Part A — Bar Models for Problem Solving
A bar model turns a word problem into a picture. Splitting a bar into equal parts, or drawing two bars side by side, makes it clear whether to multiply, divide, add or subtract.
1
The bar above shows 4 equal parts making 240. What is the value of one part?
Answer:
2
Draw your own bar for this: 3 equal parts make 180. What is one part worth? What are two parts worth?
3
2/5 of a number is 30. Draw a bar split into fifths to find the whole number.
4
Comparison bars. Anna has $40 more than Ben. Together they have $150. Draw two bars and find how much each has.
5
A ribbon 240 cm long is cut into two pieces so that one piece is three times as long as the other. Use a bar model to find both lengths.
6
Open challenge. Invent a word problem that can be solved with a bar model and whose answer is exactly 60. Draw the bar and write the problem.
Part B — Working Through the Modelling Cycle
Real problems are messy. Mathematicians use a modelling cycle: pose the problem, make sensible assumptions, do the mathematics, check whether the answer makes sense, then communicate it — looping back if it does not.
1
A school needs buses for 250 students. Each bus holds 48 students. Work through the cycle:
(a) Assumptions: what are you assuming?
(b) Calculate: how many buses?
(c) Check: would 5 buses be enough? Explain.
2
Estimation model. About how many students could stand in your classroom if there were no furniture? State your assumptions (e.g. floor area, space per student) and show your calculation.
3
A model says “a 12-year-old grows about 6 cm per year.” List two assumptions this model makes, and one reason it might not be accurate for a real person.
4
Your own model. Choose one question below, then outline how you would model it: the steps, the assumptions, and the calculation you would do.
- How much water does our class drink in a week?
- How many pizzas to feed the whole year group?
- How long would it take to count to a million?