3rd Grade Two-Step Word Problems and Patterns Worksheet Answer Key (PDF)

3rd grade two step word problems worksheet answers – Maths PDF

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This 3rd grade two step word problems worksheet answers covers two-step word problems and patterns (Common Core 3.OA.D.8, 3.OA.D.9), with a free PDF to print.

Key takeaway: This answer key helps Grade 3 teachers and parents check the two-step word problems worksheet.

Topic: Two-Step Word Problems and Patterns (3rd grade)
Content: Step-by-step answers to 24 worksheet problems
Standards: 3.OA.D.8, 3.OA.D.9
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps Grade 3 teachers and parents check the two-step word problems worksheet. First, it gives the answer to each problem. Then it shows the two steps or the equation that leads to the answer.

The notes cover groups and loose items, subtracting twice, sharing, writing and solving equations, the order of operations, estimating, and reasonable answers. Next, use the notes to talk about any missed problem. Checking the full page takes about 15 minutes, and scratch paper helps the child redo a step. Also, a pencil and scratch paper help children show each step.

Every solution shows the hidden first step, the second step, and the final equation with its letter. Use the key to check your work. If an answer is different, find the step where the numbers changed and try that step again.

Grade 3 · Common Core State Standards: 3.OA.D.8, 3.OA.D.9

3rd grade two step word problems worksheet answers: worksheet problems 1 to 10

1 – Groups, then add

First step: $4 \times 6 = 24$. Second step: $24 + 7 = 31$.

$4 \times 6 + 7 = p$, so p = 31 pencils.

2 – Groups, then subtract

$5 \times 7 = 35$ and $35 – 9 = 26$.

$5 \times 7 – 9 = r$, so r = 26 pumpkins.

3 – Add, then subtract

28 + 35 = 63 beads before using 19.

$28 + 35 = 63$, then $63 – 19 = 44$.

$28 + 35 – 19 = b$, so b = 44 beads.

4 – Subtract twice

$90 – 36 = 54$, then $54 – 27 = 27$.

$90 – 36 – 27 = t$, so t = 27 tickets.

5 – Share, then add

$24 \div 4 = 6$ stickers each, then $6 + 5 = 11$.

$24 \div 4 + 5 = s$, so s = 11 stickers.

6 – Write the equation

Books on the shelves: $3 \times 9 = 27$. Then add 4: $27 + 4 = 31$.

Equation: $3 \times 9 + 4 = b$. b = 31 books.

7 – Solve for the letter

$4 \times 8 = 32$, then $32 + 9 = 41$.

t = 41

8 – Divide, then add

$35 \div 5 = 7$, then $7 + 8 = 15$.

q = 15

9 – Multiply, then subtract

$6 \times 7 = 42$, then $42 – 15 = 27$.

w = 27

10 – Parentheses first

Do the parentheses first: $6 + 4 = 10$. Then $10 \times 3 = 30$.

z = 30

Worksheet problems 11 and up

11 – Estimate a sum

38 rounds to 40, 42 rounds to 40, and 19 rounds to 20.

Estimate: $40 + 40 + 20 = 100$. Exact: $38 + 42 = 80$ and $80 + 19 = 99$.

Estimate 100; exact sum 99.

12 – Is it reasonable?

Estimate: 48 rounds to 50 and 37 rounds to 40, so $50 + 40 = 90$.

75 is far from 90, so it is not reasonable. The exact sum is $48 + 37 = 85$.

13 – Estimate a product

19 rounds to 20, so $4 \times 20 = 80$.

Exact: $4 \times 19 = 76$. The estimate is a little high because 19 is less than 20.

Estimate 80; exact 76.

14 – Skip-counting pattern

Each number is 8 more than the one before: $20 – 12 = 8$.

The completed pattern.

So, rule: add 8. Next numbers: 44 and 52.

