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The Guides for Effective Instruction in Mathematics Revised

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B2.4 Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 10 000 and of decimal tenths, using appropriate tools and strategies, including algorithms.

Activity 1: Sums and Differences of Whole Numbers

It is important to introduce and develop a conceptual understanding of the basic facts in a problem-solving context. This will make the numbers more meaningful to students.

Here are various questions for addition and subtraction contexts. The numbers may vary depending on the students' progress.

  1. Joining Problem

    2. At the zoo I saw 20 monkeys, 2 elephants, 14 penguins and 9 bears. How many animals did I see?

  2. Separating Problem (subtraction)

    3. Amélie is so excited to see her cousin. There are only 17 days left before she arrives. How many weeks are left before she arrives?

  3. Separating Problem (subtraction)

    4. Maxime has 9 bran muffins. He eats 4 of them. How many do he have left?

  4. Joining (subtraction) problem

    5. Maxime wants to buy more muffins. He has $4. The muffins cost $9. How much money does he need to take out of his bank?

  5. Joining (subtraction) problem

    6. John must collect 500 recyclable bottles to win a computer game. He already has 138 bottles. How many bottles does he need?

  6. Comparing Problem (subtraction)

    7. I have 13 books in total. There are some on my desk and there are 5 in my backpack. How many books are on my desk?

  7. Comparing Problem (subtraction)

    8. A train has 34 cars. Eleven of them are carrying fruit. How many cars are carrying something other than fruit?

  8. Separating Problem (subtraction)

    9. Joanne had chalk. She gave 6 to Francine. Now she has 9 left. How many did she have at first?

  9. Separating Problem (subtraction)

    10. Marc-Andre has 43 stickers. After giving 27 to his friend Rosa, how many stickers does he have left?

  10. Comparing Problem (subtraction)

    11. Carla went to the orchard twice. The first time, she picked 53 apples. The second time, she picked 72 apples. How many more apples did she pick the second time?

  11. Joining Problem and Comparing Problem

    12. Dora has this amount of money:

    How much money does she need to buy a yo-yo that costs $ 1.55 ?

  12. Comparing Problem (subtraction)

    13. The red team has read 674 books and the yellow team has read 328. Find out how many books the yellow team must read to have read the same number of books as the red team.

  13. Joining Problem (addition) and Separating Problem (subtraction)

    14. Thomas found 123 fossils. He found 456 more the next day, but lost 98. How many more does he have?

Source: L'@telier - Ressources pédagogique en ligne (atelier.on.ca).

Activity 2: The Surprise Bag

Distribute to each pair of students a bag of base ten materials (that is, a few flats 10-20 rods, and 20-30 unit cubes) and 2 place-value mats as shown below.

Tens Ones . Tenths

Specify that for the activity, the rod represents one whole. The flat then represents a ten (10 rods) and the unit cube represents a tenth (0.1 of a rod). Explain to the students that they must :

  • take turns to pick a quantity of base ten material pieces from the bag with both hands;

  • place the pieces on the place value mat in the appropriate places;

  • make the possible groupings (for example, replace 10 small unit cubes by 1 rod or 10 rods by a flat);

  • calculate the sum or the difference of the two numbers.

Source: Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 156.

Activity 3: Problems to Solve

  • A weather station recorded the rainfall for the month of May. Here are the amounts in millimetres for the 5 days it rained that month: 1.2 mm, 0.8 mm, 2.1 mm, 8.9 mm and 4.7 mm. What is the total amount of rainfall for the month of May?

    • Mental Math Strategy

    1.2 and 0.8 give 2

    2.1 and 8.9 give 11

    2 and 11 give 13

    13 and 4.7 give 17.7

    Thus, 17.7 mm of rain fell in May.

  • A square playground has sides of 12.5 m.
    1. What is the perimeter of this playground?
    2. What is the perimeter of a playground whose sides are three times as long?

Student-Generated Algorithm

  1. \(\begin{array}{l}12.5\; + \;12.5\; = \;25\\25\; + \;25\; = \;50\end{array}\)
  2. \(12.5\; + \;12.5\; + \;12.5\; = \;25\; + \;12.5\; = \;37.5\)

Therefore, the perimeter of the playground with three times the length of the sides is 150 m.

Source: adapted from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).