Growth Point 4

Multiplication and Division Growth Points activities

The tasks listed on the following pages are rich tasks from various sources that may be used with multi-level groups or students who are working at a particular level.

4. Abstracting multiplication and division (no objects perceived)

Solves multiplication and division problems where objects are not all modelled or perceived.

Colour to win

Materials: One grid sheet per student, two dice per pair, coloured pencils.

Activity: This activity will introduce the idea of commutativity to students. Each student takes turns to roll the two dice, and they then colour a regular shape according to the numbers on the dice. For instance, if a student rolls 3 and 5, they can shade a 5 × 3 rectangle or a 3 × 5 rectangle. Play then passes to the other student. Students aim to use the regular shapes to fill their grid sheet. If the student is unable to colour a regular shape, play passes back to the other student. Play continues until one student completes a grid sheet or time limit has expired.

Related key ideas: Equal groups, composite units, properties of multiplication.

Variation: Repeat the activity where both options are coloured in. What is the same about these representations? What is different?

Connect three in the grid

Materials: One game board per student, two sets of cards per pair, counters

Activity: Each student has a game board and some counters. Shuffle all cards and place face-down in a pile. Students take turns to turn up a card, and cover the answer to this number sentence with a counter on their board.

The first student to cover three squares in a row in any direction is the winner.

Related key ideas: properties of multiplication.

Fill in the blanks

Materials: One worksheet per student.

Activity: Students use the × or ÷ and the = symbol to make the statements true.

Related key ideas: properties of multiplication, properties of division.

Coin toss

Materials: Cards numbered 1 to 9, one coin, calculator.

Activity: One student draws two number cards then tosses the coin. If it lands as tails, the student does a division question, and if it lands as heads, they do a multiplication question. The students must use the numbers drawn to make an appropriate algorithm number sentence. For instance, a student who draws 6 and 8 and tosses heads could make either 6 × 8 = 48 or 8 × 6 = 48 as their number sentence. If they toss tails, their number sentence could be either 48 ÷ 6 = 8 or 48 ÷ 8 = 6.

Partner checks with the calculator and the student scores one point. Play then passes to the other student. The first student to score ten points is the winner.

Related key ideas: Properties of multiplication, properties of division.

How much did they each get?

Materials: Pencil and paper or whiteboards.

Activity: Ask students to close their eyes in order to visualise the problem you are about to pose, ‘Imagine you bought 12 toy cars to school. You decide to share your cars with some friends. How many friends do you want to share them with? How many does each friend get?’ Now ask students to open their eyes and draw the problem. Prompt students to come up with more than one solution as the group of friends can change. You may repeat this activity using a different quantity.

Related key ideas: Equal groups.

Fact trees

Materials: One ‘tree’ per number.

Activity: Make a fact tree for significant numbers that you may have been using in your maths work.

For example, for a fact tree for 28, write the number 28 in large numerals on the trunk. On each of the branches write a different number sentence that relates to 28, such as 4 × 7 = 28, 14 × 2 = 28, or 28 × 1 = 28, and their reverse sentences), 28 ÷ 7 = 4, 28 ÷ 4 = 7, 28 ÷ 14 = 2.

Place these trees around the classroom so students can refer to them. Create fact trees for other numbers such as 12, 16, 18, 20, 24, 30, 36, 40.

Related key ideas: properties of multiplication, properties of division.

Modelling multiplication again

Materials: Pencil and paper, grid paper, whiteboards/interactive device.

Activity: This activity will reinforce the idea of commutativity with students. Use a grid (similar to that in ‘Colour to win’, Appendix 69) on the board/iPad to model a shape that represents 3 × 4. Then ask a student to model 4 × 3 on a grid sheet. Discuss with the class the similarities and differences between these two shapes (e.g. both cover a total of 12, both are rectangles, the different numbers of columns and rows). Model the same process again with different values (e.g. 5 × 2 and 2 × 5). Give Unifix cubes to pairs of students and ask them to explore other combinations, and then to write them on paper. Follow up with a share time of the student’s findings.

Related key ideas: Properties of multiplication.

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