Rich tasks
- These are problem solving open-ended questions that require students to investigate adding and subtracting using a variety of strategies. The tasks can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place, or given as homework, or extension.
- Make six equal sums
- You’ve won a trip!
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Teacher notes
1. Make six equal sums
- This is best done with cards so that students can easily move the cards around to make the piles.
- The sum of each pile should be 82.
- You could give students this hint: “Add up the total of all the cards and then divide by 10 to find what the total of each pile has to be.”
2. You’ve won a trip!
- You could give this to students to do for homework or as a home project. That way they could discuss the task with their family and use the internet to research the places they might like to go.
- This activity could be combined with another subject such as social studies and if you were studying a particular country you could change the air km chart to one for that country.
Adding and subtracting using reversibility - page 30
- Change a subtraction into an addition to make it easier to work out the answer.
- Change an addition into a subtraction to make it easier to work out the answer.
- Do a different subtraction to make it easier to work out the answer.
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Teacher notes
- Encourage students to use number strips to help as it is easier to see how the number sentence can be changed to an equivalent one.
- Encourage students to look at the numbers involved before turning the equation to see which ones are best turned.
- In Activity 1 question 6 you could divide the class into three groups by numbering the students 1-3. Give those students numbered 1 the first column (a, d, g and j), those numbered 2 the second column (b, e, h and k), and the remaining examples to those students numbered 3. When the students have finished ask all the 1s to meet to discuss their strategies. The 2s and 3s also discuss their strategies in their groups and produce some hints or guidelines for the other students around which strategy is most efficient based on the numbers in the equations.
Adding using near doubles - page 34 & Adding and subtracting using complementary numbers - page 35
Note: These two small sections in the book have been joined together for the purposes of the teacher file.
- Recognise numbers that are close to doubles and use the doubles to add numbers.
- Use complementary numbers up to 100 to add and subtract efficiently.
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Teacher notes
- Although not many calculations in real life involve near doubles or complements, these are powerful strategies to use when they do.
- Encourage students to look at numbers for doubles and complements when adding and subtracting.
Choosing an efficient strategy for addition and subtraction - page 36
- Practise using, comparing and evaluating different addition and subtraction strategies to solve efficiently a range of problems.
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Teacher notes
- Students need practice at identifying numbers which suit particular strategies. It is often best if they write a number sentence for the problem first.
- Students could be asked to make some posters or displays which illustrate different strategies with examples using the sorts of numbers that work best.
- Encourage students to look for doubles and complements, to look to see if the number sentence would be easier if turned, and to look for near tidy numbers. It takes practice for students to be able to identify an efficient strategy without having to try them all.
- It is helpful if students develop a shared vocabulary as a class for the strategy they are using or describing, for example “using place value partitioning” or “by using complementary numbers”.
- Adding and subtracting with dates presents particular problems for students. In the last section of the chapter students need to understand that we say someone is, for example, 12 years old right up until their birthday when they turn 13. It is important that students think about whether a birthday falls between the start and finish date, for example, the dates of birth and death when calculating lifespan.
