The Part-adder 2
This unit uses one of the digital learning objects, the part-adder, to support students as they investigate the addition of whole numbers. It is the second in a series of two units that focus on using this learning object; the first in the series outlines how it can be used with students at stage 5 of the Number Framework while this unit outlines ways to support students working at stage 6. 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.
use mental strategies to solve two digit plus two digit addition problems: using known facts, making tens, and compensation.
describe the mental strategies they are using to solve two digit plus two digit addition problems.
Relevant Stages of the Number Framework
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 working at stage 6 of the Number Framework, Advanced Additive. Students at this stage select from a broad range of strategies to solve addition problems, subdividing and recombining numbers to simplify problems. Strategies used at this stage include use of doubles facts (28 + 24 = 24 + 24 +4), making a ten (28 + 24 = 30 + 24 - 2) and using tens and ones (28 + 24 = 20 + 20 + 8 + 4). 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 draws on students' knowledge of groupings and basic facts; in particular knowledge of addition facts including doubles, the pattern of teen numbers, the number of tens in decades and groupings within one hundred.
Working with the learning object with students
- Show students the learning object and introduce them to Alex. Explain that he is going to help them solve addition sums by breaking the numbers up.
- Enter a problem into the learning object. 27 + 38 is a good problem to start with.
- Click through the instructions in Alex's speech bubble, reading the instructions with the students, and then close the instructions to experiment with the learning object.
- Show the students how to use the sliders to break up the numbers in the sum. Experiment with breaking up the numbers, and show the students that the blue bar representing 27 always stays the same length but it can be split in different ways. Find a variety of ways to split the 27, for example 25 + 2, 20 + 7, 13 + 14.
- Show the students how to use the extenders to make the numbers you are working with larger. Explain that if they make numbers larger to help solve the problem they need to remember to take this amount away from the final answer.
- Ask the students what would be a helpful way to split the numbers to solve the problem 27 + 38.
How can we split the numbers to make the problem easier to solve?
How could we break up these numbers to make it easier to find the total? - Use one of students' suggestions and the learning object to come up with an answer. For example, split the 27 into 25 and 2 so that 38 can be made into 40 easily. Use the slider on the learning object to make the split, leaving the 2 closest to the 38, and then discuss how the numbers can then be recombined.
Now we have split the number we have 25 and 2 and 38. How can we add these together easily?
Is there an easy way to combine 25 and 2 and 38?Tell the students that this way of breaking the numbers up is called making a ten.
Why do you think it is called that? (Because one of the numbers in the problem gets made up to the nearest ten).
How does it make problems easier to solve? (Ten is an easy number to add with). - Ask the students to suggest other ways to split the numbers to solve the problem.
Is there another way to split the numbers to make the sum easier? Can anybody see a different way to split the numbers? - Use the students' suggestions to work through other ways to solve the problem using the learning object. Include the following ways in your working.
27 + 38 = 2 + 25 + 25 + 13, using doubles.
27 + 38 =27 + 40 - 2, compensation.
- Once you have worked through these examples ask the students which ways they find helpful. You may like to list these ways so students can refer back to them when solving problems independently.
Which way of splitting the numbers do you find helpful? Why?
Explain to the students that they are going to use the learning object to help them work out amounts of money:
You are fund-raising to go to camp. Your class raises $48 on a car wash and $49 on a raffle. How much have you raised altogether?
Use the learning object to work through the problem, encouraging the students to split the numbers in ways that make the problem easier to solve and come up with a number of different ways to solve each problem.
How could we split the numbers to make the addition easier to do?
Do you know any number facts that could help you solve this problem?
Can you think of any other ways to split these numbers to make the problem simpler?
Pose other problems involving people on the bus. Helpful examples include:
Your class raises $74 on a sweet stall and $78 on a sausage sizzle. How much have you raised altogether?
Your class raises $67 selling pizzas and $64 on a sponsored run. How much have you raised altogether?
Your class raises $28 running a class disco and $31 selling chocolate. How much have you raised altogether?
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.
- Shopping, for example:
You go to the market to buy provisions for a class trip and spend $38 on apples and $36 on bananas. How much will you need to pay altogether? - Traffic, for example:
There is a traffic jam. 91 cars and 18 buses are stopped. How many vehicles are waiting? - Library books, for example:
In the school library one class returns 43 books and another class returns 29 books. How many books were returned altogether?
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.
How did you use the part adder?
How did you split the numbers in the problem? Why did you choose to do it that way?
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:
- Figure it Out, Number Sense and Algebraic Thinking, Book One, Levels 2-3.
Wrapping Up Wontons, page 1
50 First, page 4
The No Name Game, page 22 - Figure it Out, Number Sense and Algebraic Thinking, Book Two, Levels 2-3.
An Odd Spell of Mathematics, page 2
Serious Circus Sums, page 4
Tidying Up, page 16 - Figure it Out, Number Sense and Algebraic Thinking, Book Two, Levels 3.
Tidying Up, page 2
Crafty Combinations, page 16
Independent activities that consolidate the knowledge students require at this level include
- Addition Flashcards, Material Master 4-29.
- Number Boggle, Material Master 4-35.
Dear Family
This week at school are working on addition problems and thinking about the ways we can solve them by breaking the numbers up. Please work through the problems below with your child and encourage them to describe to you how they are solving each problem. They might like to draw a diagram for you like the one below.
- There are 18 boys and 16 girls in Adam's class. How many children are in the class altogether?
- The children held a garage sale and made $38 selling second hand toys and $33 selling second hand books. How much did they make altogether?
- Sally is collecting rugby cards. She has 43 black cards and 29 blue and yellow cards. How many cards does she have altogether?
Similar Resources
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.
Ways to Add
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 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.
The Take-Away Bar 1
This unit introduces students to "The Take-Away Bar" digital learning object, a tool to help students solve subtraction problems by breaking numbers into parts.
This unit is for students working at stage 5 of the Number Framework, Curriculum Level 2. Student at this level have just started to understand and use part whole thinking to solve problems.
This digital learning object has two versions, one where subtraction problems are generated and one where students and teachers can make up their own subtraction problems. The problems at this level involve subtracting a single digit number from a two-digit number.
