One array, four questions

Same surface, different depth · 3rd grade · Multiplication and division

Ink Designed Plain black & white All SSDD sheets

One array, four questions Grade 3 · Multiplication and division

Name
Date

Read this first

All four are about this one rectangle. Four different jobs.

All four questions are about this

A rectangle is made of squares: 4 rows with 6 squares in each row.

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

a)How many squares are there?

b)How far is it all the way round the outside, in square-side lengths?

c)Share all the squares equally into 3 groups. How many in each group?

d)Half of the squares are shaded. How many are shaded?

Scratch space — work it out here

How did it go? Tick one for every question you got right.

izzimath · Grade 3 · seed 0 · 3.OA.A.3, 3.MD.D.8, 3.OA.A.2, 3.NF.A.1
Same surface, four different methods. The key names the method each one needed.

One array, four questions Grade 3 · Multiplication and division

Name
Date

All four questions are about this

A rectangle is made of squares: 4 rows with 6 squares in each row.

1Four different questionsEach answer with the method it needed.

a)How many squares are there?

24 Multiply — rows times columns

4 rows of 6 is 4 × 6 = 24.

b)How far is it all the way round the outside, in square-side lengths?

20 Perimeter — add the edges

The long sides are 6 each and the short sides are 4 each: 6 + 6 + 4 + 4 = 20. Around the edge means add, not multiply.

c)Share all the squares equally into 3 groups. How many in each group?

8 Divide

24 shared into 3 groups is 24 ÷ 3 = 8. You need the answer to the first question before you can do this one.

d)Half of the squares are shaded. How many are shaded?

12 Fraction of a quantity

Half of 24 is 12. This one is a fraction of the total, not a count of rows.

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 3 · seed 0 · 3.OA.A.3, 3.MD.D.8, 3.OA.A.2, 3.NF.A.1

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 — A rectangle is made of squares: 4 rows with 6 squares in each row. — 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.