Worksheet · Chunking for Division · 1 of 12
Roots of Reason
Name
Date
See the Groups in the Chunks
The chunks are already made. Your only job: count the groups inside them.
1.75 ÷ 5. Every amount is matched with its groups. Finish the count.
amounts
50
20
5
= 75
↕
↕
↕
groups
10 groups
of 5
of 5
4 groups
of 5
of 5
1 group
of 5
= groups
of 5
10 + 4 + 1 = groups, so 75 ÷ 5 =
2.84 ÷ 7
70
14
↕
↕
10 groups
of 7
of 7
2 groups
of 7
of 7
10 + 2 = groups, so 84 ÷ 7 =
3.96 ÷ 8
80
16
↕
↕
10 groups
of 8
of 8
2 groups
of 8
of 8
+ = groups, so 96 ÷ 8 =
This page is not about dividing. It is about what the pieces of the answer mean.
Worksheet · Chunking for Division · 2 of 12
Roots of Reason
Name
Date
Match Amounts to Groups
chunk of amount = number of groups × group size
1.96 ÷ 6. Draw a line from each amount to the groups it holds.
60
30
6
1 group of 6
10 groups of 6
5 groups of 6
+ + = groups, so 96 ÷ 6 =
2.130 ÷ 5. Match, then total the groups.
100
25
5
5 groups of 5
1 group of 5
20 groups of 5
+ + = groups, so 130 ÷ 5 =
check one match: 60 = 10 groups of 6 because 10 × 6 =
Matching is multiplication in reverse. That is the whole secret of this unit.
Worksheet · Chunking for Division · 3 of 12
Roots of Reason
Name
Date
Build the Whole from Groups
This time the groups come first. Build the amounts, then the whole.
1.Fill each amount. Then use the amounts to finish the division.
10 groups of 7
↕
4 groups of 7
↕
2 groups of 7
↕
+ + = 112
so 112 ÷ 7 =
2.Same idea with groups of 8.
10 groups of 8
↕
5 groups of 8
↕
3 groups of 8
↕
+ + = 144
so 144 ÷ 8 =
If you can build a whole from groups, you can also take one apart. Both directions matter.
Worksheet · Chunking for Division · 4 of 12
Roots of Reason
Name
Date
Finish the Chunking
Something is missing in each one. Sometimes an amount, sometimes a group count.
1.135 ÷ 5
amounts
100
5
= 135
↕
↕
↕
groups
20 groups
of 5
of 5
6 groups
of 5
of 5
= groups
2.152 ÷ 8
amounts
72
= 152
↕
↕
groups
10 groups of 8
= groups
3.126 ÷ 6
amounts
60
60
= 126
↕
↕
↕
groups
1 group of 6
= groups
Worksheet · Chunking for Division · 5 of 12
Roots of Reason
Name
Date
Choose Useful Groups First
Do not carve the number yet. First: what groups of 7 do you know quickly?
1.Fill your fact bank.
10 groups of 7=
5 groups of 7=
2 groups of 7=
1 group of 7=
2.Build 119 from amounts in your bank. Keep each amount over its groups.
amounts
= 119
↕
↕
↕
groups
= groups
so 119 ÷ 7 =
two chunks is fine. Cross out a box you do not need.
3.Build 98 the same way.
amounts
= 98
↕
↕
↕
groups
= groups
so 98 ÷ 7 =
Worksheet · Chunking for Division · 6 of 12
Roots of Reason
Name
Date
Choose Useful Chunks
Find chunks of the whole that are easy groups of the divisor.
1.175 ÷ 7
amounts
= 175
↕
↕
↕
groups
= groups
175 ÷ 7 =
2.144 ÷ 6
amounts
= 144
↕
↕
↕
groups
= groups
144 ÷ 6 =
Two chunks, three chunks, or more. Use the boxes you need and skip the rest.
Worksheet · Chunking for Division · 7 of 12
Roots of Reason
Name
Date
Different Chunks, Same Groups
168 ÷ 6 · solve it two different ways
1.first way
↕
↕
↕
2.second way, with different chunks
↕
↕
↕
3.What stayed the same?
4.What changed?
Worksheet · Chunking for Division · 8 of 12
Roots of Reason
Name
Date
Which Chunking Would You Use?
252 ÷ 7 · three students chunked it three ways
A
210 + 42
equals 252? yes no
easy groups of 7? yes no
B
140 + 70 + 42
equals 252? yes no
easy groups of 7? yes no
C
200 + 50 + 2
equals 252? yes no
easy groups of 7? yes no
1.Which one would you actually use? Why? A chunking can keep the value and still be a poor choice.
2.Finish the division with your pick: 252 ÷ 7 =
Worksheet · Chunking for Division · 9 of 12
Roots of Reason
Name
Date
From Groups to Division Equations
The equation is shorthand for group reasoning you already understand.
1.Translate both ways. Each row is one fact, written twice.
140 = 20 groups of 7
⟶
140 ÷ 7 =
35 = groups of 7
⟵
35 ÷ 7 = 5
120 = groups of 6
⟶
120 ÷ 6 =
2.175 = 140 + 35, so the quotients add too.
175 ÷ 7 = 140 ÷ 7 + 35 ÷ 7 = + =
3.Your turn: 132 = 120 + 12.
132 ÷ 6 = ÷ 6 + ÷ 6 = + =
Nothing new happened on this page. Only the writing got shorter.
Worksheet · Chunking for Division · 10 of 12
Roots of Reason
Name
Date
Chunk Without the Scaffold
Only one hint this time: what groups do you know?
1.156 ÷ 6
=
2.245 ÷ 7
=
3.312 ÷ 8
=
4.364 ÷ 7
=
Worksheet · Chunking for Division · 11 of 12
Roots of Reason
Name
Date
Remainders: Full Groups and What Is Left
Pull out full groups. What is too small to make one more group is what is left.
1.157 ÷ 6. The chunks are made. Finish the count.
amounts
120
36
1
= 157
↕
↕
↕
groups
20 groups
of 6
of 6
6 groups
of 6
of 6
1 left
full groups, left over, so 157 ÷ 6 = R
2.118 ÷ 9. Make the chunks yourself. One piece will not fit a full group.
amounts
= 118
↕
↕
↕
groups
full groups, left over, so 118 ÷ 9 = R
Say it in words first: "26 full groups, 1 left over." Only then write 26 R1.
Worksheet · Chunking for Division · 12 of 12
Roots of Reason
Name
Date
Mixed Transfer: Find the Chunks Yourself
Nobody labeled the strategy. Can chunking make this easier? Show how.
1.6 × 38
2.175 ÷ 7
3.398 + 247
4.write 114 as a whole number and a fraction