- Organize the class into groups of two or three students.
- With larger groups, some students may not fully engage in the task.
- Give each group Card Sets A and B.
- Use the projector resource to show students how to place Card Set A.
- Introduce the lesson carefully:
- I want you to work as a team. Take it in turns to place a percentage card between each pair of money cards.
- Each time you do this, explain your thinking clearly and carefully. If your partner disagrees with the placement of a card, then challenge him/her. It is important that you both understand the math for all the placements.
- There is a lot of work to do today, and it doesn't matter if you don't all finish. The important thing is to learn something new, so take your time.
Pairs of money cards may be considered horizontally or vertically.
Your tasks during the small group work are to make a note of student approaches to the task, and to support student problem solving.
Make a note student approaches to the task.
You can then use this information to focus a whole-class discussion towards the end of the lesson. In particular, notice any common mistakes. For example, students may make the mistake of pairing an increase of 50% with a decrease of 50%.
Support student problem solving.
Try not to make suggestions that move students towards a particular approach to this task. Instead, ask questions to help students clarify their thinking. Encourage students to use each other as a resource for learning.
Students will correct their own errors once the decimal cards are added.
For students struggling to get started:
- There are two ways to tackle this task. Can you think what they are? [Working out the percentage difference between the two money cards or taking a percentage card and using guess and check to work out where to place it.]
- How can you figure out the percentage difference between these two cards?
- This percentage card states the money goes up by 25%. If this money card (say $160) increases by 25%, what would be its new value? Does your answer match any of the money cards on the table?
When one student has placed a particular percentage card, challenge their partner to provide an explanation:
- Maria placed this percentage card here. Martin, why does Maria place it here?
If you find students have difficulty articulating their decisions, then you may want to use the questions from the Common Issues table to support your questioning.
Students often assume that if an amount is increased and then decreased by the same percent, the amount remains unchanged.
- The price of a blouse is $20. It increases by ½. What is the new price? [$30]
- The price of the blouse now decreases by ½. What is the final price? [$15]
- Now let's apply this to percentages. What happens if the $20 blouse increases by 50%?
- What happens now when this new price decreases by 50%?
- What percentage does the price need to decrease by to get it back to $20? [33 ⅓%]
- What does this show?
If the whole class is struggling on the same issue, you may want to write a couple of questions on the board and organize a whole-class discussion. The projector resource may be useful when doing this.
It may help some students to imagine that the money cards represent the cost of an item, for example, the price of an MP3 player at four different stores.