Remediation sheet · Mathematics 9

Per What?

Term 1 · Week 7 · Slope as a rate of change
NameDate
For the teacher. This is for a learner giving a bare number for a rate, or naming the starting amount as the slope. It is not a shortened copy of worksheet.html — it is a different route to the same competency, starting further back. Task 4 is the first table on worksheet.html. Show each worked example first and let the learner copy the method, never the answer. If task 1 will not come: If task 1 will not come, use money and days. The units say themselves and the arithmetic gets out of the way.

1Fill the table — targets seeing a constant rate before naming one

Say: “How much does it change each step?”

Worked example. A tin gains ₱20 each week: 20, 40, 60, 80. The change each step is 20.
  1. Week: 1, 2, 3, 4   Amount: 15, 30, ______, ______   Change each week: ______
  2. Day: 1, 2, 3, 4   Litres: 50, 45, ______, ______   Change each day: ______

2Say the unit — targets a slope given as a bare number

Say: “Per what? Two words, not one.”

Worked example. Not "20". ₱20 per week. A rate without its unit is not an answer.
  1. The tin: ______ per ______
  2. The water: ______ per ______
  3. ₱96 for 8 kilos of rice: ______ per ______

3Which is the rate? — targets the intercept read as the slope

Say: “One of these is a starting amount. It is not a rate.”

Worked example. "₱30 to get in, then ₱12 a kilo." The rate is ₱12 per kilo. The ₱30 is where it starts.
  1. "₱50 deposit, then ₱8 a day." Rate: ______ per ______ Starting amount: ______
  2. In y = 12x + 30, the rate is attached to the ______, so the rate is ______

4Falling counts too — targets a negative slope read as a mistake

Say: “Is it going up or down? Keep the sign.”

Worked example. A drum losing 5 litres a day has a rate of −5 litres per day. Negative is the description, not an error.
  1. The water table above: rate = ______ litres per day
  2. Circle one: a negative rate means a mistake / something falling

Answer key — not printed on the learner's copy

  1. 45, 60 — change 15 · 40, 35 — change −5
  2. ₱15 per week · −5 litres per day · ₱12 per kilo
  3. ₱8 per day, starting ₱50 · attached to the x, so 12
  4. −5 litres per day · something falling