Mathematics, grade 3

Example

1. A sign says 462 miles to the next park. After 175 miles, ask how far is left, then ask again after another 130.
2. Ask for 703 - 268 and listen for whether they can explain the regrouping, not just do it.

Example

1. Before adding 287 and 412, ask them to round each to the nearest 100 and say roughly what to expect.
2. Ask them to round 68 and 34 to the nearest 10 before subtracting, then ask how close the estimate landed.

Example

1. Ask them to show 4 x 6 three ways: as repeated addition, as an array, and as equal jumps on a number line.
2. Ask them to skip count by fours up to 24 and say how many jumps it took.

Example

1. Give a two-step story about a drive and ask for the equation before the answer.
2. Ask them to draw the same story on a number line: 340 miles, then 155 more, then how far short of 600.

Example

1. A fuel stop takes 25 minutes and the next stop takes 40. Ask how long both come to together.
2. A hike is planned for 50 minutes and 15 have gone by. Ask them to show the rest on a clock face and say how many minutes are left.

Example

1. Cut one paper strip into thirds and another into sixths, and ask them to shade two thirds on the first and five sixths on the second.
2. Draw a number line from 0 to 1 and ask them to mark one half, then three fourths, then seven eighths.

Example

1. Draw a line from 0 to 1 divided into eighths, mark one point on it, and ask them to name the fraction that sits there.
2. Do it again with the line divided into halves, then thirds, then fourths, then sixths.

Example

1. Fold a sheet into six equal parts, point at one part, and ask what to call it and why the six matters.
2. Ask what the bottom number of one eighth is telling them about the whole.

Example

1. Ask them to write three fourths as a sum of fourths.
2. Break a cracker into sixths, put five pieces on the table, and ask what fraction is there and how many one-sixths it took.

Example

1. Cut one granola bar so three people get equal shares, and ask them to name one share.
2. Draw three sandwiches shared fairly among eight people and ask them to shade what one person gets.

Example

1. Fold one strip into halves, one into fourths, and one into eighths, line all three up, and ask which shaded pieces match.
2. Draw two number lines from 0 to 1, one in thirds and one in sixths, and ask for a point that lands on both.

Example

1. Mark two fourths and one half on the same number line and ask them to say why those are the same number.
2. Shade one fourth of one circle and two eighths of a same-size circle, and ask whether the shaded amount is equal and how they can tell.

Example

1. Ask which is bigger, three eighths or five eighths, and why.
2. Ask which is bigger, two thirds or two eighths, and ask them to write the symbol between them.

Example

1. Cut two identical squares of paper into fourths, one with straight cuts and one with diagonals, and ask whether every piece is still one fourth.
2. Ask them to name one piece as a fraction of the whole square, then ask whether equal shares are always the same shape.

Example

1. Draw a line from 0 to 2 and ask them to mark one half, then three fourths, then seven eighths, measuring from zero each time.
2. Point at five eighths on the line and ask how far that is from zero, not which tick it sits on.

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. Count four kinds of vehicle at a rest stop, then ask them to put the counts in a frequency table and a dot plot.
2. Ask them to draw a bar graph of the same counts with each square standing for five.

Example

1. Show a pictograph where one symbol stands for 10 and ask how many more there are of one category than another.
2. Off the same graph, ask a two-step question: how many in two categories together, then how many fewer that is than a third.

Example

1. Ask them to measure every side of the picnic table and say the distance all the way around.
2. Say a four-sided figure has a perimeter of 30 inches and three sides of 9, 6, and 9 inches, and ask for the fourth side.

Example

1. Hold up a water jug and a bag of apples and ask which one you would weigh and which one you would measure by volume.
2. Ask which of the two tells you more about what fits in a cooler, and why.

Example

1. Hand over two dollar bills, three quarters, and four dimes and ask for the total.
2. Empty the change out of the cup holder onto the seat and ask what it comes to.

Example

1. Ask what a ranger does all day and how that work turns into a paycheck.
2. Ask what a person would learn or practice to get paid more for the same hours.

Example

1. After a gas-station stop, go down the receipt and ask which things were planned and which were not.
2. Point at the unplanned one and ask what it was good for, and what you gave up to buy it.

Example

1. Ask for three reasons to leave money in the jar instead of spending it, and whether college is one of them.
2. Ask what saving $5 a week comes to by the end of a month, and what that pile is for.

Example

1. Read out five choices — taking a job, buying a snack, putting money in a jar, borrowing from you, dropping a coin in a donation box — and ask which is income, spending, saving, credit, and charitable giving.
2. Hand over $10 of chore money and ask them to say what part is for spending, what part is for saving, and what part is for giving away.

Example

1. Ask 7 x 8 and 6 x 9 in the car with no paper. Listen for an answer in a couple of seconds, not a count.
2. Right after 7 x 8, ask for 56 divided by 8.

Example

1. Ask for 34 x 6, then ask them to do it a second way with partial products.
2. Ask for 48 x 5 and listen for whether they break the 48 apart or go straight to the standard algorithm.

Example

1. Ask for 63 divided by 9, then ask which multiplication fact they used to get there.
2. Write 8 x ? = 48 and ask them to say the division fact that answers it.

Example

1. Nine campsites hold four tents each. Ask how many tents that is, then how many are still to go up if 30 are already standing.
2. Ask how many packs of six water bottles it takes to fill a cooler that holds 42.

Example

1. Tell a story about 5 rows of 8 camp chairs and ask them to draw the array and write the equation.
2. Ask them to draw a strip diagram for 48 crackers split among 6 people before they say the answer.

Example

1. Write 4 x 15 and ask them to say it out loud as a comparison, not as a total.
2. Say one tent sleeps 3 people and the group is 5 times that, and ask for the expression.

Example

1. Write 6 x ? = 42 and ask for the missing number, then ask how they found it.
2. Write 56 divided by 7 = ? and ask which multiplication fact gives the answer.

Example

1. Draw a rectangle five squares across and four squares down, ask for the area, and listen for a multiplication rather than a count.
2. Ask how many square feet of tarp covers a floor 7 feet by 6 feet, and listen for whether the answer carries a unit.

Example

1. Ask why a person hands over a card when the thing they want costs more than the cash in their pocket, and who pays the store that day.
2. Ask what a person owes back on a $20 loan, and why it comes to more than $20.

Example

1. Write 34,208 and ask how many ten thousands, thousands, hundreds, tens, and ones it holds, then ask them to write it as 30,000 + 4,000 + 200 + 8.
2. Ask how many hundreds are in 4,300, then how many tens are in the same number.

Example

1. Point at the two 4s in 44,000 and ask what makes the left one worth ten times the other.
2. Ask how many hundreds it takes to make one thousand, then how many thousands make one hundred thousand.

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. Put out a party hat, a soup can, a ball, a wedge-shaped block, a shoebox, and a die. Ask them to sort the pile and name each group: cone, cylinder, sphere, triangular prism, rectangular prism, cube.
2. Draw a triangle, a square, a pentagon, and a hexagon, and ask them to sort those by number of sides and name each one.
3. Ask what makes a cube a rectangular prism as well, using the words faces, edges, and vertices.

Example

1. Draw a rhombus, a parallelogram, a trapezoid, a rectangle, and a square. Ask them to name each and say what makes all five quadrilaterals.
2. Ask them to draw a four-sided figure that is none of those five, and explain why it still counts as a quadrilateral.

Example

1. Draw an L-shaped room, ask them to cut it into two rectangles with one line, find the area of each, then the whole.
2. Ask whether the two rectangles overlap anywhere, and why that matters to the total.