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Simple Linear Patterns

Simple Linear Patterns using diagrams and tables. MTH 2-13a & MTH 3-13a. Square Numbers. Triangular Numbers. Simple Linear Patterns. www.mathsrevision.com. Harder Linear Patterns. Flower Bed Investigation. 3cm. 5cm. 4cm. 2cm. MTH 2-13a & MTH 3-13a. Starter Questions.

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Simple Linear Patterns

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  1. Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Square Numbers Triangular Numbers Simple Linear Patterns www.mathsrevision.com Harder Linear Patterns Flower Bed Investigation

  2. 3cm 5cm 4cm 2cm MTH 2-13a & MTH 3-13a Starter Questions Q1. Calculate Area and perimeter Q2. 30% of 200 Q3. www.mathsrevision.com Q4. If a = 1 , b = 2 and c = 4 Find

  3. MTH 2-13a & MTH 3-13a Simple Linear Patterns using diagrams and tables Learning Intention Success Criteria • Construct tables. • We are learning how tables can help us to come up with formulae for Simple Linear Patterns. • Find the difference value in patterns. www.mathsrevision.com • Using the difference value • to write down a formula.

  4. 1 Table 2 Tables 3 Tables Task : Find a formula connecting the number of tables and the number of surfers. Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a In an internet café 3surfers can sit round a triangular table. www.mathsrevision.com

  5. 2 4 5 1 3 6 3 9 1 Table 2 Tables 3 Tables 3 3 3 3 Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Fill empty boxes Number of Tables Step 1 : Number of Surfers 12 15 www.mathsrevision.com Step 2 : Find difference What is the formula Same difference linear pattern

  6. Number of Tables Number of Surfers 12 15 2 4 5 3 3 6 9 1 3 3 3 3 HINT : Let the number of surfers be the letter S and the number of tables be the letter T Step 3 : Can you write down formula connecting the number of surfers and the number of tables. Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a www.mathsrevision.com S = 3 x T S = 3T

  7. Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Key-Points Write down the 3 main steps 1. Make a table www.mathsrevision.com 2. Find the difference 3. Use the difference to write down the formula

  8. Simple Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Now try Ex 3 Ch11 (Page 135) www.mathsrevision.com

  9. 6cm 10cm 7cm 3cm Complicated Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Q1. Calculate Area and perimeter Q2. 32% of 200 www.mathsrevision.com Q3.

  10. MTH 2-13a & MTH 3-13a Complicated Linear Patterns using diagrams and tables Learning Intention Success Criteria • Construct tables. • We are learning how tables can help us come up with formulae for complicated Linear Patterns. • Find the difference value in patterns. www.mathsrevision.com • Calculate correction factor 4. Use the difference value to write down a formula connecting the table values.

  11. 3 Tables 1 Table 2 Tables Task : Find a formula connecting the number of tables and the number of surfers. MTH 2-13a & MTH 3-13a A internet café decides to change it’s table design to. Complicated Linear Patterns using diagrams and tables www.mathsrevision.com

  12. 3 Tables 1 Table 2 Tables 2 4 5 1 3 6 4 8 2 2 2 2 MTH 2-13a & MTH 3-13a Complicated Linear Patterns using diagrams and tables Fill empty boxes Number of Tables Step 1 : Number of Surfers 10 12 www.mathsrevision.com Step 2 : Find difference What is the formula Same difference linear pattern

  13. Number of Tables Number of Surfers 10 12 6 4 8 2 4 5 1 3 2 2 2 2 S = 2 x T Part of the Formula Can you write down formula connecting the number of surfers and the number of tables. MTH 2-13a & MTH 3-13a Complicated Linear Patterns using diagrams and tables www.mathsrevision.com Find a number so formula works Step 3 : Step 4 : S = 2T + 2 Correction factor “add on 2”

  14. MTH 2-13a & MTH 3-13a Complicated Linear Patterns using diagrams and tables Key-Points Write down the 4 main steps 1. Make a table www.mathsrevision.com 2. Find the difference 3. Write down part of formula 4. Find the correction factor and then write down the full formula

  15. Complicated Linear Patterns using diagrams and tables MTH 2-13a & MTH 3-13a Now try Ex 4 Ch11 (Page 137) www.mathsrevision.com

  16. 114o MTH 2-13a & MTH 3-13a Starter Questions 6 cm 10 cm www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  17. Square Numbers MTH 2-13a & MTH 3-13a Learning Intention Success Criteria • To understand what a square number is. • We are learning what a square number is. • Calculate the first 10 square numbers. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  18. Write down the next square number MTH 2-13a & MTH 3-13a Square Numbers 1 4 9 16 42 12 22 32 www.mathsrevision.com Write down the first 10 square numbers. 1 4 9 16 25 36 49 64 81 100 Created by Mr.Lafferty Math Dept

  19. Square Numbers MTH 2-13a & MTH 3-13a Now try Ex1 Ch11 (page 131) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  20. 122o MTH 2-13a & MTH 3-13a Starter Questions 8 cm 6 cm www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  21. Triangular Numbers MTH 2-13a & MTH 3-13a Learning Intention Success Criteria • To understand what a • triangular number is. • We are learning what a triangular number is. • Calculate the first 10 triangular numbers. www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  22. Which numbers are both square and triangular number Write down the next square number MTH 2-13a & MTH 3-13a Triangular and square Numbers 15 1 3 6 10 www.mathsrevision.com 2 3 4 5 Write down the first 10 triangular numbers. 1 3 6 10 15 21 28 36 45 55 Created by Mr.Lafferty Math Dept

  23. Special Patterns MTH 2-13a & MTH 3-13a Now try Ch11 (page 133) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  24. Flower Bed Investigation MTH 3-13a David is designing a flower bed pattern for the local garden show. He wants to use regular hexagonal shapes for the bed and slabs. This is the flower bed shape www.mathsrevision.com This is a slab shape

  25. Draw this design on the isometric dot paper provided. (Ensure that your paper is portrait) Flower Bed Investigation MTH 3-13a Here is the design that has one flower bed surrounded by slabs. How many slabs are required to surround the flower bed? www.mathsrevision.com 1 flower bed 6 slabs

  26. Flower Bed Investigation MTH 3-13a Now draw two flower beds surrounded by slabs. How many slabs are required to surround the flower bed? www.mathsrevision.com 2 flower bed 11 slabs

  27. Flower Bed Investigation MTH 3-13a How many slabs are required to surround the flower bed? Now draw three flower beds surrounded by slabs. 16 slabs 3 flower bed www.mathsrevision.com

  28. Flower Bed Investigation MTH 3-13a Task In your group discuss how best to record these results and work out a formula to calculate the number of slabs for given number of flower beds. www.mathsrevision.com As a group you are required to hand in a single solution for this task showing all working.

  29. Flower Bed Investigation MTH 3-13a Number Flower Beds (f) 1 2 3 4 Number of Slabs (s) 6 11 16 21 www.mathsrevision.com s = 5f + 1 126 How many hexagonal slabs are needed for 25 flower beds. If we had 76 available slabs how many flower beds could we surround 15

  30. Flower Bed Investigation MTH 3-13a Task What is the maximum number of flower beds you could surround if you had 83 slabs www.mathsrevision.com 16

  31. Flower Bed Investigation MTH 3-13a Homework Now align the flower beds vertically and investigate if the formula is still the same? www.mathsrevision.com

  32. Vertical Flower Bed Investigation MTH 3-13a Number Flower Beds (f) 1 2 3 4 Number of Slabs (s) 6 10 14 18 www.mathsrevision.com s = 4f + 2

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