Educational Designer

Makes the incorrect assumption that a percent increase/decrease means the calculation must include an addition/subtraction

For example: 40.85 + 0.6 or 40.85 + 1.6 (Q1).

A single multiplication by 1.06 is enough.

Or: 56.99 − 0.45 or 56.99 − 1.45 (Q2).

A single multiplication by 0.55 is enough.

• Does your answer make sense? Can you check that it is correct?
• “Compared to last year 50% more people attended the festival.” What does this mean? Describe in words how you can work out how many people attended the festival this year. Give me an example.
• In a sale an item is marked “50% off.” What does this mean? Describe in words how you calculate the price of an item in the sale. Give me an example.
• Can you express the increase/decrease as a single multiplication?

Converts the percent to a decimal incorrectly

For example: 40.85 × 0.6 (Q1).

• How can you write 50% as a decimal?
• How can you write 5% as a decimal?

Uses an inefficient method

For example: The student calculates 1%, then multiplies by 6 to find 6% and then adds this answer on: (40.85 ÷ 100) × 6 + 40.85 (Q1).

Or: 56.99 × 0.45 = ANS, then 56.99 − ANS (Q2).

A single multiplication is enough.

• Can you think of a method that reduces the number of calculator key presses?
• How can you show your calculation with just one step?

Is unable to calculate percent change

For example: 450 − 350 = 100% (Q3).

Or: The difference is calculated, then the student does not know how to proceed or he/she divides by 450 (Q3).

The calculation (450 − 350) ÷ 350 × 100 is correct.

• Are you calculating the percent change to the amount $350 or to the amount $450?
• If the price of a t-shirt increased by $6, describe in words how you could calculate the percent change. Give me an example. Use the same method in Q3.

Subtracts percents

For example: 25 − 20 = 5% (Q4)

Because we are combining multipliers: 0.8 × 1.25 = 1, there is no overall change in prices.

• Make up the price of an item and check to see if your answer is correct.

Fails to use brackets in the calculation

For example: 450 – 350 ÷ 350 × 100 (Q4).

• In your problem, what operation will the calculator carry out first?

Misinterprets what needs to be included in the answer For example: The answer is just operator symbols.

• If you just entered these symbols into your calculator would you get the correct answer?

Has difficulty getting started

• What do you know? What do you need to find out?
• How could you simplify the problem?

Ignores the units

For example: The student calculates the volume of a matchstick in cubic inches and the volume of the tree trunk in cubic feet.

• What measurements are given?
• Does your answer seem reasonable if you consider the size of a matchstick compared to the size of a pine tree?

Makes incorrect assumptions

For example: The student multiplies the volume of the tree trunk in cubic feet by 12 and assumes this gives the volume of the tree trunk in cubic inches.

• Can you explain why you have multiplied by 12?
• When you figure out a volume how many dimensions do you multiply together? How does this calculation effect how you convert the volume from cubic feet to cubic inches?
• Can you describe the dimensions of the tree in inches? What do you notice?

Uses an inappropriate formula

For example: The student calculates the surface area of a rectangular prism from the dimensions given for the tree.

• Does your choice of formula make good use of all the wood in the tree trunk?
• Is this the best model for a tree trunk?
• What is the difference between area and volume?

Works unsystematically

• Would someone in your class who has not used this method be able to follow your work?
• Can you describe your method as a series of logical steps?

Work is poorly presented

For example: The student underlines numbers and it is left to the reader to work out why this is the answer as opposed to any other calculation.

• Can you explain each part of your solution?
• What does each of these calculations represent?
• Can you justify the choices you have made?

Difficulty substituting into a formula

For example: The student multiplies the radius by 2, rather than squaring, when using the formula for the volume of a cone/cylinder.

Or: The student substitutes diameter rather than radius into the formula for the volume of a cone/cylinder.

• What is the difference in meaning between 2r and r²?
• Does your answer seem reasonable?
• How can you check your work against the information given in the problem?