Mathematics, grade 7

Example

1. A campground charges $32 a night. Ask what four nights comes to, then hand over the receipt and ask whether it matches.
2. Ask how many packs of 8 water bottles it takes to get 40 bottles into the cooler.

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. 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. Ask them to keep a tally of something on a drive and turn it into a table at the end.

Example

1. Ask what 6 x 4 has to do with 6 x 40.
2. Ask why knowing 5 x 8 helps with 6 x 8.

Example

1. Ask them to convince you that one third is bigger than one fourth, using the word "parts". Listen for whether the bigger bottom number pulls them the wrong way.

Example

1. Draw a Venn diagram of whole numbers, integers, and rational numbers, and ask them to place -8, 0, 6, two thirds, and -3.4 where each one belongs.
2. Give the set {-2, 0, 1/2, 5} and ask which members are integers and which are only rational.

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. 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. A 12-ounce box costs $3. Ask for the price per ounce.
2. A printer makes 80 pages in 4 minutes. Ask for the unit rate and what one unit of it means.

Example

1. A table pairs 2 pounds with $6 and 5 pounds with $15. Ask for k and what it means in the story.
2. Give y = 4x and ask for the constant of proportionality.

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. 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. 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. 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 two coins and ask them to list every outcome, then draw the tree that shows the same four.
2. Roll a single die. Ask for the sample space as a list.

Example

1. Toss a coin 30 times by hand and run 300 tosses in a spreadsheet, then ask which result sits nearer one half.
2. Roll two dice 50 times by hand and 500 times in a spreadsheet, then ask which share of sevens sits nearer one sixth.

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. A bag holds 3 red and 2 blue marbles. Ask for the theoretical probability of red, then compare it with 20 pulls.
2. Ask for the theoretical probability of HH when flipping two coins.

Example

1. The chance of rain is 0.3. Ask for the chance of no rain, and how the two are related.
2. A spinner lands on blue one fourth of the time. Ask for the probability it does not, and what the two add to.

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. 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. 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. Fill a rectangular pyramid with rice and pour it into the matching prism with the same base and height. Ask how many pours it takes, and what that says about the two formulas.

Example

1. Ask them to say in words and in symbols why a triangular pyramid holds one third of its matching prism with the same base and height.

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 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. 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. 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. A plumber charges $40 plus $25 an hour, and a bill comes to $115. Ask for the two-step equation for hours h.
2. A club has 45 members and needs at least 60. Ask for the inequality for additional signups n.

Example

1. Ask them to solve 2x + 1 = 7 first, then graph the solution on a number line.
2. Ask them to graph 3x - 2 ≤ 10 on a number line, with the circle filled or open as it belongs.

Example

1. Give 2n + 5 = 17 and ask for a story it could tell.
2. Give 3p - 4 > 11 and ask for a real situation it fits.

Example

1. Model 2x + 3 = 13 with tiles and ask for x.
2. Model 3n - 4 ≤ 11 and ask for the solution set.

Example

1. Ask whether 4 makes 2x + 3 = 11 true, and whether it makes 2x + 3 > 11 true.
2. Ask which of 2, 3, and 6 make 3n - 9 ≥ 0 true.

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.

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. 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. List assets of $1,500 and liabilities of $900. Ask them to organize the record and build the net worth statement.
2. Ask what goes on the assets side of the record versus the liabilities side.

Example

1. Look up a family budget estimator for your city and ask what minimum budget and hourly wage it gives for a family of four.

Example

1. Put $100 in an account at 5% simple interest and $100 at 5% compounded yearly. Ask them to compare the two balances after 3 years.
2. Ask which of the two earns more over 10 years, and by about how much.

Example

1. A $60 game is 20% off in one store and $15 off by mail rebate in another. Ask which saves more.
2. A coupon takes $5 off $25. Ask whether that beats a 10% sale on the same $25.