The Part-adder 1
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 first in a series of two units that focus on using this learning object and outlines how it can be used with students working at stage 5 of the Number Framework. The second unit in the series looks at using the learning object with students at stage 6. The unit 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 one digit addition problems: using known facts, making tens and compensation;
describe the mental strategies they are using to solve two digit plus one 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 in transition between stages 4 and 5 of the Number Framework, moving from Advanced Counting to Early Additive. This transition involves students moving from using counting strategies to solve addition problems to being able to partition and recombine numbers. For example, when adding 8 and 5 students working at stage 4 will count (8...9,10,11,12,13) to get the answer; students working at stage 5 will repartition the numbers to find a solution, for example 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. 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 the addition facts to 10, doubles facts, the pattern of teen numbers and groupings within 10 and 20.
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. 18 + 8 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 use the sliders to break up the numbers in the sum. Experiment with breaking up the 8, and show the students that the yellow bar representing 8 always stays the same length but it can be split in different ways. Find all the ways you can to split the 8, for example 7+1, 2+6, 4+4.
- 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 them away from the final answer.
- Ask the students what would be a helpful way to split the numbers to solve the problem 18 + 8.
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 8 into 6 and 2 so that 18 can be made into 20 easily. Use the slider on the learning object to make the split, leaving the 2 closest to the 18, and then discuss how the numbers can then be recombined.
Now we have split the number we have 18 and 2 and 6. How can we add these together easily?
Is there an easy way to combine 18 and 6 and 2?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.
18 + 8 = 10 + 8 + 8 = 10 + 16 = 26, using doubles.
18 + 8 = 20 + 8 - 2 = 26, 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 how many people are on a bus. Pose the problem:
There are 16 adults and 6 students on the bus going to town. How many people are on the bus 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 other 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:
22 adults and 9 students are on the bus. How many people altogether?
25 adults and 6 students are on the bus. How many people altogether?
17 adults and 8 students are on the bus. How many people 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.
- Fruit bowls, for example:
There are 14 pears and 8 apples in a bowl. How many pieces of fruit altogether? - Money, for example:
You go to the toy shop and buy a Barbie doll for $17 and some new felt pens for $7. How much will you need to pay altogether? - Collections, for example:
You have 35 matchbox cars in your collection and you receive 9 cars for your birthday. How many cars do you now have in your collection?
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, 43 + 29:
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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:
- Playing the game Bridges, which can be found on Material Master 4-34.
- Playing the game Double Somersaults Plus or Minus One, which can be found on Material Master 4-33.
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 we 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 17 boys and 7 girls in Adam's class. How many children are in the class altogether?
- The children held a garage sale and made $26 selling second hand toys and $9 selling second hand books. How much did they make altogether?
- Sally is planning a party for her friends. She has 28 green balloons and 5 yellow balloons. How many balloons 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 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.
