الرياضيات (بالإنجليزية) الصف السادس الابتدائي، الأسبوع 9: Writing an equation that links two quantities

Dependent and independent variables

الأسبوع 9 · المتغيران التابع والمستقل: العلاقات والقواعد · 3 دروس

Writing an equation that links two quantities

Discover Mathematics P6: Term 1, Unit 5, Lessons 1–2

GoalWrite an equation for a story and find the rule from a table.

New words

rule · what we do to the input to get the outputtable of values · a table of inputs and the outputs they giveequation · the rule written with letters, like y = 5x

Explanation

To write an equation for a story: first name the independent variable (input) and the dependent variable (output) with letters. Then find the rule: what do we do to the input to get the output? If we multiply, the equation looks like y = 5x. If we add, it looks like y = x + 4, as when one person is 4 years older than another. Sometimes there are two steps, like y = 5x + 10 for a fixed fee plus a price for each ride. To find a rule from a table, look at how the output changes when the input goes up by 1.

ƒFormula

y = 5x

y changes by 5 each time x goes up by 1

Worked examples

h	1	2	6
w = 40h	40	80	240

A worker is paid 40 LE for each hour. With h hours worked, the wage is w = 40h. For 6 hours: 40 × 6 = 240 LE.

d	5	10	12
m = d + 25	30	35	37

Mariam is 25 years older than her daughter. If the daughter is d years old, Mariam is m = d + 25. When d = 10, m = 35. The difference of 25 years never changes.

Table	x = 1	x = 2	x = 3	x = 4
First, y	7	14	21	28
Second, y	6	7	8	—

Finding rules from tables. First table: the output goes 7, 14, 21, 28, so each time it grows by 7: y = 7x. Second table: 6, 7, 8, so it grows by 1 and starts at 6 when x = 1: y = x + 5.

Class activity

Rule riddles. A grown-up secretly picks a rule such as “multiply by 3” and says only the outputs for the inputs you give. You give 1, 2 and 5. Write the table, find the rule and write the equation. Then swap and choose a rule that adds.

Practice

A pump moves 12 litres each minute. Write an equation for the litres l after m minutes.

Rana is 4 years older than her brother. His age is b. Write Rana’s age r.

Find the rule: x = 2, 4, 6, 8 gives y = 6, 12, 18, 24.

Find the rule: x = 1, 2, 3 gives y = 4, 5, 6.

A playground charges 10 LE to enter and 5 LE for each ride r. Write the cost c and find it for 4 rides.