15 – Pattern in a chart

The ones digits are 4, 8, 2, 6, 0, and then the same digits repeat. So, every shaded number is even.

Counting by 4s adds an even number each time, and even + even = even.

16 – Even or odd sums

$7 + 9 = 16$, $13 + 11 = 24$, $21 + 5 = 26$.

All three sums are even. So, the sum of two odd numbers is always even.

17 – Multiples of 6

6, 12, 18, 24, 30, 36.

Since $6 = 2 \times 3$, every multiple of 6 is a number of pairs. So, a number made of pairs is even.

Worksheet problem 18 and after

18 – Savings pattern

The totals go up by 4, so week 5 is $26 + 4 = 30$, or $30.

After 8 weeks he added $8 \times 4 = 32$ dollars. Then $10 + 32 = 42$.

$10 + 8 \times 4 = t$, so t = $42.

19 – Farm stand

$7 \times 9 = 63$, then $63 – 26 = 37$.

$7 \times 9 – 26 = p$, so p = 37 peaches.

20 – Bake sale

$4 \times 12 = 48$ cookies, and $48 \div 6 = 8$ bags.

Then $8 \times 3 = 24$.

So, he earns d = $24.

21 – Road trip

The missing part is 87 miles.

$145 + 168 = 313$ miles so far.

$400 – 313 = 87$.

$400 – 145 – 168 = m$, so m = 87 miles.

22 – Team practice

$36 \div 4 = 9$, then $9 + 2 = 11$.

$36 \div 4 + 2 = n$, so n = 11 players.

23 – Unknown at the start

Work backward. Undo the last step: $30 – 5 = 25$. Undo the first step: $25 + 8 = 33$.

Check: $33 – 8 + 5 = 30$. n = 33 stickers.

24 – Check with an estimate

Estimate: $3 \times 20 + 8 = 68$.

Exact: $3 \times 19 = 57$ and $57 + 8 = 65$.

Maya spent $65, not $75, so Maya is not correct.

Key facts behind this 3rd grade two step word problems worksheet answers

Key facts

A two-step problem has a hidden question that is solved first.
Next, a letter such as m stands for the unknown number in an equation.
Rounding to the nearest 10 gives a quick estimate to check an answer.
Then, an arithmetic pattern follows a rule such as add 7 each time.
Odd + odd = even, even + even = even, even + odd = odd.

Common mistakes with this 3rd grade two step word problems worksheet answers

Marking only the final number hides the first step. Check that the child wrote or drew the hidden question first.
In problem 10, (6 + 4) times 3 equals 30. A child who writes 22 multiplied 4 times 3 first and ignored the parentheses.
In problem 12, Liam says 48 plus 37 equals 75. The estimate 50 plus 40 is 90, so 75 is not reasonable. The exact sum is 85.

How to use these solutions

First, ask the child to explain the hidden question in a story. Then check that the second step uses the first answer.
Also, ask the child to check one answer with an estimate. This habit catches many errors. As a result, small mistakes are easier to catch.
Sort errors into the first step, the second step, parentheses, and estimates. Then practice the type with the most misses.

Download the 3rd grade two step word problems worksheet answers as a PDF with the button below and keep it with your notes.

3rd grade two step word problems worksheet answers: frequently asked questions

What is the answer to 6 times 7 minus 15?

The answer is 27. Multiply first: 6 times 7 is 42. Then subtract 15 to get 27. Problem 9 asks for this, and the letter w stands for 27. Then check the result once more before moving on.

How should an estimate be scored?

Accept any estimate made by rounding each number to the nearest ten and then adding or multiplying. The exact answer should be close. For 38 plus 42 plus another number, the rounded numbers show the estimate.

What if a child writes one equation for both steps?

Accept it if the equation matches the story and the answer is correct. For example, 4 times 8 plus 9 equals t is a valid single equation. Ask the child to explain each part. In other words, slow and careful work pays off here.

All Grade 3 chapters: Grade 3 math.

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