Week 26 · Fact families, mass and perimeter · 3 lessons
3
Multi-step problems and polygon perimeter
Discover Mathematics P3: Term 2, Lessons 101–110
GoalSolve two-step add and subtract problems and find the perimeter of polygons, including an octagon.
New words
two-step problem · a problem that needs two calculationspolygon · a closed shape with straight sidesoctagon · a polygon with 8 sides
Explanation
Some problems need two steps. Seif has 250 LE. He buys shoes for 135 LE and a shirt for 78 LE. How much is left? Step 1: find the total spent: 135 + 78 = 213 LE. Step 2: subtract from 250: 250 − 213 = 37 LE. Read the question, do one step at a time and check that the answer makes sense. To find the perimeter of any polygon, add the lengths of all its sides. This house-shaped pentagon has sides 6, 5, 5, 5 and 5 cm, so its perimeter is 6 + 5 + 5 + 5 + 5 = 26 cm. An octagon has 8 sides. If all 8 sides are equal, multiply: with sides of 5 cm the perimeter is 8 × 5 = 40 cm.
Worked examples
Seif has 250 LE and spends 135 LE on shoes and 78 LE on a shirt. Step 1: 135 + 78 = 213 LE. Step 2: 250 − 213 = 37 LE left.
This hexagon has sides 8, 3, 4, 3, 4 and 6 cm. Add them: 8 + 3 + 4 + 3 + 4 + 6 = 28 cm.
A regular octagon has 8 equal sides, and each side is 5 cm. The marks show equal sides. The perimeter is 8 × 5 = 40 cm.
Class activity
Perimeter walk. Draw a polygon with 5 or 6 straight sides on squared paper. Measure every side with a ruler and add to find the perimeter. Then make up a two-step money problem about a shop, using amounts under 300 LE, and solve it with a partner.
Practice
1
Find the perimeter of the triangle.
6 + 8 + 10 = 24 cm.
2
A regular octagon has sides of 7 cm. What is its perimeter?
An octagon has 8 sides, so 8 × 7 = 56 cm.
3
A pentagon has sides of 8, 6, 9, 7 and 5 cm. Find the perimeter.
8 + 6 + 9 + 7 + 5 = 35 cm.
4
Hana has 500 LE. She buys a bag for 185 LE and a book for 95 LE. How much money is left?
Step 1: 185 + 95 = 280 LE. Step 2: 500 − 280 = 220 LE.
5
A book has 200 pages. Karim reads 48 pages on Monday and 67 pages on Tuesday. How many pages are left?
