Count what you find outside
Leaves, steps, raindrops and garden beds all hold numbers. Build the skills to measure and make sense of them.
Place value and numbers
Each digit has a value that depends on its place. In 4,729 the digit 4 means 4,000 only because of where it sits.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 4 | 7 | 2 | 9 |
4,729 = 4,000 + 700 + 20 + 9. This is called expanded form.
Comparing numbers
Start from the left-most place. 4,729 > 4,692 because 7 hundreds is more than 6 hundreds.
Addition and subtraction
Adding
Line up the places and add from the ones. If a column reaches 10 or more, carry to the next place.
368 + 475 = 843
Subtracting
Subtract from the ones. If the top digit is too small, regroup from the next place.
602 − 278 = 324
Check your work: addition and subtraction undo each other. If 368 + 475 = 843, then 843 − 475 must equal 368.
Multiplication and division
Multiplication is repeated addition: 4 × 3 means four groups of three. Division shares a total into equal groups or finds how many groups fit.
Times table helper
Tricks
- ×2: double it.
- ×5: answers end in 0 or 5.
- ×9: the digits of the answer add up to 9 (9 × 4 = 36, and 3 + 6 = 9).
- ×10: add a zero.
Fractions
A fraction names equal parts of a whole. In 3/4, the bottom number (denominator) says how many equal parts, and the top number (numerator) says how many we have.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
Equivalent fractions
Multiply or divide the top and bottom by the same number. 1/2 = 2/4 = 4/8 = 50/100.
Adding fractions with the same denominator
Add the numerators and keep the denominator: 2/8 + 3/8 = 5/8.
Geometry and measurement
Perimeter
Distance around a shape. Rectangle: 2 × (length + width).
Area
Space inside a shape. Rectangle: length × width.
Volume
Space inside a solid. Box: length × width × height.
| Shape | Sides | Fact |
|---|---|---|
| Triangle | 3 | Angles add to 180° |
| Square | 4 | All sides equal, 4 right angles |
| Pentagon | 5 | Angles add to 540° |
| Hexagon | 6 | Honeycomb cells |
Word problems
- Read the whole problem and say it in your own words.
- Underline the question and circle the numbers.
- Choose an operation: total means add, left means subtract, groups mean multiply, sharing means divide.
- Solve, then check that your answer makes sense.
A class has 6 tables with 4 students each. 3 students are absent. How many students are present?
6 × 4 = 24, then 24 − 3 = 21.
Practice generator
Choose a type and answer as many as you like.