Mathematics, grade 6

Example

1. Ask for -6 plus 11, -6 minus 11, -6 times 11, and -66 divided by 11.
2. Ask for 8 minus -3 and -8 minus 3, and notice the two answers are not the same.

Example

1. Write three fourths and ask them to work out 3 divided by 4, then say what the fraction bar was doing all along.
2. Write 7 over 2 and ask for its value as a division, then as a mixed number.

Example

1. Ask whether 48 times three fourths comes out bigger or smaller than 48, before working anything out.
2. Ask whether 20 times five fourths comes out bigger or smaller than 20, then work it out to check.
3. Ask them to sort one half, five fourths, and 1 into growers and shrinkers for multiplication, then test each one on 60.

Example

1. Shade 30 squares of a 10-by-10 grid and ask them to name the shaded part as a ratio, a fraction, a decimal, and a percent.
2. Ask them to show 1 to 4 with counters, then write it as a fraction and a decimal.

Example

1. Shade 25 squares of a 10-by-10 grid and ask what fraction and what percent that is.
2. Shade one third of a strip diagram and ask what benchmark percent it matches.
3. On a number line from 0 to 100, ask them to mark 1%, 10%, 50%, and 75%, and name the fraction each one matches.

Example

1. A $40 shirt is marked 25% off. Ask for the discount three ways: as a fraction of 40, as a decimal times 40, and in dollars.
2. Ask them to write three fourths as a decimal and a percent first, then work out how many cents three quarters of a dollar is.

Example

1. Shade one half of one circle, two fourths of a second, and five tenths of a third, and ask what the three shadings share.
2. Ask them to write 0.2 as a fraction and a percent, then shade that share of a grid.

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. Give the rules y = 3x and y = x + 3 with tables for x = 1 through 4, and ask which one grows by adding and which by multiplying.
2. Graph y = 2x and y = x + 2 on the same axes and ask them to say in words how the two lines climb differently.

Example

1. A map uses 1 inch for every 25 miles. Ask them to build a table for 1, 2, 3, and 4 inches, graph the pairs, then read off the miles for 3.5 inches.
2. A recipe for 2 doubles to serve 6. Ask for the scale factor, then set up the proportion that scales one ingredient and apply it to the rest.

Example

1. Show a table of hours driven and miles covered and ask which quantity depends on the other.
2. Show a graph of a plant’s height over weeks and ask which axis holds the independent quantity.

Example

1. A taxi charges $3 plus $2 a mile. Ask them to describe it in words, make a table for 1 through 4 miles, graph the pairs, and write the equation.
2. A recipe triples cups of flour per bag of sugar. Ask for the table, the graph, and the equation, each in the form the rule names.

Example

1. Ask them to plot (2, 3), (3, -2), (-4, 5), and (-1.5, -2.5), naming the quadrant each one lands in.
2. Ask them to plot (0, 4) and (2.5, 0) and say why neither point sits inside any quadrant.

Example

1. Give the values 12, 13, 13, 15, 18, and 21 and ask for a dot plot.
2. Give the same six values and ask for a stem-and-leaf plot, then a histogram, then a box plot.

Example

1. Show a dot plot bunched at 6 through 8 with one point out at 20, and ask what that single point does to the center, the spread, and the shape.

Example

1. Give the data 4, 6, 7, 7, and 11 and ask for the mean, the median, and the range, then ask what the three say about the center, the spread, and the shape.
2. Give the data 2, 5, 6, 8, 9, and 12 and ask for the median and the interquartile range, then ask what the two say about the center and the spread.

Example

1. Take a vote on favorite fruit and ask for the mode, a relative frequency table, and a percent bar graph of the result, then ask what the three summaries say about how the vote split.

Example

1. Show a box plot of quiz scores with the median marked and ask what share of the class scored above it.
2. Show a histogram of daily temperatures and ask which range holds the most days.
3. Show a dot plot of pets per family and ask how many families have more than two pets, then show a stem-and-leaf plot of spelling scores and ask for the highest score and how many scored above 90.

Example

1. Ask whether "the ages of dogs at a shelter" yields data with variability, and whether "the number of days in June" does.

Example

1. Ask how many inches are in 5 feet, set up as a proportion.
2. A recipe calls for 3 quarts of water. Ask how many gallons that is, worked out with a unit rate.

Example

1. Give two angles of a triangle, 50° and 60°, and ask for the third.
2. Ask whether sides 3, 4, and 8 can form a triangle, and why not.
3. Give a triangle with sides 5, 5, and 8 and ask which two angles are equal.

Example

1. Ask them to name five ways to pay for college — savings, grants, scholarships, student loans, work-study — and sort them into money earned, money given, and money borrowed.

Example

1. Compare a $45,000 delivery-driver salary needing no post-secondary schooling with a $55,000 electrician salary needing a two-year certificate and a $65,000 nursing salary needing a four-year degree, and ask for the lifetime gaps over 40 years.
2. Ask how that gap changes if the higher-paying job needs four years of tuition paid first.

Example

1. Ask for 6 divided by one half, then for 6 times 2, and ask what they notice about the two answers.
2. Ask for two thirds divided by four fifths two ways: by the division, and by multiplying two thirds by five fourths.

Example

1. Ask for three eighths times four ninths.
2. Ask for 2.5 divided by 0.5, then for 5 times 0.5, and ask what they notice about the two answers.

Example

1. A hiker covers 9 miles in 3 hours. Ask for the rate as a quotient, in miles per hour.
2. A faucet fills 20 gallons in 4 minutes. Ask for the unit rate and what each single unit means.

Example

1. Ask them to explain the difference between a debit card and a credit card: whose money moves in each case.
2. Show a $20 purchase made both ways and ask what happens to the bank balance that same day in each case.

Example

1. Ask them to explain why a landlord or a lender cares about on-time payments going back years. Listen for the future looking at the past.

Example

1. Show a sample credit report and ask what kinds of information appear on it, and how long each kind stays.

Example

1. Ask what a lender learns from a credit report that a borrower cannot just say about themselves.

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. Two bags of trail mix sell at the same price: one holds 12 ounces, the other 18. Ask which is the better buy and how they know without dividing.
2. A car covers 240 miles on 8 gallons. Ask how far it goes on 12 gallons at the same rate.

Example

1. 30 campers are 25% of the group. Ask for the whole group, using a strip diagram cut into fourths.
2. Ask for 10% of an $80 bill, then for what percent $20 is of $80.

Example

1. Model x + 6 = 14 with tiles and ask for x.
2. A rectangle has area 36 and length 9. Ask them to model 9w = 36 with a drawing and solve for the width.

Example

1. Cut a paper parallelogram and rearrange it into a rectangle, then ask what that says about its area formula.
2. Fit two copies of a triangle together into a parallelogram, then ask what that says about the triangle’s area formula.
3. Cut a paper trapezoid into two triangles and ask what the two triangle areas add up to say about the trapezoid’s area formula.

Example

1. A rectangle measures 4.5 by 2. Ask for the equation that gives its area.
2. A right rectangular prism measures 3 by 2 by 5. Ask for the equation that gives its volume.
3. A parallelogram has base 6 and height 4, a trapezoid has bases 6 and 10 and height 4, and a triangle has base 7.5 and height 4. Ask for the equation that gives each area.

Example

1. A trapezoid has bases 6 and 10 and height 4. Ask for its area.
2. A triangle has base 7.5 and height 4. Ask for its area.
3. A rectangle measures 4.5 by 2, a parallelogram has base 6 and height 4, and a right rectangular prism measures 3 by 2 by 5. Ask for each area and the volume.