Guess, check and improve

Primary 3 More Word Problems study guide: the whole chapter, step by step

About this subtopic

The idea in brief. Keep the total count fixed while changing the two counts, then check their combined contribution. Each trial must keep the total number of items fixed. Check the total value as well. In the lesson. In Primary 2, you learned that 5 bags of 2 shells make 5 times 2, which is 10 shells. Today, we will try, check and improve, using a table. Try, check the total, then improve the try. Keep the number of bags the same every time.

Lesson video, with the working

Try and check

5 min 55 s

The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.

Watch on its own page

Today's question

Mei has 10 bags of shells. Each small bag has 2 shells. Each large bag has 4 shells. There are 26 shells altogether. How many large bags are there?

  1. Large bags = 10 − 5 = 5
  2. Small bags = 5
  3. Shells in small bags = 5 × 2 = 10
  4. Shells in large bags = 5 × 4 = 20
  5. Trial total = 10 + 20 = 30
  6. Small bags = 6
  7. Large bags = 10 − 6 = 4
  8. Shells in small bags = 6 × 2 = 12
  9. Shells in large bags = 4 × 4 = 16
  10. Trial total = 12 + 16 = 28
  11. Small bags = 7
  12. Large bags = 10 − 7 = 3
  13. Shells in small bags = 7 × 2 = 14
  14. Shells in large bags = 3 × 4 = 12
  15. Trial total = 14 + 12 = 26
  16. There are 3 large bags.

Ans: 3 large bags

Example 1 of 2

Siti has 9 bags of shells. Each small bag has 2 shells. Each large bag has 5 shells. There are 33 shells altogether. How many large bags are there?

  1. Small bags = 6
  2. Large bags = 9 − 6 = 3
  3. Shells in small bags = 6 × 2 = 12
  4. Shells in large bags = 3 × 5 = 15
  5. Trial total = 12 + 15 = 27
  6. Small bags = 5
  7. Large bags = 9 − 5 = 4
  8. Shells in small bags = 5 × 2 = 10
  9. Shells in large bags = 4 × 5 = 20
  10. Trial total = 10 + 20 = 30
  11. Small bags = 4
  12. Large bags = 9 − 4 = 5
  13. Shells in small bags = 4 × 2 = 8
  14. Shells in large bags = 5 × 5 = 25
  15. Trial total = 8 + 25 = 33
  16. There are 5 large bags.

Ans: 5 large bags

Example 2 of 2

Ravi has 12 bags of shells. Each small bag has 3 shells. Each large bag has 5 shells. There are 46 shells altogether. How many small bags are there?

  1. Small bags = 6
  2. Large bags = 12 − 6 = 6
  3. Shells in small bags = 6 × 3 = 18
  4. Shells in large bags = 6 × 5 = 30
  5. Trial total = 18 + 30 = 48
  6. Small bags = 7
  7. Large bags = 12 − 7 = 5
  8. Shells in small bags = 7 × 3 = 21
  9. Shells in large bags = 5 × 5 = 25
  10. Trial total = 21 + 25 = 46
  11. There are 7 small bags.

Ans: 7 small bags

How to solve it
  1. Keep the number of bags the same in every try. Mei has 10 bags altogether.
  2. Make a try, such as 5 small bags and 5 large bags, and work out the shells in each kind.
  3. Check the total against the one you need. 30 is too many, because we need 26.
  4. Improve the try. A large bag has more shells, so change 1 large bag into a small bag.
  5. Keep going until the total is right, then answer with the kind of bag the question asks for.

Try, check the total, then improve the try. Keep the number of bags the same every time.

Practice questions with worked solutions

Question 1 is free to try. The other 11 open in the free trial, each with its solution film.

Basic

1Free234

Intermediate

5678

Challenge

9101112

Print this subtopic · included with a plan

11 more questions, each with its solution film.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 12 · Basic · free to tryA workshop has 13 activity cards. They are either silver cards carrying 2…A workshop has 13 activity…

A workshop has 13 activity cards. They are either silver cards carrying 2 stars each or gold cards carrying 5 stars each. Their total is 41 stars. How many silver cards are there? Use a trial table, starting with 6 silver cards.

cards

Show the working and the answer

Video solution · 2 min 21 s

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Working

  1. silver cards | stars from silver cards | gold cards | stars from gold cards | Total stars | Check
  2. Trial: number of gold cards = 13 − 6 = 7
  3. Contribution from silver cards = 6 × 2 = 12
  4. Contribution from gold cards = 7 × 5 = 35
  5. Trial total = 12 + 35 = 47
  6. 6 | 12 | 7 | 35 | 47 | too high
  7. Trial: number of gold cards = 13 − 7 = 6
  8. Contribution from silver cards = 7 × 2 = 14
  9. Contribution from gold cards = 6 × 5 = 30
  10. Trial total = 14 + 30 = 44
  11. 7 | 14 | 6 | 30 | 44 | too high
  12. Remaining excess = 44 − 41 = 3
  13. Decrease for one replacement = 5 − 2 = 3
  14. Number of replacements = 3 ÷ 3 = 1
  15. Next number of silver cards = 7 + 1 = 8
  16. Trial: number of gold cards = 13 − 8 = 5
  17. Contribution from silver cards = 8 × 2 = 16
  18. Contribution from gold cards = 5 × 5 = 25
  19. Trial total = 16 + 25 = 41
  20. 8 | 16 | 5 | 25 | 41 | correct
  21. Number of silver cards = 13 − 5 = 8

Answer: 8 cards

For parents

How do you set up a table for P3 guess and check questions?

Guess and check is a problem-solving heuristic, and the MOE curriculum framework asks children to use heuristics on non-routine problems.

What your child learns here

Guess and check is a problem-solving heuristic, and the MOE curriculum framework asks children to use heuristics on non-routine problems. On this page your child uses it with two kinds of item, such as small and large bags, when both the number of items and the total are given. Each try is checked with Primary 3 multiplication and addition.

  • Set up a table with one row per try: the count of each kind, the amount from each kind, and the total.
  • Keep the total number of items the same in every row.
  • Compare each trial total with the target and decide which way to move the next try.
  • Use multiplication within the tables, and addition, to check each try.
  • Read off the kind the question asks for once the total matches.
Does the answer make sense?

The count of each kind must be less than the number of cards, packets, tokens or kits, and their stars, beads, points or rods must add exactly to the target. Your child can check both totals in the final row of the trial table before reporting the kind asked for.

How to practise these questions

The Basic questions practise making a sensible first guess and checking it against the total. The Intermediate questions add using a table to improve each guess in a steady direction. The Challenge questions bring larger numbers or an extra condition, so a smarter starting guess saves time. If guess and check is stuck, watch the solution film for that question and try again later from Revision.

Questions parents ask

Is guess and check a proper method or just guessing? It is a problem-solving heuristic, and the MOE curriculum framework names the use of heuristics as part of problem solving. The method is systematic: each try is recorded, checked against the total, and improved in a planned direction.

How many tries should my child need? There is no fixed number. A sensible first try, such as half of each kind, and a planned change after each row usually reaches the answer in a few rows. The lesson film on this page shows tables that get there in three rows.

How should my child set out a guess and check table? Use one column for each kind's count, one for each kind's amount, and one for the total, with a row for every try. Writing every try down, including the ones that do not fit, is part of the working and shows which way to adjust.