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.
- Alien multiplication
> More on "Rich tasks for this Chapter"...
1 Alien multiplication
- Encourage students to find a systematic way of multiplying all the combinations of three numbers together.
- Remind students they are looking for different answers.
- Encourage students to check their calculations carefully because it is easy to make a mistake that will lead to false results.
Multiplying using facts already known
- Multiply numbers using 2s, 5s and 10s facts.
- Multiply numbers by adding some on or taking some off of facts already known.
- Use 2s facts and doubling to find 4s, 8s, 16s etc, facts.
> More on "Multiplying using facts already known"...
Teacher notes
- The “using 2s, 5s and 10s” strategy is the beginning of understanding place value partitioning to find the answers to multiplications. This is explored in book 3B.
- Arrays are useful to show the “using 2s, 5s and 10s” strategy and also the “adding a bit on or taking a bit off” strategy.
- Using 10s facts and then adding a bit on or taking a bit off is the beginning of understanding rounding and compensating to find the answers to multiplications. This is explored in book 3B.
- Encourage students to think about which numbers work best with each type of strategy.
- It is helpful if in modeling books etc, the number properties are written alongside number lines or diagrams.
- Students are often held up because they don’t know their basic facts. It is important to check these again before starting this section.
Multiplying tens
- Multiply tens, hundreds and thousands numbers using basic facts.
> More on "Multiplying tens"...
Teacher notes
- Students need to understand place value, e.g. 70 = 7 tens etc.
- Students may need to use materials such as play money to start with to understand this strategy. Money or Unifix cubes or similar are useful.
- It is very important to check that students know their basic facts before starting this section. Without quick recall of these facts progress can be delayed.
Multiplying by choosing a strategy
- Multiply by choosing one of the strategies learnt in this chapter.
> More on "Multiplying by choosing a strategy"...
Teacher notes
- Emphasise that some numbers suit a particular strategy. For example, when multiplying by 4s, 8s, 16s or 32s, using 2s and doubling can be a good strategy to use. For multiplications by 11, 12, or 9, adding a bit on or subtracting a bit off is useful. For multiplying by 6, 7, 8, 14, 17 etc, using a combination of 2s, 5s and 10s is a good strategy.
- It is important that students have practice at using all of the strategies before being able to choose the one they think is best. Encourage them to try more than one way for each problem. Then choose which one works best and think about why.
- You could get students to work in groups for this Activity and share their ways of working out each answer. They could try and convince each other that their way is better.
