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Measurement and Algebra Integration

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Measurement and Algebra Integration

A community garden is being planned. Use measurement and algebra to check lengths, dimensions and materials. Show working where needed, and include units in every measurement answer.

Measure and convert

Garden plans use different metric units. Remember: 10 mm = 1 cm, 100 cm = 1 m, and 1,000 m = 1 km.

1.A garden-bed side measures 2.4 m. Convert this length to centimetres.
2.A metal edging strip is 3,650 mm long. How many metres is that?
3.Choose the most sensible unit for each measurement: (a) thickness of a wooden garden label, about 4 ___; (b) distance from the gate to the garden, about 18 ___.

Set up the garden beds

Use algebra to find unknown dimensions. Let the letter in each question represent the stated unknown length.

4.A rectangular herb bed has a length 1.2 m greater than its width. Its perimeter is 10.8 m. Let w be its width. Write an equation and find the width and length.
5.A straight path needs two equal timber lengths and a 0.6 m gap between them. The total span is 4.2 m. If each timber is x metres long, which equation models the span?
  • 2x + 0.6 = 4.2
  • x + 0.6 = 4.2
  • 2(x + 0.6) = 4.2
  • x ÷ 2 + 0.6 = 4.2
6.Solve the path equation from the previous question to find the length of each timber.

Track a growing border

A garden border is built from identical short sections, plus one 0.35 m corner connector. Each section is 0.45 m long.

Sections, n

Total length, L (m)

1

0.80

3

1.70

6

3.05

7.Write a rule for the border length L in terms of n, then use it to find the length for 10 sections.

Materials and perimeter

Check the plan before ordering materials. Keep units consistent when adding or subtracting lengths.

8.A rectangular compost area is 2.5 m wide and has a perimeter of 13 m. Let its length be l metres. Form and solve an equation to find l.
9.A 9.6 m roll of edging is used around the herb bed from Question 4. The bed perimeter is 10.8 m. How much more edging is needed?
10.A rectangular seedling tray has a length of 56 cm, which is 8 cm more than its width. Write an equation for the width w and find the tray's area.
11.A rectangular play lawn has perimeter 84 m. Its length is 6 m more than its width. Let w be its width. Write an equation and find both dimensions.

3 printable pages

  • Measurement and Algebra Integration, page 1 of 3: Measure and convert, Set up the garden beds

    Page 1

  • Measurement and Algebra Integration, page 2 of 3: Track a growing border, Materials and perimeter

    Page 2

  • Measurement and Algebra Integration, page 3 of 3: 9. A 9.6 m roll of edging is used around the herb bed from Question 4. The bed perimeter…

    Page 3

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