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Level One > Number and Algebra

Achievement Objectives:

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.

Specific Learning Outcomes:
• draw representations to show a simple addition equations
• write an equation/number sentence to match their diagram
Description of mathematics:

In this unit students are introduced to different ways to represent addition. Using the representations students will be able to communicate their thinking. 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.

Required Resource Materials:
Animal strips Material Master 5-2 (available from Material Masters)
Tens Frame Material Masters 4-6 (available from Material Masters)
Copymaster of 0-10 number line
Key Vocabulary:

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.
2. Ask the students: how many blue counters are there?
3. 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 Stage 4-Advanced Counting of the Number Framework will be able to count on from the 5, i.e. 6, 7.

4. Using two different colours will help encourage students to count on. Draw another circle and place 5 blue counters in it.
5. Ask the students: how many blue counters are there?
6. Ask the students: Count with me as I add more counters. (Add 3 counters and count 6,7,8)
7. Ask the students: how many counters are there in the circle?
how many red counters did we put in?
8. Introduce the idea of recording what the diagram shows. Tell the students you are going to write the number sentence.
9. Ask the students: 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?

10. 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.
11. 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. Ask the students: 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:

Ask the students: how many dots are on the frame? (6)
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. In this unit we want to encourage students to use counting on strategies. So using a coloured pen draw 2 more dots and count with the students, 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 may 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. Ask the students: how many animals are on the strip? (6)
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. Ask the students: how many animals are on the strip? (7)
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.
2. Ask the students: if we count on 2, what number on the number line will we be at?
3. Count with students as you mark the jumps, 5, 6 and slide the counter along to the new place.

4. Discuss with the students the number sentence 4 and 2 makes 6 and write it below the number line.
5. Give the students a copy of a number line. Ask the students to show on the number line 6 and 3 makes ?
6. Encourage the students to count on as they mark the jumps with their counter and their pencil.
7. Ask the students to write the number sentence under the number line.
8. 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.

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## Partitions

This unit is about partitioning whole numbers. It focuses on partitioning numbers to “make a ten” or a decade when adding whole numbers, for example 8 + 6 can be solved as (8 + 2) + 4. The unit uses measurement as a context.

## The Number Partner

This unit uses one of the digital learning objects, the number partner, to support students as they investigate possible pairings for numbers from 10 to 30. It is suitable for students working with Advanced Counting and Early Additive strategies (Stage 4-5 of the Number Framework). It includes problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

## Up we go

In this unit we work on word problems about climbing up steps and riding in a lift. We learn about different types of problems that can be modelled on number lines. We practice mental calculations with sums to 10 and to 20.

## Make a Ten

This unit follows naturally from the Smart Doubling unit.
In this unit students are encouraged to further develop part/whole mental methods by using the strategy of "make a ten".

## Making ten

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of combinations to ten. The purpose is also to develop a recognition of the importance of knowing facts to ten and being able to generalise by seeing and applying these patterns with numbers to 100.

These teaching and learning activities support Student e-ako Place Value 1, pages 4 and 5. This unit of work complements learning activities found in Book 5, Teaching Addition, Subtraction and Place Value.

This is the third of a series of units developing place value concepts. This unit builds on the previous units of work: