Mathematics, grade 4

Example

1. Draw a number line from 0 to 1 marked in eighths and ask them to start at three eighths and jump four eighths further.
2. Ask for seven eighths minus three eighths on the same number line, then check it against a paper strip folded into eighths.

Example

1. Ask for 312.47 plus 58.90 using the standard algorithm, lining up the decimal points first.
2. A campsite bill comes to $84.35 and you hand over $100. Ask for the change, worked out by subtracting.

Example

1. Three water bottles hold 20 fluid ounces each and four bags of trail mix have a mass of 250 grams each. Ask for the total volume of water and the total mass of the food.
2. A drive runs 118 miles in 2 hours 15 minutes, then 65 more miles after a 40-minute stop. Ask for the total distance and the total time.
3. A campsite costs $28 a night for 5 nights. Ask for the total bill.

Example

1. Ask what fraction matches 0.7, and what decimal matches three tenths.
2. Ask what fraction matches 0.35, and what decimal matches 42 hundredths.

Example

1. Ask them to write three fourths as a sum of three one-fourths.
2. Ask them to write nine fourths as a sum of fourths, and notice that it takes more than four of them.

Example

1. Ask for two different ways to break five sixths into a sum of sixths — for example one sixth plus four sixths, and two sixths plus three sixths.
2. Cut a strip into eighths and ask for two different sums of eighths that both equal six eighths.

Example

1. Ask whether two thirds and eight twelfths are equal, and how they can check it.
2. Fold one strip into fourths and a same-size strip into eighths, shade one fourth and two eighths, and ask whether the shaded amount matches.

Example

1. Ask which is bigger, three fourths or five sixths, and which symbol goes between them.
2. Ask which is bigger, two fifths or three eighths, and how they decided without drawing a picture.

Example

1. Before adding three eighths and one eighth, ask them to guess whether the answer lands closer to one half or closer to one whole, then check.
2. Before subtracting seven eighths minus five eighths, ask them to guess whether the answer lands closer to zero or closer to one fourth, then check.

Example

1. Draw a line from 0 to 1 and ask them to mark both three tenths and 0.3 on it, then ask what they notice.
2. Draw a line from 0 to 1 and ask them to mark 0.75 and three fourths on it.

Example

1. Count hours of daylight at camp over five days, including one half-hour reading, and ask them to put the counts on a dot plot marked in halves.
2. Record the miles hiked each day as whole numbers with one half-mile day, and ask them to build a stem-and-leaf plot.

Example

1. From a dot plot of daily high temperatures, ask how many more days landed above a marked line than below it.
2. From a frequency table of gas fill-ups in gallons, one of them a decimal amount, ask for the total across two stops.
3. From a dot plot of daily hiking miles marked in halves, ask how much farther the longest day ran than the shortest.

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. Draw a circle with a wedge cut out like a slice of pie and ask them to point to the angle at the vertex and say that its measure is how much of the circle that slice takes up.
2. Draw two angles, one a thin sliver and one nearly half the circle, and ask which one takes up more of the circle and why.

Example

1. Ask how many degrees are in a whole circle, then how many in half of it, and how they got there by dividing.
2. Ask what fraction of the circle a 90-degree angle cuts out, working from 90 out of 360.

Example

1. Hand over a protractor and an angle drawn on paper and ask them to line up the base and read the measure to the nearest whole degree.
2. Draw an angle that lands between two marks on the protractor and ask which whole number it sits closer to.

Example

1. Ask them to use a protractor to draw a 55-degree angle from a starting ray.
2. Ask for a 120-degree angle drawn from the same ray, then which of the two angles is wider.

Example

1. Draw two adjacent angles that together form a straight line, tell them one measures 65 degrees, and ask for the other.
2. Draw two adjacent angles sharing a ray that together measure 100 degrees, tell them one is 38 degrees, and ask for the other.

