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Working with partial units

The purpose of this activity is to support students measure the areas and perimeters of the rectangle when the side lengths have simple fractions.

Two tamariki measuring a box together with measuring tapes.

Tags

  • AudienceKaiako
  • Curriculum Level3-4
  • Education SectorPrimary
  • Resource LanguageEnglish
  • Resource typeActivity
  • SeriesAccelerating learning

About this resource

These activities are intended for students who understand how to use metric units of measure to find lengths. When working with units, they should understand the following:

  • Units relate to the attribute being measured (for example, length is measured with iterations of length).
  • Identical units need to be used when measuring.
  • Units should be tiled (or iterated) with no gaps or overlaps to create a measure.
  • Units can be equally partitioned into smaller units when greater accuracy is needed.

Students should also know how to use a measurement scale, such as a ruler or tape measure. They should be familiar with the most common metric units of length: metres, centimetres, and possibly millimetres, though they may not be able to convert measures (e.g., 45 cm = 450 mm). Students should also have a partial or full grasp of their basic multiplication and division facts.

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    Working with partial units

    Achievement objectives

    GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.

    Required materials

    • rulers
    • calculators

    See Materials that come with this resource to download:

    • Working with partial units activity (.pdf)
    • Working with partial units CM (.pdf)
     | 

    1.

    Remind students how the area and perimeter of a rectangle can be found using the side lengths. Draw a rectangle measuring 20cm x 15cm on a large sheet of paper. Let students use calculators if needed.

    • What is the perimeter of this rectangle? (2 x (20 + 15) = 2 x 35 = 70 cm)
    • What is the area of this rectangle? (20 x 15 = 300 cm2).

    2.

    Provide the students with copies of the Working with partial units CM and calculators.

    • What do you notice about all these rectangles?

    Look for students to recognise that many of the side lengths are decimals and fractions.

    • Your task is to find the area and perimeter of each rectangle.
    • Put the rectangles in order by area, then order them by perimeter.
    • Are the orders the same?

    You might introduce relevant te reo Māori kupu such as roa (length), tapawhā hāngai (rectangle), paenga (perimeter), and horahanga (area).

    3.

    Let the students work in pairs to calculate areas and perimeters. Organise students in pairs that will encourage peer scaffolding and extension, as well as productive learning conversations. Roam as they work and look for students to:

    • collect part units to form whole units, such as two halves to make one unit
    • use whole number multiplication to calculate most of the area in each rectangle
    • convert fractions of units to decimals
    • use multiplication on the calculator to find both perimeters and areas.

    At times during the investigation, you might gather the students or ask pairs to discuss the important teaching points.

    4.

    After sufficient progress is made, gather the group. Discuss, focusing on strategies for dealing with partial units of both length and area. This might include discussion of the following:

    • Change fractions to decimals to find areas by multiplication. For example, the two rectangles below both have an area of 5 x 8.75 = 43.75 square units.
    Two rectangles, each labelled C, with the area 5 x 8 = 43.75 units noted in their decimal and fraction forms.
    • Add fractions and decimals to find perimeters. For example, the perimeter of this rectangle equals 2 × (6½ + 5½) = 2 × 13 = 26 units.
    Rectangle labelled B in the centre, with the top length 6 ½ units and the left side length 5 ½ units.
    • Find fractions of fractions of a unit. For example, the shaded area is one half of one half (1/2 × 1/2 = 1/4).
    Rectangle labelled B in the centre, with the top length 6 ½ units and the left side length 5 ½ units. A tiny area at the bottom right corner is shaded.

    5.

    The areas and perimeters are shown below. Note that the orders are different for area and perimeter.

    Rectangle

    A

    B

    C

    D

    E

    Area

    38 sq units

    35.75 sq units

    43.75 sq units

    40 sq units

    30 sq units

    Perimeter

    27 units

    26 units

    27.5 units

    30 2/3 units

    29 units

    1.

    Provide rectangles with decimal side lengths for students to measure, then use to work out areas and perimeters. Encourage students to estimate the areas before calculating. For example, the rectangle below measures 12.8 cm x 7.4 cm so an estimate of 13 x 7 = 91 cm2 is reasonable for area and 2 x (13 + 7) = 40 cm is reasonable for perimeter.

    A grey rectangle with a wooden ruler placed along the bottom and a second ruler placed along the right hand side, measurement in centimeters. Base is 12.8cm, right hand side is 7.4cm.

    2.

    Extend area and perimeter with problems to include situations where area or perimeter is given but a side length is not. Two examples might be:

    • The perimeter is 42.2 cm. What is the width of the rectangle?

    Grey rectangle with a single measurement given along the base of 12.4 cm.
    • The area is 99.54 cm2. What is the width of the rectangle marked?
    Grey rectangle with an unknown height and a width measuring 7.9 centimetres.

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