Rich tasks
- The fun fair
> More on "Rich tasks for this Chapter"...
1. The fun fair
- Students will need to be familiar with the value of each rod. You could display The fun fair (Getting started 9)which shows the values assigned to each rod. Make sure that students write equations with numbers as shown in the example on page 179 of the Student Resource Book, rather than colours (such as “green + black = orange”).
- Students could take photos of their mats or draw and colour them on one-centimetre grid paper for ease of sharing or for presentation.
Equals page 180
- Understand that the equals sign shows that both sides of an equation balance because they have the same value.
- Create or complete equations so that each side has the same value.
> More on "Equals"...
Teacher notes
- This section explicitly covers the meaning of the ‘equals’ symbol (=) which is used to indicate that quantities have the same value and they ‘balance’.
- There are several misconceptions about the equals sign. The most common is that this symbol is used to indicate that a calculation should be completed, and the answer written after the equals sign. Use of calculators may contribute to this misunderstanding since pushing the equals button results in an answer on the screen.
Students who interpret equals in this way frequently become confused when the answer precedes the equation (for example, 10 = 3 + ?), or where there is a calculation on either side of the equals sign (for example, 3 + 7 = 15 - 5). - An excellent reading by Charles Darr on the meaning of ‘equals’ and common student misconceptions can be found at this link:
https://www.nzcer.org.nz/system/files/set2003_2_04.pdf
Writing equations page 183
- Use an equation to record and solve additive problems.
> More on "Writing equations"...
Teacher notes
- It is important that students become familiar with equations that have the equals symbol in a range of locations and realise that wherever it is placed the numbers on either side must balance, for example, 7 = 3 + 4 and 2 + 3 = 5 = 6 – 1.
- Ensure that when students record their thinking they use the equals symbol correctly. Some students use an equals sign almost like a comma in speech, without checking that each side is actually equal. For example, when solving a problem such as 34 + 22 they will record their thinking incorrectly as 34 + 22 = 34 + 20 = 54 and 4 + 2 = 6 = 56.
Encouraging students to begin each new equation on a new line is a good idea, for example
30 + 40 = 50
4 + 2 = 6
50 + 6 = 56
Number machines page 185
- Identify operations and ‘outputs’ from a number machine.
- Record an equation for each ‘input’.
> More on "Number machines"...
Teacher notes
- Some students have difficulty understanding how a number or function machine works. To help them understand, a confident student could play the role of the processing part of the machine from inside a large box.
A number can be put into the box (‘the input’), the student inside performs the addition or subtraction operation, and then passes the answer out of the box (‘the output). Use well-known addition and subtraction facts initially so that students can easily identify the operation that takes place within the box.
- Students will sometimes try to identify the operation after just one input. Encourage students to try two or three inputs to check their initial hypothesis.
Sometimes doubling and adding give the same answer, for example, 5 + 5 = 10, and 2 × 5. The only way to be sure if the number has had five added or has been doubled is to input another number.
Using a calculator page 187
- Use a calculator to add, subtract, multiply and divide large numbers.
- Check to see whether an answer from a calculator makes sense.
> More on "Using a calculator"...
Teacher notes
- Calculators are a mathematical tool often used in algebra to explore or extend number patterns beyond the range that a student can work out mentally. Calculators are not a substitute for learning basic facts or using a range of known strategies to solve problems, but it is important that students become familiar with this commonly-used piece of technology.
- Students should always be encouraged to check their answers to ensure that they make sense, whether they use a calculator or not.
- If possible, have identical models of calculator for each student, and choose a basic rather than scientific model at this level. This makes it easier to give explanations and for students to understand instructions and support each other.
