Rich tasks
- These are problem solving open-ended questions that require students to investigate adding and subtracting using place value. 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.
- The history of place value
- Don’t get cross
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Teacher notes
- Students will learn a lot about place value by investigating the place value practices of early civilisations.
- Exploring how the Maori write numbers can also help with place value.
- You could give a different civilisation to each group and then get them to present their findings to the rest of the class.
- This activity will give students practice at adding and subtracting numbers. Ensure that students do not use a calculator or it defeats the idea of the task.
Adding and subtracting using place value
- Add and subtract by adding, one at time, the numbers in a particular place value (hundreds, tens and ones) together.
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Teacher notes
- This is one of the main strategies for students to grasp for adding and subtracting mentally.
- Students must have a good grasp of place value before doing this chapter.
- Students may need to use place value materials for some time before proceeding to recording their strategy using equations. It is helpful if in modeling books etc, the number properties are written alongside number lines or diagrams.
- Some weaker students may draw their subtraction number lines so that smaller numbers are on the right and then work from left to right on the number line. Remind them that larger numbers are always to the right of smaller numbers.
- Students are often held up because they don’t know their basic facts. It might be a good idea to check these again before starting this section.
- It is important to encourage students to use mental strategies in their head and not always rely on paper.
Adding and subtracting using nested place value
- Add and subtract by writing both of the numbers as a number of tens, hundreds, thousands etc, using nested place value.
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Teacher notes
- Students must have a good grasp of place value before doing this section.
- Students may need to use place value materials to help them understand nested place value.
Using place value partitioning to solve “How many more” problems
- Add and subtract using understanding of nested place value.
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Teacher notes
- This strategy works best when the larger number has a greater or equal number in each place value.
Example: In 255 + ? = 287, 287 has more tens and more ones than 255. All of the examples in the Activity are like this. - Students may need to use materials at the beginning to develop an understanding of this strategy.
- Using a number line illustrates this strategy well.
- Students are often held up because they don’t know their basic facts. It might be a good idea to check these again before starting this section.
Adding and subtracting using place value strategies
- Practise adding and subtracting using strategies learnt in this chapter.
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Teacher notes
- Students need practice at identifying which place value partitioning strategy is most efficient for specific questions. It may be helpful for students to discuss which strategies they could use for each question and which they consider to be most efficient and why. Sharing decisions enables less confident students to better understand why some strategies are more efficient than others in different situations.
