Rich tasks
- This is an open-ended activity that requires students to solve difference problems using either addition (with change unknown) or subtraction. The task can be done as the students gain enough knowledge to complete it, or towards the end of the chapter to review strategies that have been learned.
- Diver Dan
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1. Diver Dan
- This activity provides a valuable opportunity for every student to explain to a partner the strategy they have used. It is a good idea to suggest students record their strategy in some way, or practise their explanations (with materials perhaps) in case they are asked to share the strategy later.
- Roaming the class as students talk with their partners gives teachers an opportunity to think about the order students might share back to the whole class (e.g. having students with the least efficient strategies begin and then progressing to the most efficient strategy; or having students share according to whether they solved the problem by addition or subtraction).
- When sharing back to the whole group it is a good idea for teachers to choose only one or two students to share popular strategies so that there is not too much repetition. You could ask other children to indicate (for example with a ‘thumbs up’), if they used a strategy that others have explained so they feel a sense of shared accomplishment.
- Students in the audience also benefit from being given a focus for their listening. For example, they can be asked to compare different strategies. (Prompts that might be helpful are: “What is the same?” “What is different?” “How is this strategy more or less efficient than my strategy or a previously shared strategy?”)
- Encourage students to question their peers if they don’t understand or need clarification about a strategy. It is good if answers can be given by other students, but the students who answer don’t need to be the students who are presenting.
- The final part of the task asks students to create similar problems for their peers which have answers of either 85 metres, or 230 metres. Being able to compose a question for a particular equation is often challenging for students, and even more so when there are many possible correct answers. Asking appropriate questions as well as providing answers to questions posed by others is a very important skill, since it helps students to apply mathematical knowledge to real world situations.
Jumping through tens numbers page 88
- Solve problems involving difference by using basic addition and subtraction facts to pass through a tens number (tidy ten).
- Explore ways of recording each strategy, including empty number lines and equations.
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Teacher notes
- Number lines are very helpful for identifying an appropriate tens number and recording the size of each jump to calculate the total. Initially some students may require number lines with appropriate scales marked on them, but as students’ ability to sequence improves, empty number lines are more flexible.
- Differences can be calculated by adding or subtracting through a tens number. It is helpful to remind students of this, so they can consider whether addition or subtraction might be more efficient (quicker or easier) for a particular problem.
Using place value partitioning page 91
- Solve problems involving difference using place value partitioning.
- Explore ways of recording each strategy, including empty number lines and equations.
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Teacher notes
- Some students have difficulty aligning the places in two numbers, particularly if the equation is written horizontally or is not symmetrical e.g. 3 digits – 2 digits.
For these students it may be helpful to:- use place value materials to make each number, e.g. abacus, ice block sticks
- expand each number, e.g. 324 + 45 = 300 + 20 + 4 + 40 + 5
- indicate place above the digits in each number.
H T O T O
e.g. 3 2 4 + 4 5 - draw ‘rainbows’ to link the same place in each number
• e.g. 25 + 46 - record the equation vertically on a place value chart, e.g. on page 92 of the Student Resource Book.
Add or subtract? page 95
- Decide whether to solve difference problems using addition or subtraction strategies.
- Explore ways of recording each strategy, including empty number lines and equations.
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Teacher notes
- This section gives students practice at deciding which operation to use when solving a difference problem. Encourage students to justify their choice of operation and reflect on why their choice seemed more efficient.
