Reasoning: Measures and Geometry
Reasoning: Measures and Geometry is where Year 5 pupils apply their measurement skills (converting between metric units, perimeter, area and volume) and their geometry skills (angles, properties of 2D shapes, and reflection) to multi-step word problems and reasoning questions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the question twice and identify whether it is really a measures question (units, perimeter, area, volume), a geometry question (angles, shape properties, reflection), or a mixture of both.
- For measures, check every unit given in the question and convert everything to the same unit before calculating - mixing units, such as cm and m, is the most common mistake.
- For perimeter, add every side length; for area of a rectangle, multiply length by width; for a compound (L-shaped or composite) shape, split it into rectangles first, find each area, then add or subtract as needed.
- For angle questions, remember angles on a straight line sum to 180 degrees, angles around a point sum to 360 degrees, and angles in a triangle sum to 180 degrees; use these facts to find a missing angle by subtraction.
- For reflection questions, count the squares from each point of the shape to the mirror line, then count the same number of squares on the other side to plot the reflected point.
- Sketch a quick diagram if the question does not provide one, and label the measurements or angles you are given - this often reveals the calculation needed.
- Check the final answer is a sensible size and has the correct unit, such as cm, cm squared or degrees, for what was actually asked.
Worked example
A rectangular garden is 8 m long and 5 m wide. A square flower bed with sides of 2 m is built in one corner of the garden. What is the area of the garden that is NOT covered by the flower bed?
- Find the area of the whole garden: 8 x 5 = 40 square metres.
- Find the area of the square flower bed: 2 x 2 = 4 square metres.
- Subtract the flower bed's area from the garden's total area: 40 - 4 = 36 square metres.
- The area of the garden not covered by the flower bed is 36 square metres.
Practice questions
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Q1A rectangular field is 60 m long and 35 m wide. What is the perimeter of the field?Show answer
Answer: 190 m
Q2Nadia has three pieces of ribbon: 1.2 m, 85 cm and 340 mm. What is the total length of ribbon in centimetres?Show answer
Answer: 239 cm (120 + 85 + 34)
Q3Two angles lie on a straight line. One angle is 68 degrees. What is the size of the other angle?Show answer
Answer: 112 degrees
Q4Three angles meet at a point. Two of them are 145 degrees and 95 degrees. What is the size of the third angle?Show answer
Answer: 120 degrees
Q5A box in the shape of a cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its volume?Show answer
Answer: 60 cubic cm
Q6A point is 3 squares above a horizontal mirror line. How many squares below the mirror line will its reflection be?Show answer
Answer: 3 squares
Q7An L-shaped room is made from a large rectangle 6 m by 4 m, with a smaller rectangle 2 m by 3 m removed from one corner. What is the area of the room?Show answer
Answer: 18 square metres (24 - 6)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Oliver is fitting skirting board around a rectangular room that measures 4.5 m by 3.2 m. He needs to leave a 0.9 m gap for the doorway, where no skirting board is needed. How many metres of skirting board does Oliver need in total?
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A triangle has angles of 55 degrees and 72 degrees. Work out the size of the third angle.
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Sienna is tiling a rectangular kitchen floor that measures 5 m by 4 m. Square tiles have sides of 50 cm and cost 3 pounds each. Assuming there is no wastage, how much will it cost Sienna to tile the whole floor?
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Free printable worksheet
Want more practice on paper? Download the reasoning: measures and geometry worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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