Solve Two-Step Multi-Operation Problems - 3rd Grade Math

1. What is $n$ in the equation $n - 9 = 20$?

   $n = 29$. Add $9$ to both sides: $n = 20 + 9 = 29$.

2. Identify the equation: A pack has 8 markers, you buy $p$ packs, then give away 6 markers.

   $8p - 6$. Multiply packs by 8 markers each, then subtract the 6 given away.

3. What equation matches: "A book costs $b$ dollars; you buy $3$ books and then pay $5$ dollars shipping; total is $26$"?

   $3b + 5 = 26$. Cost of books plus shipping equals total.

4. What does the letter $n$ represent in an equation like $n + 7 = 15$?

   The unknown number. Letters stand for values we need to find.

5. What is $m$ in $m = 6 \times 4 - 5$?

   $19$. $6 × 4 = 24$, then $24 - 5 = 19$.

6. What is a quick estimate of $196 - 83$ using rounding to the nearest ten?

   $200 - 80 = 120$. Round 196 to 200 and 83 to 80 for easier mental math.

7. What is a reasonable estimate for $48 + 19$ using rounding to the nearest ten?

   $50 + 20 = 70$. Round $48$ to $50$ and $19$ to $20$.

8. What operation order should you follow in $3 + 4 \times 2$?

   Multiply, then add. Follow order of operations: multiplication before addition.

9. Which equation matches: "$18$ cookies shared by $3$ friends, then each friend gets $2$ more; cookies per friend is $c$"?

   $c = 18 \div 3 + 2$. Each friend's share plus extra cookies.

10. What is $m$ if $m = 5 \times 4 - 3$?

    $m = 17$. Calculate: $5 \times 4 = 20$, then $20 - 3 = 17$.

11. Identify the equation: $t$ stickers are shared equally by 4 friends, then each gets 2 more.

    $\frac{t}{4} + 2$. Divide total stickers by 4 friends, then add 2 more per friend.

12. Identify the equation: 5 bags with $b$ apples each, then 3 more apples are added.

    $5b + 3$. Multiply bags by apples per bag, then add the extra apples.

13. What is a reasonable estimate for $94 \div 3$ using compatible numbers?

    $90 \div 3 = 30$. Use $90$ instead of $94$ for easier division.

14. What operation should you do first in $8 + 3 \times 4$?

    Multiply: $3 \times 4$ first. Order of operations: multiplication before addition.

15. Which equation matches: $18$ pencils, buy $12$ more, then put them into $6$ equal groups. Pencils per group is $g$.

    $g = \frac{18 + 12}{6}$. Add pencils first, then divide by groups.

16. Which is a reasonable estimate for $49 + 28$ using rounding to the nearest $10$?

    $80$. $49 ≈ 50$ and $28 ≈ 30$, so $50 + 30 = 80$.

17. Identify the best reasonableness check for $6 \times 9 - 5 = 49$ using mental math.

    $6 \times 10 - 5 \approx 55$, so $49$ is reasonable. Estimate using $6 × 10 = 60$, then subtract $5$.

18. What is the unknown $x$ in $x - 9 = 4 \times 3$?

    $21$. $4 × 3 = 12$, then $12 + 9 = 21$.

19. Which equation matches: Start with $50$, spend $6$ dollars each day for $5$ days. Money left is $d$.

    $d = 50 - 6 \times 5$. Subtract total spent ($6 \times 5$) from starting amount.

20. What is the value of $c$ if $c = \frac{24}{6} + 2$?

    $c = 6$. Calculate: $\frac{24}{6} = 4$, then $4 + 2 = 6$.

21. Find $m$: A class has $5$ tables with $4$ students each, then $3$ students leave. Total students is $m$.

    $m = 5 \times 4 - 3$. Total students minus those who left.

22. Assess reasonableness: If $7 \times 8 = 56$, is $7 \times 8 = 65$ reasonable?

    No; $65$ is too large because the exact product is $56$. Compare to the exact answer to check reasonableness.

23. What is a quick estimate of $48 + 27$ using rounding to the nearest ten?

    $50 + 30 = 80$. Round 48 to 50 and 27 to 30 for easier mental math.

24. What is a reasonable estimate for $6 \times 19$ using rounding to the nearest ten?

    $6 \times 20 = 120$. Round $19$ to $20$ for easier multiplication.

25. What is $b$ in $3b + 5 = 26$?

    $7$. $26 - 5 = 21$, then $21 ÷ 3 = 7$.

26. What is $t$ if $t = 4 \times 9 + 10$?

    $t = 46$. Calculate: $4 \times 9 = 36$, then $36 + 10 = 46$.

27. Which is a reasonable estimate for $198 \div 4$ using rounding to make division easier?

    $200 \div 4 = 50$. Round $198$ to $200$ for easier division.

28. What is $g$ in $g = 20 \div 4 + 3$?

    $8$. $20 ÷ 4 = 5$, then $5 + 3 = 8$.

29. What is the unknown $p$ in $p \div 6 + 4 = 9$?

    $30$. $9 - 4 = 5$, then $5 × 6 = 30$.

30. Which equation matches: $24$ cookies shared equally into $6$ bags, then $2$ more cookies added to each bag. Cookies per bag is $c$.

    $c = \frac{24}{6} + 2$. Divide total by bags, then add extra per bag.

31. What equation matches: "Start with $20$, split into $4$ equal groups, then add $3$; result is $g$"?

    $g = 20 \div 4 + 3$. Divide first, then add to the result.

32. What is a quick estimate of $19 \times 6$ using rounding to a friendly number?

    $20 \times 6 = 120$. Round 19 to 20 for easier multiplication.

33. Which is the more reasonable answer for $198 \div 3$: $66$ or $600$?

    $66$. $198 \div 3$ is about $200 \div 3 \approx 67$, so 66 is reasonable.

34. What is the value of $y$ in $y = 5 \times 6 + 4$?

    $y = 34$. Calculate: $5 \times 6 = 30$, then $30 + 4 = 34$.

35. What is $g$ if $g = \frac{18 + 12}{6}$?

    $g = 5$. Calculate: $18 + 12 = 30$, then $30 \div 6 = 5$.

36. What is $a$ in $a = 5 \times 3 - 4$?

    $11$. $15 - 4 = 11$ apples remain.

37. What is $c$ in $c = 18 \div 3 + 2$?

    $8$. $18 ÷ 3 = 6$, then $6 + 2 = 8$.

38. Identify the equation: You have $m$ cookies, eat 5, then share the rest equally among 3 friends.

    $\frac{m - 5}{3}$. Subtract eaten cookies first, then divide remainder by 3 friends.

39. Identify the correct equation for: "$6$ boxes hold $4$ markers each; $5$ markers are lost; markers left is $m$."

    $m = 6 \times 4 - 5$. Total markers minus lost equals remaining.

40. What is a quick estimate of $143 \div 7$ using a compatible number?

    $140 \div 7 = 20$. Use 140 instead of 143 since it divides evenly by 7.

41. What equation matches: "$5$ bags with $3$ apples each, then eat $4$ apples; apples left is $a$"?

    $a = 5 \times 3 - 4$. Total apples minus eaten equals remaining.

42. What is the unknown $t$ in $2 \times t - 6 = 10$?

    $8$. $10 + 6 = 16$, then $16 ÷ 2 = 8$.

43. Identify the correct equation: $6$ bags with $4$ apples each, then eat $5$ apples. Total left is $a$.

    $a = 6 \times 4 - 5$. Total apples minus eaten: $6 \times 4 - 5$.

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