Division

Learning Focus/Learning Objectives

Counting Strategies.

(See Mathematics Developmental Continuum Division Progression Points)

Vocabulary:

Adding, Addition, Counting on, counting up, 100’s chart, open number line, more, less, same, total, sum,

Subtraction, minus, counting back, counting backwards, difference.

Multiplication, repeated addition, skip counting, array, columns, rows.

Sharing, division, equal groups, each, whole, fairly.

 

Warm Up Game

Whole Class Introduction

Student Activity

Share/Reflection

 

5 mins

10 mins

25 - 35

 

Monday

Skip Counting.

Around the World. Discuss counting by 2’s. (2,4,6,8,0)

Play  counting by 2’s and see how far you can get in 4 minutes. Provide token to each student who says a number ending with a zero. 3 tokens for two zeros.

On the weekend I bought a bag of lollies. There were 18 lollies. How could I share them with my friends? (Do not discuss solutions)

Students show all possible solutions. Provide 18 counters per pair of students. P/N/W

Discuss solutions.

Put into a table.

How come when you share with more people each person gets less lollies?

Tuesday

Skip Counting.

Around the World. Discuss counting by 3’s. (3,6,9,2,5,8,1,4,7,0)

Play  counting by 3’s  and see how far you can get in 4 minutes. Provide token to each student who says a number ending with a zero. 3 tokens for two zeros.

I bought 24 fish to put into my fish bowls. I want the same number of fish in each bowl. How many fish do I put in each fish bowl.

Students show all possible solutions. Provide 24counters (different from yesterdays) per pair of students. P/N/W

Discuss strategies.

Compare # sentences.

Make explicit the link s between division, multiplication, repeated addition, repeated subtraction.

( eg.,123=4,   4x3=12,   4+4+4=12, 12-4-4-4=0 )

Wednesday

Skip Counting.

Around the World. Discuss counting by 4’s. (4,8,2,6,0)

Play  counting by 4’s  and see how far you can get in 4 minutes. Provide token to each student who says a number ending with a zero. 3 tokens for two zeros.

At my party we had ½ an hour to play as many games as we liked. Each game was played for the same amount of time. How long did we play each game? Discuss what games we might play.

Students show all possible solutions. Provide 30counters (different from yesterdays) per pair of students. P/N/W

Discuss strategies.

Compare # sentences.

Make explicit the link s between division, multiplication, repeated addition, repeated subtraction.

( eg.,123=4,   4x3=12,   4+4+4=12, 12-4-4-4=0 )

Thursday

Skip Counting.

Around the World. Discuss counting by 5’s. (5,0)

Play  counting by 5’s  and see how far you can get in 4 minutes. Provide token to each student who says a number with a 50 in it. 3 tokens hundreds.

We baked some cookies and decided to share them. How many cookies did each person get? Use Play Doh or similar to make cookies.

Students show all possible solutions. Provide counters. P/N/W

Discuss strategies.

Compare # sentences.

Make explicit the link s between division, multiplication, repeated addition, repeated subtraction.

( eg.,123=4,   4x3=12,   4+4+4=12, 12-4-4-4=0 )

Friday

Greedy Pig

The zoo keeper wanted the same number of animals in each enclosure. Each type of animal stood in an array.  How many animals did she put into each enclosure and how many animals were there?

Students draw solution and write matching number sentences.  P/N/W

Discuss solutions.

Discuss division words and make Sharing Word Wall.

 

Division - Progression Points

Dimension

Level

Progression Point

 

Number

1.25

  • Drawing of diagrams to show sharing of up to 20 items

1.75

  • Identification of half of a set of objects, including recognition of the need for 1/2 when sharing an odd number of objects

2.0 Standard

… Students describe simple fractions such as one half, one third and one quarter in terms of equal sized parts of a whole object, such as a quarter of a pizza, and subsets such as half of a set of 20 coloured pencils.

They describe and calculate simple multiplication as repeated addition, such as 3 × 5 = 5 + 5 + 5; and division as sharing, such as 8 shared between 4.

2.25

  • Use of written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition) and ‘how many?’ (quotition) processes

2.75

  • Use of fact families (5 × 7 = 35, 35 ÷ 7 = 5) to solve division problems

3.0 Standard

… Students devise and use written methods for: division by a single-digit divisor (based on inverse relations in multiplication tables).

3.75

  • Use of inverse relationship between multiplication and division to validate calculations

Working Mathematically

2.75

  • Selection of multiplication and division as more efficient processes than repeated addition and subtraction

Structure

3.0

… Students recognise that the sharing of a collection into equal-sized parts (division) frequently leaves a remainder.

 

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