This week we focus on finding rules for linear relationships, graphing linear relationships, and solving linear equations.

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 Visual Linear Algebra version 1.
- Look at this video to see how to use the learning object.
- Spend at least ten minutes solving simple linear equations.

**Patterns e-ako**

- Go to the Problem Solving pathway in e-ako maths.
- Choose Deep Thinking (the third yellow button in the fourth row).
- Work through pages 1-12 which are about finding relating climbing patterns to graphs of those patterns.
- Explain to a family member; “Which creature is climbing in a linear pattern? Which creature is most likely to escape the well first? Why?”

**Patterns Activity**

- Go to the activity Stacking Patterns.
- Complete the task then check your answers at the bottom of this page.
- Are the three stacking patterns linear? Explain why.

**Day 2**

**Solving linear equations**

- Go to the learning object Visual Linear Algebra version 1.
- Spend at least ten minutes solving simple linear equations.

**Patterns e-ako**

- Go back to Deep Thinking on the Problem Solving pathway in e-ako maths.
- Work through pages 13 -15 which are about predicting how the creatures will climb for times, 4, 5, and 6 hours.
- On page 16, Choose the snail to investigate how that creature climbs. After you complete page 58 you are taken back to page 16.
- Explain to a family member; “Why is the growth pattern of the snail linear? What does the formula h = 2t + 5 mean?”

**Patterns activity**

- Go to the activity Stick Houses.
- Complete the task then check your answers at the bottom of this page.
- Are the stick house patterns linear? Explain why.

### Day 3

**Solving linear equations**

- Go to the learning object Visual Linear Algebra version 2.
- Look at
- Spend at least ten minutes solving simple linear equations.

**Patterns e-ako**

- Go back to Deep Thinking on the Problem Solving pathway in e-ako maths.
- Go back to page 16, Choose the frog to investigate how that creature climbs.
- Explain to a family member; “What is the climbing pattern of the frog?"

**Patterns Activity**

- Go to the activity Where to sit? and follow the instructions. You may need to draw diagrams of the desk arrangements on isometric paper.
- Check your answers at the bottom of this page.

**Day 4**

**Solving linear equations**

- Go to the learning object Visual Linear Algebra version 2.
- Spend at least ten minutes solving simple linear equations.

**Patterns e-ako**

- Go back to page 16 of Deep Thinking on the Problem Solving pathway in e-ako maths.
- Choose the spider to investigate how that creature climbs. After page 35 the right arrow takes you back to page 16 again.
- Explain to a family member; “What is meant by a periodic function?”

**Patterns activity**

- Go to the activity Mats, patterns and rules and complete the challenge. There are two pages. Try to write rules such as
*2×x+2×(x-1)*without the multiplication signs. - Check your answers at the bottom of this page.
- Show a family member how to use a spreadsheet to continue linear patterns.

**Day 5**

**Solving linear equations**

- Go to the learning object Visual Linear Algebra version 2.
- Spend at least ten minutes solving simple linear equations.

**Patterns e-ako**

- Go back to page 16 of Deep Thinking on the Problem Solving pathway in e-ako maths.
- Choose Gordon, the gecko, then the Wally the weta to investigate how each creature climbs.
- After you return to page 16 finally, choose the checked flag to finish the e-ako.
- Explain to a family member; “What is meant by powers of two?”

**Patterns activity**

- Go to the activity Patterns and designs.
- Complete only Question 3 of this challenge.
- Check your answers at the bottom of this page.