Reason

The Same Idea Keeps Coming Back

57 + 26break an addend to reach a friendly number
↓
7 × 16break a factor and multiply each chunk
↓
175 ÷ 7break a dividend into compatible multiples
↓
114break a fraction into wholes and parts
↓
7(x + 3)break an expression using distribution: 7x + 21
decompose
↓
work
↓
recompose
Break it into useful chunks.
Work with the chunks.
Put the results back together.