Mathematics, grade 7

Example

1. Ask for -2.5 plus 4, -2.5 minus 4, -2.5 times 4, and -10 divided by 4.
2. Ask for three fourths divided by one half, and one half divided by three fourths, and notice the two answers are not reverses of each other.

Example

1. A recipe needs 2.5 cups of flour and the batch doubles. Ask how much flour that takes, and what operation answered it.
2. The temperature falls 3.5 degrees each hour for 4 hours from 10 degrees. Ask for the final temperature.

Example

1. Ask them to show 6 x 7 two ways: with a drawing, and with a number sentence.
2. Ask them to explain a division out loud, without pointing at the page.

Example

1. A car travels at 60 miles an hour. Ask them to show that rate as a picture, a table, a sentence, a pair of numbers, a graph, and an equation.
2. Give d = 45t and ask what the 45 means in words, and where it shows on the graph.

Example

1. Pull a marble from a bag of 3 red and 2 blue, 20 times with replacement, and ask what the results predict for 100 pulls.
2. Flip two coins 40 times and ask what the data predicts about HH versus the other outcomes.

Example

1. Survey 20 students and find 12 prefer tacos. Ask what that predicts for a school of 500.
2. Ask what could make that prediction wrong: who was asked, and how they were picked.

Example

1. Show a circle graph of a $100 budget split 50/25/25 and ask what share each slice owns, part-to-whole and then part-to-part.
2. Show a bar graph of pets per household and ask which category doubles another.
3. Show a dot plot of books read per month and ask for a part-to-part comparison of two counts plus an equivalent restatement.

Example

1. Roll a die 60 times, tally the sixes, and ask how the experimental share compares with the theoretical one sixth.
2. Draw the sample space for two coins, then flip 40 times and compare the HH share with one fourth.

Example

1. A plant is 5 cm tall and grows 2 cm a week. Ask them to describe it in words, build a table for weeks 0 through 3, graph the pairs, and write the equation.
2. Give a table pairing 0, 1, 2, and 3 with 4, 7, 10, and 13, and ask for the graph and the equation in y = mx + b form.

Example

1. Show comparative dot plots of two classes’ quiz scores and ask which class centers higher and which spreads wider.
2. Show two box plots of race times and ask them to compare the shapes, the centers, and the spreads.

Example

1. Survey 20 students and find 12 prefer tacos. Ask what that predicts for a school of 500.
2. Ask what could make that prediction wrong: who was asked, and how they were picked.

Example

1. Sample 30 sparrows in each of two parks and find mean wingspans of 3.1 and 3.4 inches. Ask what informal inference that supports about the two populations.

Example

1. Ask how many kilometers are in 5 miles, set up as a proportion with 1 mile ≈ 1.61 kilometers.
2. A bottle holds 2 liters. Ask how many fluid ounces that is, worked out with a unit rate of about 34 ounces per liter.

Example

1. A $40 book carries 8% sales tax. Ask for the tax and the total.
2. A worker earns $500 a week with 10% withheld for income tax. Ask for the take-home pay.

Example

1. Give a $2,000 monthly budget — $800 housing, $400 food, $300 savings, $200 taxes, $300 other — and ask what percent each category is of the whole.
2. Ask them to list the parts a personal budget needs: income, planned savings for college, retirement, and emergencies, taxes, and fixed and variable expenses.

Example

1. A $50 shirt rises 20% then falls 20%. Ask for the final price, and whether it lands back at $50.
2. A savings account holds $200 and earns 5% in a year. Ask for the balance at year’s end.

Example

1. Give a two-step problem and ask what they would do first, before any arithmetic happens.
2. After an answer, ask why it is reasonable. Listen for a reason rather than a re-check of the steps.

Example

1. Ask for 5 x 60 and watch whether they reach for paper. Reaching for it at this size is the thing worth noticing.
2. Ask which is easier for 47 x 6, mental math or writing it down, and why.

Example

1. A scale drawing uses 1 cm for 2 meters. A room measures 4 cm by 6 cm on paper. Ask for the real floor area.
2. Two triangles are similar with matching sides 3 and 9. Ask for the side matching a side of 4.

Example

1. Flip a coin 10 times, then ask them to predict the next 10 twice: once qualitatively ("about half") and once quantitatively ("about 5 heads"), and compare the two predictions.

Example

1. A rectangular prism measures 4 by 3 by 5 and a triangular prism has base area 10 and height 6. Ask for each volume.
2. A triangular pyramid has base area 12 and height 9 and a rectangular pyramid has base area 20 and height 6. Ask for each volume.

Example

1. Draw the net of a rectangular prism 3 by 2 by 4 and ask for the lateral and total surface area from it.
2. A triangular prism’s net shows two triangular faces of area 6 and three rectangular faces of areas 10, 12, and 14. Ask for the total surface area.
3. A rectangular pyramid has a 4-by-4 base and four triangular faces of area 10 each, and a triangular pyramid has four triangular faces of areas 6, 6, 8, and 8. Ask for the lateral and total surface area of each from its net.

Example

1. Give two rectangles, 3-by-6 and 5-by-10, and ask whether they are similar and what the side ratios say.
2. Give a 4-by-4 square and a 4-by-6 rectangle and ask what fails the similarity test.

Example

1. Measure three lids of different sizes, divide each circumference by its diameter, and ask what they notice about the three answers.
2. Ask them to explain what π means as a ratio, in one sentence.

Example

1. Cut a paper circle into wedges and rearrange them into a near-parallelogram, and ask what the length and the width of that shape stand for.
2. Measure the circumference and diameter of three cans with string, ask what the three ratios share, and what formula for the circumference that gives.

Example

1. A circle has radius 7. Ask for its circumference and its area.
2. A circle has diameter 10. Ask for its area.

Example

1. A figure joins a 6-by-4 rectangle with a semicircle of diameter 4. Ask for the total area.
2. A shape joins a 5-by-5 square with a parallelogram of base 5 and height 3. Ask for the total area.
3. A figure joins a quarter circle of radius 5 with a trapezoid with bases 6 and 10 and height 4 and a triangle with base 6 and height 5. Ask for the total area.

Example

1. A triangle has angles x, 2x, and 3x. Ask them to write the equation and solve it.
2. Two angles on a straight line measure x + 10 and 3x - 30. Ask them to write and solve the equation for x.