Example

1. Ask which is larger, a foot or a yard, and how many feet make a yard.
2. Ask which is larger, a liter or a milliliter, and about how many milliliters fill a liter.

Example

1. Give a table showing 1 foot equals 12 inches and ask how many inches are in 5 feet.
2. Give a table showing 1 kilogram equals 1,000 grams and ask how many kilograms 3,000 grams make.

Example

1. Ask them to make $0.85 out of quarters and a dime, and say what the 8 and the 5 each stand for.
2. Ask them to shade 0.7 on a strip cut into ten equal parts, then shade 0.34 on a grid of 100 squares.

Example

1. Ask what's better about a piggy bank than a savings account, and what's worse about each.
2. Ask why a savings account that pays interest beats a jar for money that sits untouched a year.

Example

1. Hand over $10 of chore money and ask them to split it three ways: spending now, saving toward something bigger, including college, and giving away.
2. Ask them to explain why they picked those three amounts.

Example

1. Ask what a bank does with money it holds for people, and how that helps someone who wants to borrow.
2. Ask why a family might keep money at a bank instead of in a box at home.

Example

1. Ask for 3,214 times 6 using the standard algorithm.
2. Ask for 34 times 27 two ways: with partial products, then with the standard algorithm.

Example

1. Draw an area model for 1,236 divided by 4 and ask them to fill in the missing side.
2. Ask them to write 2,408 divided by 8 as an equation before they solve it.

Example

1. Ask for 4,536 divided by 7 using the standard algorithm.
2. Ask for 3,050 divided by 5, then to check the answer by multiplying back.

Example

1. A cooler holds 6 rows of 7 water bottles. Ask how many bottles fill it.
2. One box holds 6 rows of 7 juice pouches, and 3 more come out of a second box. Ask how many pouches there are in total.
3. Fifty sandwiches get split evenly into 6 coolers, with the leftovers going in one bag. Ask how many go in each cooler and how many are left over.

Example

1. Write 402,617,000 and ask them to expand it as 400,000,000 + 2,000,000 + 600,000 + 10,000 + 7,000.
2. Write 3.58 and ask what the 5 and the 8 are each worth, then ask them to write it as 3 + 0.5 + 0.08.

Example

1. Round 748,362 to the nearest ten thousand, then round the same number to the nearest hundred thousand, and ask what changed.
2. Round 6,449 to the nearest hundred and ask which two hundreds it sits between.

Example

1. Ask for 36 x 10, then 36 x 100, and what pattern they notice in the zeros.
2. Ask for 4 x 100 and 40 x 10 back to back, and whether the two answers turn out the same.

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 rectangular fire-ring pad measures 12 feet by 7 feet. Ask for the perimeter of edging needed and the area of gravel needed to cover it.
2. A garden plot has a perimeter of 30 feet and one side of 9 feet. Ask them to find the missing side, then the area.

Example

1. Draw a 9-by-5 rectangle and ask them to add all four sides, then check that against 2 x 9 plus 2 x 5, and say why the two match.
2. Draw a square pad 6 feet on a side and ask why 4 times 6 gives the same perimeter as adding four 6s.
3. Draw a 9-by-5 rectangle split into unit squares and ask them to count the squares, then check that against 9 times 5.

Example

1. Hand over a paper heart, an uneven triangle, and a regular hexagon. Ask them to fold or draw every line of symmetry each shape has, including none if there is none.
2. Draw a scalene triangle and ask them to look for a line of symmetry, then explain why it has none.

Example

1. Draw three triangles — one with a square corner, one with all sharp corners, one with one wide corner — and ask them to sort right, acute, and obtuse using the square corner as the test.
2. Hand over the corner of an index card and ask them to check each triangle's widest angle against it before naming the triangle.

Example

1. Draw a rectangle, a rhombus, a trapezoid, and a kite and ask which ones have a pair of parallel sides and which have a right angle.
2. Give a mixed stack of quadrilaterals and ask them to sort by "has a perpendicular corner" versus "does not," checking each corner.