☰ Year plan · Mathematics

Term 2 review

Week 30 · Term 2 review · 3 lessons
2

Review: percent, conversion and the coordinate plane

Discover Mathematics P6: Term 2, Units 8–13, Review
GoalReview percent, conversion factors, and points and distances on the coordinate plane.
New words
percent · out of 100conversion factor · a ratio of equal measures, such as 1,000 m : 1 kmordered pair · (x, y): x first, then y
Explanation

Percent: 15% of 80 is found by 10% (8) plus 5% (4), giving 12. A fraction becomes a percent by making the denominator 100: 3/5 = 60/100 = 60%. A discount of 20% on 250 LE takes off 50 LE and leaves 200 LE. Conversion: multiply by the factor that cancels the old unit; 2.4 km × 1,000 = 2,400 m, and 72 km/h = 72 × 1,000 ÷ 3,600 = 20 m/s. Coordinate plane: x comes first; the signs show the quadrant. Reflecting across the x-axis changes the sign of y; across the y-axis it changes the sign of x. Points on a horizontal or vertical line are 8 apart if they are 5 and 3 away from 0 on opposite sides: add the absolute values.

SkillKey ideaExample
Percent of a quantity10%, 5%, 1% steps15% of 80 = 12
Conversionmultiply by the factor2.4 km = 2,400 m
Reflectionone sign changes(−3, 4) → (−3, −4)
Worked examples
A coat costs 250 LE with 20% off. 20% of 250 = 50 LE. Sale price = 250 − 50 = 200 LE. 15% of 80 = 8 + 4 = 12.
Convert 2.4 km to metres: 2.4 × 1,000 = 2,400 m. Convert 72 km/h to m/s: 72 × 1,000 ÷ 3,600 = 20 m/s.
xy−6−5−4−3−2−1123456−6−5−4−3−2−11234560ABC
A(−5, 2) and B(3, 2) are on a horizontal line on opposite sides of the y-axis, so AB = 5 + 3 = 8. The reflection of C(−3, 4) across the x-axis is (−3, −4).
Class activity

Review poster. Make a small poster with one example of each idea: percent, conversion and reflection. Use your own numbers and show the steps.

Practice
1
Find 35% of 60.
2
18 is 30% of a number. Find the number.
3
Change 4,500 g into kilograms.
4
Change 54 km/h into m/s.
5
Reflect (−2, −5) across the y-axis, and find the distance from (−2, −5) to (−2, 4).