1. Ten dollars and eighty-nine cents
- The answer always comes to ten dollars and eighty-nine cents UNLESS the first and last digits are the same.
Example $3.43 - $3.43 in step 2. Try to get students to discover this for themselves.
2. Egyptian fractions
- This will be challenging for many students, as it requires them to add fractions with unrelated denominators. You could use this as extension or allow students to use the fraction buttons on their calculator. Doing the latter defeats the purpose of them practising adding fractions but may still add to their understanding of fractions.
Teaching ideas
This link displays a thermometer so that you can give some practice at adding and subtracting integers in the context of temperatures before moving to the more abstract task of adding and subtracting using patterns and number lines without a context.
Students are asked questions such a:
Starting temperature 6ºC and Change drops 8ºC.
What is the temperature now?
Ask students to write the equation for each one on their mini whiteboards or similar and hold them up for you to see.
+6ºC – + 8ºC = –2ºC
This link displays some bank statements with debits and credits and tells students to find the bank balance.
They are asked to write an equation to match each and find the answer.
If you display this onto a write on surface these equations could be written beside each statement.
You could use them to introduce addition and subtraction of integers using patterns and number lines.
You could use this as a class discussion to remind students about how subtracting a negative (taking away cold blocks) is the same as adding a positive (adding hot blocks).
Extend the discussion to debt examples, such as
“I owed my friend $12 so I had a debt of $12 or –12.
My mother took away $7 of this debt or – – 7 which is the same as –12 + 7 so when you take away a negative amount this is the same as adding an amount."
Ask students to think up a similar one for themselves and write an equation.
Teacher notes
- Encourage the use of a number line if students are having difficulty. It is better if students have an understanding of why they are moving left or right rather than learning the directions as rules.
- It is important that students understand the difference between the use of – and + as operations and to indicate whether a number is negative or positive (its value).
Teaching ideas
This link displays some decimal additions and subtractions.
Students are asked to work in pairs or groups to find an efficient strategy to work out the answers and be prepared to defend
their choice.
You could use this as a class discussion and divide the class into groups first for them to do the discussion. You could ask some groups to present their answers and defend them.
Teacher notes
- Remind students that they can use nested place value and whole number strategies to work out the answers.
- It is important not to introduce the written algorithm until students fully understand the place value strategy and nested place value.
- Encourage students always to use a mental strategy if they can before using a written strategy.
- Some of the written method practice may be more efficiently done using a mental strategy. Encourage students to look for these and do them both ways. Students will tend to use a calculator or written strategy if allowed, so it is important to motivate students to keep up their mental agility.
Teaching ideas
This link displays some additions and subtractions to put into one of three groups depending on which way the students
think they should be done, using a mental, written or machine method. You could divide the class into groups and then discuss
any differences.
Teacher notes
- Encourage students to justify their choices to their partner or group.
Teaching ideas
This link displays the addition 3/5 + 7/10 and some diagrams of fifths and tenths.
Students are asked
“Can the fifths and tenths be added together?” (No)
"Can both fractions be made to have the same denominator?” (Yes, they can both be made into tenths).
How could you show this using the diagrams?
Ask the students
"Why did you choose tenths?" (Because three fifths can be made into tenths but it is harder to make seven tenths into fifths, or similar answer)
Show me how to do this.
Teacher notes
- Encourage students to use diagrams or fraction pieces if they are struggling.
- You may need to demonstrate several examples for some students.
- Discourage students from learning how to do this using an algorithm. It is important that students understand what they are doing.
Teaching ideas
You could use any of the teaching ideas from “Adding and subtracting integers”, “Adding and subtracting decimals” or “Adding and subtracting fractions with related denominators” that you have not already used.
Teacher notes
All of the points under the sections “Adding and subtracting integers”, “Adding and subtracting decimals” or “Adding and subtracting fractions with related denominators” also relate to this section.
What is the temperature now? (Teaching resource sheet 29)