Purpose

In this unit students explore different ways to communicate and explain adding numbers within ten. The representations included are number lines, set diagrams, animal strips and tens frames.

Achievement Objectives
NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
NA1-4: Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
Specific Learning Outcomes
• Draw representations to show simple addition equations.
• Write an equation/number sentence to match their representation.
Description of Mathematics

In this unit students are introduced to different ways to represent addition. Students will be able to communicate their thinking using the representations. Teachers may choose to spend more time on some representations depending on students’ familiarity with them. The unit is designed to help students transition from Counting All to Advanced Counting, using a counting on strategy.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. The difficulty of tasks can be varied in many ways including:

• adjusting the size of numbers used as appropriate
• encouraging students to work collaboratively.

The contexts for this unit are strictly mathematical but the materials used can be adapted. Physical items that have significance to your students might be better used than standard mathematical equipment. For example, if you have a big set of shells for environmental studies you might use those shells as the materials for session 1.

Required Resource Materials
Activity

#### Session 1

In this session students are introduced to using a diagram or picture to communicate an addition equation.

1. Draw a circle and place 5 blue counters in the circle.
How many blue counters are there?
2. Place 2 red counters in the circle and ask:
How many counters are in the circle now?

Students at a Counting All stage of the Number Framework will count from one, i.e. 1, 2, 3, 4, 5, 6, 7.
Students at an Advanced Counting of the Number Framework will be able to count on from the five i.e. 5... 6, 7.
Using two different colours will help encourage students to count on.

3. Draw another circle and place 5 blue counters in it.
How many blue counters are there?
Count with me as I add more counters.
4. Add 3 counters and count as each counter is added "6","7","8".
How many counters are there in the circle now?
How many red counters did we put in?
5. Introduce the idea of recording what the diagram shows. Tell the students you are going to write the number sentence.
How many blue counters are there? (Write 5 in blue.)
And how many red counters are there? (Write 3 in red)
5 and 3 makes how many counters?

6.
7. Work with the students to draw set diagrams. Use coloured pens to draw circles instead of using counters (or use coloured round stickers). Use the coloured pens to write the number sentence beside the set diagram. Number sentences can focus on facts to five or facts to ten depending on the students’ knowledge.
8. Students can work in pairs or as individuals to practise using the set diagram.

#### Session 2

In this session students are introduced to tens frames as way to represent addition equations.

1. Show the students the tens frames.
How many dots are on the frame?
2. Students should be able to recognise the patterns and answer instantly, rather than counting each dot.
3. Show the students a tens frame. For example:

How many dots are on the frame?
How many dots will there be if I add another 2 dots?

Students may be able to image 2 more dots and then count all the dots, or they may need you draw the 2 dots before they can count all the dots.

4. To encourage students to use counting on strategies use a coloured pen to draw 2 more dots and count with the students as each dot is added "7", "8".
5. Write beside the tens frame the number sentence 6 and 2 makes 8. Again using coloured pens to match the coloured dots to help students connect the representation with the number sentence.
6. Make copies of the tens frames and ask pairs or individual students to complete addition equations. For example, add 3 dots. Encourage them to count on as they add the dots. Students then write the number sentence.
7. Number sentences can focus on facts to five or facts to ten depending on the students’ knowledge.

#### Session 3

In this session students are introduced to animal strips as a way to communicate addition equations.

1. Show the students the animal strips.
How many animals are on the strip?
2. Students should be able to recognise the patterns and answer instantly, rather than counting each animal. Show the students that the dotted line after the 5th animal can help them recognise the number.
3. Show the students an animal strip.
How many animals are on the strip?
4. Show the students another animal strip and ask the students:
How many animals are there altogether?
5. Encourage the students to count on. i.e. "8", "9".
6. Write under the animal strip the number sentence "7 and 2 makes 9”.
7. Make copies of the animal strips and ask pairs or individual students to make their own addition equations. Encourage them to count on as they add the animals. Then ask the students to write the number sentence underneath.
8. Give students animal strips appropriate for their knowledge stage, for example facts to 5, facts with 5, doubles, or facts to 10.

#### Session 4

In this session students are introduced to the number line as a way to communicate addition equations.

1. Draw a number line and mark a number by putting a coloured counter over the number 4.
If we count on 2, what number on the number line will we be at?
2. Count with students as you make the jumps, "5", "6" and slide the counter along to the new place.
3. Discuss with the students the number sentence 4 and 2 makes 6 and write it below the number line.
4. Give the students a copy of a number line. Ask the students to show on the number line 6 and 3 makes ?
5. Encourage the students to count on as they mark the jumps with their counter and their pencil.
6. Ask the students to write the number sentence under the number line.
7. Give the students copies of the number line and ask them to show addition equations.

#### Session 5

In this session students choose two or three addition facts and show each of them using the 4 different representations covered in this unit.

Attachments