Te Kete Ipurangi
Communities
Schools

### Te Kete Ipurangi user options:

Level One > Number and Algebra

# The Number Partner

Purpose:

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.

Achievement Objectives:

Specific Learning Outcomes:

identify number pairs that sum to numbers from 10 to 30

use number pairs to solve addition and subtraction problems

Description of mathematics:

The strategy section of the New Zealand Number Framework consists of a sequence of global stages that students use to solve mental number problems. On this framework students working at different strategy stages use characteristic ways to solve problems. This unit of work and the associated learning object are useful for students in transition between Stages 4 and 5  of the Number Framework, moving from Advanced Counting to Early Additive. This transition involves students moving from starting the count from the highest number and then "counting on" to find the total number to beginning of part whole thinking. For example, when adding 5 and 3 students working at stage 4 start counting at 5 and add the extra three, (5...6,7,8) to get the answer and students at stage 5 will perhaps see double 3 and 2 more. The Number Framework also includes a knowledge component which details the knowledge students will need to develop in order to progress through the strategy stages of the framework. This unit can be used to develop students' knowledge in the areas of grouping and basic facts; in particular knowledge of the pattern of teen numbers, groupings within 20 and doubles with a sum greater than 10 can be built up.

Activity:
1. Show students the learning object and introduce them to Alex, explain that he is going to help them break numbers into pairs.
2. Enter a number into the learning object. 12 is a good number to start with.
3. Show the students that the top bar is the number to be broken up into pairs and confirm that it is 12 by counting the bars that represent ones.
4. Explain to the students that part of the number is hidden under the light blue bar and that the number on the bar shows how many are hidden. Confirm by counting along the top bar that it is 10 that are hidden in the first example.
5. Ask the students "Ten and how many more are twelve?" Count the ones to confirm the answer and enter this into the box. Check this using the green button.
6. Complete another number pair for 12 in the same way. Questions that can be used include: 9 and how many more are 12? What is the number partner that will join with 9 to make 12?
7. Click the "next" button to find further number pairs for 12. Show the students how the slider works, including the button that can show and hide the ones.
8. Ask the students to choose a number to work with and enter this into the learning object. Have the students identify the number partner for this example, initially with the ones hidden, then check this answer by showing the ones and counting them to confirm the result.
9. Continue for several more number partners of 12 then show the students the "show pairs" button which keeps a track of the pairs that have been found.
10. Continue to find all the number pairs for 12. The number pairs found can be printed by clicking on the print icon in the top right of the screen.

Explain to the students that they are going to use the learning object to help them work out how many jumps Freddy the frog will have to make to his friend's house.

1. First select the distance between Freddy's house and his friend's house in metres and enter this as a new number to be broken into pairs. 15 would be a good example to use.
2. Explain that Freddy is going cover the 15 metres to his friend's house in 2 jumps. Ask the students how many metres he will cover in his first jump and enter this into the number partner.
3. Use the number partner to help work out how many metres he will have to cover in his second jump to arrive exactly at his friend's house.
4. Use the number partner to work out the other combinations of jumps Freddy could do to get to his friends house 15 metres away, using 2 jumps each time.
5. As students work encourage them to count on from the highest number when working out the second number in a pair.
We know he's already jumped 11 metres, let's start counting from there. What's the next number after 11? (This is most easily asked when the ones in the bottom bar are hidden.) We know 11 and 4 are number partners to make 15. Let's check that 11 and 4 are 15: 11...12, 13, 14, 15. (Most easily asked when the ones are shown in the bottom bar).
6. Develop the idea that the order of numbers does not matter in addition. For example, adding 11 and 4 is the same as adding 4 and 11. Clarify that counting on from the largest number is the most efficient strategy.
If we are adding 11 and 4 what is the best number to start counting from? Why?
7. Repeat the problem using different distances between Freddy's house and his friend's place.

### Students working independently with the learning object

Use one of the contexts below to set problems for the students to solve independently, either on their own or in pairs, using the learning objects.

• Savings, for example:
You are saving for a skateboard which costs \$20. If you have saved \$8 so far, how much more do you need to save before you have enough for the skateboard? What if have \$13 saved, how much more do you need?
• Traveling, for example:
If you are going to visit your Nana who lives 26 km away and you have traveled 7 km already, how much further do you need to travel? What if you have already traveled 13 km?
• Monkeys in trees, for example:
If there are 14 birds playing in two trees and 8 of the birds are in one tree, how many are in the other tree? What if there are 10 birds in the first tree?

Once students have solved the problem ask them to draw a diagram to show how they used the learning object in their solution. Using a number line in their representation would be useful but encourage students to use a variety of methods to record their thinking. For example:

How did you use the number partner?
What numbers did you use?
What numbers did you need to count to work out the answer?
How could you show what you did in a diagram?

When all students have described their solutions in a diagram, reassemble as a group and have students describe their solutions to each other using their diagrams.

### Students working independently without the learning object

Independent activities that develop the same concepts as the learning object include:

• Students play a game of "How Many are Hiding?" with a partner. To play this game one student assembles a collection of objects, and hides some of them under a container or a piece of card. They tell their partner how many there are in total and their partner then works out how many are hiding. For example, "I have 26 buttons, and there are 12 in this pile. How many are hiding?"
• Use multilink cubes to make up "packets of lollies" using 2 colours. "If there are 12 lollies in a packet and there are 8 red ones, how many green ones are there? What if there are 6 red ones?" Record all the possible combinations of the two colours of lollies.

## 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.

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.

## Addition and Subtraction Pick n Mix

In this unit we look at a range of strategies for solving addition and subtraction problems with whole numbers with a view to students anticipating from the structure of a problem which strategies might be best suited.

## The Difference Bar 2

This unit introduces students to "The Difference Bar" digital learning object, a tool to help students work out the difference between two numbers by breaking numbers into parts.

This unit is for students at Stage 6-Advanced Additive of the Number Framework, Curriculum Level 3, i.e. students who have developed more than one part-whole strategy for addition and subtraction and can use these strategies to solve problems involving large numbers.

This digital learning object has two versions, one where difference problems are generated and one where students and teachers can make up their own difference problems. The problems at this level involve solving the difference between 2 two-digit numbers.