Between each question and the next, only one aspect is changed. Can you see how this affects the answer in each case? Click the “New questions” button for a new set of randomly generated questions. Click “show all answers” to show all answers at once, or click on each individual question to show answers one at a time.

Teachers: log in to access the following:

• Slides in PPTX
• Slides in PDF (one slide per page, suitable for importing into IWB software)

• Worksheet (with space for student work)
• Handout (slides with exercises only; 4 per page for reduced printing)
  • Worked solutions to all questions

• See Teacher resources under Part 3 for a card sort covering all four operations with fractions

• Addition pyramid generator – suitable for use on an interactive whiteboard. Answers available.

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 Here is a sequence of calculations:

 \(12 \times 8 = 96 \)

 \(12 \times 4 = 48 \)

 \(12 \times 2 = 24 \)

 \(12 \times 1 = 12 \)

 What are the next three calculations in this sequence?

Teachers: log in to access the following:

• Slides in PPTX (with click-to-reveal answers)
• Slides in PDF (one slide per page, suitable for importing into IWB software)

• Worksheet (with space for student work)
• Handout (slides with exercises only; 4 per page for reduced printing)
  • Worked solutions to all questions

• See Teacher resources under Part 3 for a card sort covering all four operations with fractions

Teachers: log in to access these.

• Consider \(\frac{4}{4} \times \frac{1}{3}\). This is equivalent to \(1 \times \frac{1}{3}\) so we would expect the product to be \(\frac{1}{3}\), as shown in the applet’s initial configuration.
• Tick the box to show the vertical splits.
• Start reducing the numerator of the first fraction while holding everything else constant for a visualisation of \(\frac{3}{4} \times \frac{1}{3}, \frac{2}{4} \times \frac{1}{3},\) and \( \frac{1}{4} \times \frac{1}{3}\).
• Continue to play around with this applet!

 1) Here is a sequence of calculations:

 \(40 \times 8 = 320 \)

 \(40 \times 4 = 160 \)

 \(40 \times 2 = 80 \)

 \(40 \times 1 = 40 \)

 What are the next three calculations in this sequence?

 2) Here is a different sequence of calculations:

 \(40 \div 8 = 5 \)

 \(40 \div 4 = 10 \)

 \(40 \div 2 = 20 \)

 \(40 \div 1 = 40 \)

 What are the next three calculations in this sequence?

Teachers: log in to access the following:

• Slides in PPTX (with click-to-reveal answers)
• Slides in PDF (one slide per page, suitable for importing into IWB software)

• Worksheet (with space for student work)
• Handout (slides with exercises only; 4 per page for reduced printing)
  • Worked solutions to all questions

• Card sort covering all four operations, not just division.

Teachers: log in to access these.