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Level Three > Number and Algebra

# Goesintas

Achievement Objectives:

Specific Learning Outcomes:

Solve division problems by using multiplication facts.

Solve division problems by using multiplication facts.

Description of mathematics:

Number Framework Stages 6 and 7

Required Resource Materials:
The Happy Hundred (Materials Master 6-5)
Beans, unifix cubes or counters.
Activity:

#### Using Equipment

Expose a row of six faces on the Happy Hundred array using two masking cards. Pose the problem, Joneen needs to get forty-eight doughnuts to feed all the players in her chess club. Doughnuts come in packets of six. How many packets should she get?

Record the problem using the equation, ? × 6 = 48.

Invite students to predict the answer using whatever mental strategies they have available, such as, 5 × 6 = 30 so that leaves 18, 6 + 6 + 6 = 18, 5 + 3 = 8.

Their strategies can be verified using the array, for example, by uncovering five rows of six to show thirty, then successively revealing the other three rows of six. Pose corresponding problems that involve sharing sets into subsets, Geeta has 48 stickers to share out between six people. How many stickers will each person get?

Record the problem using the equation 48 ÷ 6 = ?

Ask the students to attempt the problem mentally at first though fold back to using the materials if necessary. Discuss any strategies the students use. In responding to a dealing strategy focus on how the results of the dealing could have been anticipated. Use the Happy Hundred sheet to link the random arrangement of counters to the ordered array that students have used for multiplication.

Each person is given one sticker, how many stickers is that? (six);

Each person is given two stickers, how many stickers is that? (12);

.

Ask how many more sixes can be dealt out with the remaining counters.
The students may say that another four stickers can be given to each person as the
dealing is halfway through and there are 24 stickers left.
Ask the students to refl ect on the relationship between the two problems you have
set. The key idea is that both “sets of” and “sharing” division problems can be
solved as multiplication problems where one factor is unknown.
For example, 48 ÷ 6 = □ can be solved as 6 x □ = 48 or □ x 6 = 48.
Give the students several examples of sharing problems, like:
35 ÷ 5 = □ (as 5 x □ = 35 or □ x 5 = 35)
28 ÷ 4 = □ (as 4 x □ = 28 or □ x 4 = 28)
27 ÷ 3 = □ (as 3 x □ = 27 or □ x 3 = 27)
42 ÷ 6 = □ (as 6 x □ = 42 or □ x 6 = 42)
Use the Happy Hundreds array and counters simultaneously so that the students
can see how the dealing operation is mapped by successively revealing rows of faces
on the array.
Record the problems as both division and multiplication equations

#### Using Imaging

Role Playing: Henry (student’s name) is working out how to share thirty-six lollies   equally among his nine friends. How many lollies should he give each friend? Ask the students how the problem could be recorded as an equation,  36 ÷ 9 = ?= 9 or 9 × ? = 36.

Ask the students to image what Henry is doing as he shares out the lollies and what  that would look like on the Happy Hundred array. Invite them to provide easy ways  for Henry to anticipate the answer, like, “Two nines as eighteen so four nines must be  thirty-six.”

Where necessary fold back to using the materials to illustrate students’ explanations  or where confusion exists.

Pose similar examples in the context of story problems about sharing objects. Ask  students to describe the actions of a person solving the problems with materials.

Record the results as equations.

45 ÷ 5 = ? (as 5 × ? = 45) 36 ÷ 4 = ? (as 4 × ? = 36)

24 ÷ 3 =  ? (as 3 × ? = 24) 49 ÷ 7 = ? (as 7 × ? = 49)

#### Using Number Properties

60 ÷ 5 = □ (as □ x 5 = 60 or 5 x  = 60)
44 ÷ 4 = □ (as □ x 4 = 44 or 4 x  = 44)
42 ÷ 3 = □ (as □ x 3 = 42 or 3 x  = 42)
54 ÷ 6 = □ (as □ x 6 = 54 or 6 x  = 54)
7 √ 21 (as □ x 7 = 21 or 7 x □ = 21)
6 √36 (as □ x 6 = 36 or 6 x □ = 36)
8 √24 (as □ x 8 = 24 or 8 x □ = 24)
9 √54 (as □ x 9 = 54 or 9 x □ = 54)

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