Today we work as a class to investigate the rectangular arrays for some given numbers. We record the appropriate equation with each array.

**Adaptation for ESOL students: **Write the lesson overview on the board and check that all students understand the key words for this section - an array, to record, an appropriate equation, a rectangle, a row, a column.

Give each child 12 cubes and ask them to form a rectangle. What size is the rectangle you have made? Discuss the description of rectangles using rows and columns. Use "scaffolding" techniques to coach your students into mathematical language.

**Adaptation for ESOL students:**

- Write 'rows' and 'columns' on the whiteboard and ask, pointing to a column "Which word can we use to describe this shape - row or column?"
- Ask students to write a definition of a 'row' and a 'column'.
- Students share their definition with a neighbour, and then some share with the class. Think - pair - share.
- In pairs, ESOL student with a native speaker, students describe their rectangles to their partner, using the words 'rows' and 'columns'. You may need to model the language needed here. This rectangle has 3 columns or four rows.

Have we found all the rectangles? How do you know? (Expect the children to check each of the numbers to 12 although some may realise that you only need to check as far as 6.)

As a class make recordings of each of the rectangles using squared paper. Attach these rectangles to an A3 page headed with a 12. Record the equation with each rectangle. Organise the rectangles from 1x12 to 12x1. (This will allow for more easy comparison with the factors of other numbers.)

Give each pair of children a number (1-11) and ask them to form the rectangles for their number. As they form the rectangles, first with cubes and then on squared paper, ask questions that focus on the factors of the number.

- How many rectangles have you found for your number?
- How do you know you have found them all?
- Why do some numbers have more rectangles than others?

Ask each pair to attach their rectangles to the "page" for their number. As a class share the number pages. Today we work as a class to investigate the rectangular arrays for some given numbers. We record the appropriate equation with each array.

**Adaptation for ESOL students:** Check that the students know the meanings of 'least'/ 'fewest'/ 'most'. Ask the students to work with another pair to answer the questions, and then discuss the answers in the class. Ask each student to write out the answers to the 'why' questions using 'because'.

- Which number has the least rectangles? (1) Why?
- Which number has the most rectangles? (12) Why?
- Which numbers have only 2 rectangles?
- Can a number have 3 rectangles?

Published on: 09 Jan 2018