Year+3+Numeracy

MATHEMATICS Year 3 || =Arrays in motion=

Information ||

Objectives
• To understand multiplication as repeated addition and as an array • To recognise that multiplication can be done in any order

Prior learning
To benefit from this lesson, children should: • be able to count in 2s, 3s, 5s and 10s.

Vocabulary
repeated addition, multiplication, multiplied by, division, array

Resources
• interactive whiteboard and/or data projector linked to a laptop • presentation software that allows for the display and modelling of arrays (in this Example, //Arrays PowerPoint file//) • counting stick //•// pupil dry wipe boards

ICT skills needed by teachers
To teach this lesson, teachers need to know how to: • load, display and show a presentation file.

Preparation for this lesson
Before the lesson, become familiar with the chosen arrays resource. Prepare the software on your own computer ready for display.

Lesson extract ||

Starter
Use the counting stick to support counting from zero in steps of 2, 3, 5 and 10, forwards and then backwards. Repeat each count from zero, but stop at various points to ask questions such as: Q We have counted up 7 steps of 2 to 14. What is 2 multiplied by 7? Q How many steps of 3 did we count up to get to 18? What is 18 divided by 3? Q How many steps of 5 did we count up to get to 15? What is 15 divided by 5? Q If we count on 3 more steps of 5, what will that give us? How many steps of 10 would we count up to get to the same number? Write the number 20 on the board. Q Was this number one of the numbers in our count when the step size was 2, 3, 5 or 10? Ask children to discuss this with a partner. Collect answers and have the class count aloud in steps of 2, 3, 5 and 10 to confirm the answer. Repeat with other numbers. Include a prime number that is not in any of the counts.

Main activity
L aunch the resource (in this Example, //Arrays PowerPoint file//) and choose ‘Slide show’ to begin the presentation. On each click of the mouse (or right-arrow key), a column of five coloured dots will appear. Count with the children as each of the columns appears. The presentation continues in this way until four columns of five dots are presented. Q How many dots are there altogether? How many columns? How many dots in each column? Ask the children to think of an addition number sentence to describe how many dots there are in the array of dots and write this on their whiteboards. Collect children’s answers. Agree that the number sentence is 5 + 5 + 5 + 5 = 20. Q Can you think of a number sentence that uses a different operation? Ask the children to show their number sentences and discuss the possible alternatives. Agree that it is 5 × 4 = 20. Click to reveal a repeated addition 5 + 5 + 5 + 5 and a multiplication 5 × 4. Ensure that the children see the second operation as meaning ‘five dots four times’. The presentation continues, and this time rows of four dots appear. Count with the children as the rows of dots appear. Continue counting until five rows of four dots are presented on the screen. Q How many dots are there altogether this time? How many rows? How many dots in each row? Ask the children to think of an addition number sentence to describe these dots and write it on their whiteboards. Collect their answers. Agree that the number sentence is 4 + 4 + 4 + 4 + 4 = 20. Q Can you think of a number sentence that uses a different operation? Agree that it is 4 × 5 = 20. Click to show a repeated addition 4 + 4 + 4 + 4 + 4 and again to show a multiplication 4 × 5. Ensure that the children see the second statement as meaning ‘four dots five times’. Q What can you tell me about these two arrays of dots? Encourage the children to identify what is the same about the two arrays and what is different. Draw out that one way to count them is to count how many dots there are in each row, and how many rows there are. Another way is to count how many dots there are in each column, and how many columns there are. Each time there is the same number of dots. Clicking again shows an equals sign between each of the pairs of statements and the sets of dots. Slide 2 begins by showing two multiplications: 6 × 3 and 3 × 6. Ask the children to choose one of these statements and with a partner draw a picture of the array they would expect to go with the statement. Ask the children to write down the addition number sentence to go with their picture. Collect the children’s pictures and number statements and discuss their reasons and ideas. Clicking again, the dots begin to drop on the screen in groups of six followed by the repeated addition 6 + 6 + 6. The second set of dots appears in groups of three followed by the repeated addition 3 + 3 + 3 + 3 + 3 + 3. Again, an equals sign appears between each of the statements and the sets of dots. Ask the children to work in pairs to draw a picture of an array they choose to represent each of the numbers 10, 12, 15 and 20. They should write two addition number sentences and two multiplication number sentences for each of their arrays. Collect and discuss the children’s pictures of arrays and their number sentences. Establish that for 12 and 20 there are arrays with different numbers of rows and columns. For these arrays the number statements are different. With the class, represent 20, working through the two arrays 2 by 10 and 4 by 5. Refer children to the counting they did in the starter to help them to identify the two possible arrays.

Plenary
Launch slide 3, showing the two arrays of 18 dots with two division statements. Q How can we divide 18 dots into equally sized groups? How many dots will be in each group? How many groups will there be? Draw 18 dots on the board. Discuss with the class how the dots might be arranged into equally sized groups. Refer them back to the counting they did earlier, and ask them to discuss with a partner the step size that gave a count with 18 in it. Collect responses and circle the dots in groups of the size suggested by the children. As you do so have the children count up in steps of that size. Slides 4 to 6 shows the 18 dots being divided into groups of 6 with a repeated addition statement building up underneath the array. Q How many groups of 6 have we made from the 18 dots? Agree that it is 3. Slide 7 completes the division statement 18 ÷ 6 = 3. Read this with the children as ‘18 divided into groups of 6 gives 3 groups’. Slides 8 to 14 repeat the sequence, this time dividing the 18 dots into groups of 3. Say that these division statements are another way to describe what we see in the picture of rows or columns of dots.

Notes ||

Links to the Framework for teaching mathematics
The lesson links to units on understanding multiplication and division.

Context of this lesson
This lesson could be used in Unit 9 of the autumn term from the sample medium-term plans.

Why use ICT?
The advantages of using ICT are as follows. • ICT allows teachers to project enlarged visual images for whole-class demonstration and discussion. • The interactivity of the software is motivating and stimulating.