Introduction
Welcome to today's lesson on multiplication and division!
In the next few lessons you will study the patterns and the relationship between multiplication and division.
Click the "task" button to see what's next.
Task
Get into partners to complete the following tasks.
Task 1: Use counters to work out multiplication and division problems.
Find the answers to the following problems by rearranging counters.
4 x 7 =
7 x 4 =
28 ÷ 4 =
28 ÷ 7 =
What patterns do you notice? Discuss with your partner.
8 x 9 =
72 ÷ 8 =
9 x 8 =
72 ÷ 9 =
What patterns do you notice? Discuss with your partner.
11 ÷ 12 =
12 x 11 =
12 ÷ 11 =
11 x 12 =
What patterns do you notice?
Why do you think these patterns are happening even though some problems use multiplication and some use division? Discuss with your partner.
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Task 2: Rearrange numbers to correct the maths problem.
Use a scrap piece of paper to rearrange and record the correct maths problem. The ~ symbol is used to replace x or ÷. You must figure out which symbol is correct.
24 ~ 4 = 6
2 ~ 7 = 14
4 ~ 16 = 4
60 ~ 12 = 5
10 ~10 = 100
11 ~ 33 = 3
72 ~ 9 = 8
9 ~ 5 = 45
6 ~ 12 = 72
28 ~ 4 = 7
Did you find these problems difficult? Do you notice anything surprising about these problems? Discuss with your partner.
If you have completed all problems before the end of the lesson you can watch this video about multiplication and division.
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Task 3: Use animals to help you create your own division problems.
Count the number of arms and legs on each animal, then count the number of fingers and toes on the same animal. Use those numbers to create your own division problem.
1. Human: https://images.app.goo.gl/XXzinvQHzRLBTMBq8
2. Sloth: https://images.app.goo.gl/vygXNkZkZ8zvB8BKA
3. Chicken: https://images.app.goo.gl/jD8C4jo4osiu5onw9
4. Frog: https://images.app.goo.gl/3bFxHBKKM5ohwb2GA
5. T-Rex: https://images.app.goo.gl/vw98wc3u9y1zmt9Y8
Record your problems and answers on a piece of paper. Now rearrange the numbers in each problem to create a multiplication problem.
If you have completed task 3 before the end of the lesson, you may draw your own animal of your choice and create a division problem to go with it. Work independently without your partner. Make sure the animal is detailed with fingers and toes and coloured in.
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Task 4: Create your own city of numbers.
For this task you will use Word document. In this word document you will draw your own city made up of 6 different buildings in a line next to each other. To draw on Word you must click on insert > shapes and then select the lines you wish to use. It will be easiest to use straight lines or squares to draw buildings. You must include windows on your buildings. Each building should have a different amount of windows.
When you have completed your 6 buildings, use the number of windows on each building to create a multiplication problem. Use the windows on the first and second building for your first problem and insert a text box in between the two buildings to write your problem. Do the same between the rest of the buildings.
If you complete this task before the end of the lesson you can use the multiplication problems between each building to create division problems with the same numbers. Insert them between the buildings, above or below the multiplication problem.
Teacher Page
The desired learning outcomes of this lesson sequence is for students to gain a clear understanding of the relationship between multiplication and division. This topic is based on the Australian Curriculum year 4 content descriptor: Develop efficient mental and written strategies and use appropriate digital technology for multiplication and division with no remainder.
These activities are designed to achieve the desired learning outcomes by allowing the class to create and solve their own problems, rather than being lead by the teacher. The tasks are intended to be completed over 3 lessons of 45 minute duration. Task 1 and 2 should be completed in the first lesson, task 3 should be completed in the second lesson and task 4 in the third lesson. Tasks 3 and 4 incorporate both mathematics and art to create a more engaging interaction with multiplication and division.
These lessons are enhanced by the use of a technology based recourse. While it adds technology as another learning area to the lessons, it also creates a more efficient lesson what would otherwise take much longer to complete. It allows the students to follow written instructions and work at their own pace. It also allows you, as the teacher to use your time more appropriately to assist or guide students who need extra help.
For these lessons you will need to ensure that the class has access to enough counters for task 1 (if you don't have counters you can use an alternative like bottle caps). You will also need paper, writing utensils and coloured pencils.
By the end of the sequence the class will demonstrate their understanding of the topic by putting their knowledge into practice. The students' understanding will be assessed in task 4, where you may view their final product of their City of Numbers.
Here is an example of what a completed City of Numbers should look like: https://1drv.ms/w/s!AjmZNCGcoV0FgQRPOVFl6xgZmlzN