Math strategies A–Z
Your kid came home talking about "number bonds" or "making ten"? Look it up here. Each page explains it in plain English and shows how it compares to the way you learned it.
A
- Area modelThe area model is a way to multiply by drawing a rectangle, splitting each number into tens and ones, and multiplying the smaller pieces. Adding the pieces gives the answer, so 23 × 14 becomes 200 + 30 + 80 + 12 = 322.
C
- Common denominatorsTo add or subtract fractions with different denominators, kids rename them so the pieces are the same size. 1/2 + 1/3 becomes 3/6 + 2/6, which is 5/6. Fraction strips or drawings show why the renamed fractions are equal.
- Coordinate gridA coordinate grid is two number lines that cross at zero. An ordered pair like (3, 4) gives a point's address: start at (0, 0), go over 3 along the bottom (the x-axis), then up 4 (the y-axis).
D
- Decimal gridsA decimal grid is a 10-by-10 square that stands for 1 whole. Each column is one tenth (0.1) and each small square is one hundredth (0.01). Kids shade squares to see decimals and to add, subtract, and multiply them.
- Dividing with unit fractionsIn 5th grade, kids divide only with unit fractions (fractions with 1 on top, like 1/3). They answer two kinds of questions with drawings: "How many 1/3s fit in 4?" (12) and "If 1/2 is shared by 3 people, how much does each get?" (1/6).
F
- Fractions as divisionIn 5th grade, kids learn that a fraction is a division problem: 3/4 means 3 ÷ 4. If 3 pizzas are shared equally by 4 people, each person gets 3/4 of a pizza.
L
- Line plots with fractionsA line plot shows data on a number line, with an X above the line for each measurement. In 4th and 5th grade the measurements are fractions like 1/8, 1/4, and 1/2, so kids also practice adding and comparing fractions to answer questions about the data.
M
- Measurement conversion tablesKids use two-column tables to convert between units in the same system, like feet and inches or meters and centimeters. The table shows the pattern (1 foot = 12 inches, 2 feet = 24 inches) so they can see when to multiply and when to divide.
- Multiplying as scalingScaling means thinking of multiplication as resizing. Multiplying by a fraction less than 1 shrinks a number, multiplying by a fraction greater than 1 stretches it, and multiplying by 1 keeps it the same. Kids can predict the size of an answer before they calculate it.
N
- Number bondsA number bond is a simple picture that shows how a number breaks into two parts. The whole goes in the top circle, and the two parts go in the circles below it, like 10 splitting into 6 and 4.
O
- Open number lineAn open number line is a blank line your kid draws to add or subtract by making "jumps". Instead of stacking numbers, they hop from one number to the next in friendly chunks, like jumping to the next ten.
- Order of operations (GEMS)The order of operations is the agreed order for working out a math problem: grouping symbols first, then exponents, then multiplication and division, then addition and subtraction. Many schools now teach it as GEMS instead of PEMDAS.
P
- Partial quotientsPartial quotients is a way to divide by taking away easy chunks, like 10 or 20 groups of the divisor at a time, and keeping track of how many groups you took. Add up the groups at the end, and that is the answer.
- Place value chart (powers of 10)When you multiply by 10, every digit moves one place to the left on a place value chart, because each place is worth 10 times the place to its right. Dividing by 10 moves every digit one place to the right. The decimal point stays where it is.
R
- Rounding on a number lineTo round on a number line, kids write the two "neighbor" numbers the number sits between, mark the halfway point, and see which neighbor it is closer to. 3.47 sits between 3.4 and 3.5, past the halfway point of 3.45, so it rounds to 3.5.
S
- Shape hierarchyA shape hierarchy is a family tree for shapes. Every shape in a group has all the features of the groups above it. A square has 4 right angles, so it is a rectangle, and it has 4 equal sides, so it is a rhombus too.
T
- Tape diagramsA tape diagram (also called a bar model) is a rectangle split into equal parts that shows how the numbers in a word problem fit together. For "3/8 of 24 stickers", kids draw a bar for 24, split it into 8 parts of 3, and shade 3 parts: 9 stickers.
V
- Volume as layers of cubesVolume is how many unit cubes fit inside a solid. Kids count the cubes in one layer (length × width), then multiply by the number of layers (height). That is where the volume formula V = length × width × height comes from.