Year 10: week 2 (linear relationships and exponents)

This week we focus on finding rules for linear relationships, and working with exponents (powers of numbers).

This page suggests activities for each day. Click to download a printable PDF to help keep track of progress.


Day 1

Solving linear equations

  • Go to the learning object Plasers: choose coordinates (+/-).
  • In this version the plane has positive and negative numbers. Can you figure out how the four quadrants work?
  • Spend at least ten minutes playing the game.

Problem Solving e-ako

  • Go to the Problem Solving pathway in e-ako maths.
  • Choose King Arthur's problem (the third yellow button in the second row). 
  • Work through pages 1-7.
  • Explain to a family member; “How does King Arthur choose only one knight to marry his daughter?”

Exponents activity

  • Go to the activity Powerful Thought and complete the task, using a calculator if necessary.
  • Check your answers at the bottom of this page.

Day 2

Solving linear equations

  • Go to the learning object Plasers: enter an equation (+).
  • Spend at least ten minutes playing the game.
  • Try to work out how changing the numbers in the boxes affects the laser line.

Problem Solving e-ako

  • Go back to King Arthur’s Problem on the Problem solving pathway in e-ako maths.
  • You may need to use the simulator on Page 7 to remind you of the safe seats to sit in.
  • Work through pages 8-10 and try to figure out a pattern.
  • On page 10 click on the “Try Simpler Cases” path and answer the questions on page 13.
  • When you return to page 10, choose “Try Every Case” to see what happens.
  • Explain to a family member why trying every case is not sensible.

Exponents activity

  • Go to the activity Cubic Capacity and complete the task.
  • Check your answers at the bottom of this page.
  • What is the connection between Island Roads and the corner pattern for One Bad Apple?
  • Explain that connection to a family member.

Day 3

Solving linear equations

  • Go to the learning object Plasers: enter an equation (+/-).
  • Spend at least ten minutes with the learning object.
  • Can you work out the effect on the laser line of changing the numbers in the boxes?

Problem Solving e-ako

  • Go back to King Arthur’s Problem on the Problem solving pathway in e-ako maths.
  • Go to Page 10 and click on the “Create a Table to look for a Pattern” path.
  • Work through to page 20.

Exponents activity

  • Go to the task called Growing Pains and complete the challenge.
  • Check your answers at the bottom of this page.
  • Explain to a family member how powers of three are involved in the challenge.

Day 4

Solving linear equations

  • Go to the learning object Plasers: place bubbles (+)
  • Spend at least ten minutes with the learning object.
  • Can you use the equation to work out coordinates that lie on the line?

Problem Solving e-ako

  • Go back to King Arthur’s Problem on the Problem solving pathway in e-ako maths and go to page 21.
  • Work through to page 24.
  • Have you got a rule for the seat a knight should choose? Explain your rule to a family member.

Exponents activity

  • Go to the task called Fold and Crease and complete the task.
  • Check your answers at the bottom of this page.
  • Write how you found a rule for the number of creases and sections. Explain your strategy to another person.

Day 5

Solving linear equations

  • Go to the learning object Plasers: place bubbles (+/-).
  • Spend at least ten minutes with the learning object.
  • Write down an example of how you find coordinates that a linear equation passes through.

Problem Solving e-ako

  • Go back to King Arthur’s Problem on the Problem solving pathway in e-ako maths and go to page 25.
  • Complete the e-ako.
  • Can you write instructions for a brave knight about where to sit?

Exponents activities

  • Go to the task called Pip’s Pay and complete the challenge.
  • Check your answers at the bottom of this page.
  • Explain to a family member what how repeated doubling affects the amount of money. In real life that is called interest.
  • Go to the rich task Power Play and complete the challenge, using a calculator if necessary.
  • Scroll down the page to see how other students solve the challenge.