Two decimals, four questions

Same surface, different depth · 5th grade · Decimals to thousandths

Ink Designed Plain black & white All SSDD sheets

Two decimals, four questions Grade 5 · Decimals to thousandths

Name
Date

Read this first

Same pair of decimals in all four. The operation is the thing that changes.

All four questions are about this

The two numbers are 2.4 and 0.6.

1Four different questionsThey look alike. They are not. Answer each one.

a)Add them.

b)Multiply them.

c)Divide 2.4 by 0.6.

d)Which of the two is closer to 1?

Scratch space — work it out here

Challenge. Pick the one you found hardest, cover your answer, and do it again from scratch. Getting the same answer twice is how you know you have it — and testing yourself is worth more than reading it over again.

izzimath · Grade 5 · seed 0 · 5.NBT.B.7, 5.NBT.A.3
Same surface, four different methods. The key names the method each one needed.

Two decimals, four questions Grade 5 · Decimals to thousandths

Name
Date

All four questions are about this

The two numbers are 2.4 and 0.6.

1Four different questionsEach answer with the method it needed.

a)Add them.

3 Add — line up the points

2.4 + 0.6: 4 tenths and 6 tenths make 10 tenths, which is a whole. 3.0, written 3.

b)Multiply them.

1.44 Multiply — count the decimal places

24 × 6 is 144. There is one decimal place in each number, so two altogether: 1.44.

c)Divide 2.4 by 0.6.

4 Divide — how many of the small fit in the big

How many 0.6s fit in 2.4? Scale both by 10: 24 ÷ 6 = 4. Notice dividing made it bigger.

d)Which of the two is closer to 1?

0.6 Compare distances — no arithmetic on the pair

0.6 is 0.4 away from 1. 2.4 is 1.4 away from 1. So 0.6 is closer.

For the grown-up. If they get stuck, work through the first one together, then hand it back. Reading the working aloud is worth more than marking it — feedback that explains is worth several times feedback that only says right or wrong, and the gap is wider in maths than in any other subject.

izzimath · Grade 5 · seed 0 · 5.NBT.B.7, 5.NBT.A.3

Why four questions is the whole sheet

A column of twenty subtractions trains the procedure. It cannot train deciding which procedure the question wants, because on a page of subtraction the answer to “what do I do here” is always the same. That decision is where most mistakes on mixed work come from.

So these four questions share one surface — The two numbers are 2.4 and 0.6. — and need four different methods. The answer key names the method each one wanted, which is the column to read together afterwards.

The format is Craig Barton's, published as a large open bank at ssddproblems.com. These sets are ours; the idea is his.