Shapes, Arrays, Even and Odd, and Equal Shares: Grade 2 Study Guide
Grade 2 prepares children for multiplication with arrays, and for fractions with equal shares.
Children identify shapes by their attributes: triangles, quadrilaterals (4 sides), pentagons (5), hexagons (6) and cubes. They draw shapes with given features, such as 'a shape with 4 sides and 4 equal angles'.
They also meet arrays, which are objects in equal rows and columns, and learn to write them as repeated addition: 3 rows of 5 is 5 + 5 + 5 = 15. This prepares them for multiplication in Grade 3.
Even and odd numbers
A number is even if it can be split into two equal groups or paired with nothing left over (2, 4, 6, 8, 10…). It is odd if one object is left over (1, 3, 5, 7, 9…). Look at the ones digit: 0, 2, 4, 6 or 8 means even. Doubles are always even: 6 + 6 = 12.
Arrays
An array with 4 rows and 3 columns has 12 objects. The equation is 3 + 3 + 3 + 3 = 12 (adding the rows) or 4 + 4 + 4 = 12 (adding the columns). Arrays show that the order does not change the total.
| Array | Repeated addition | Total |
|---|---|---|
| 2 rows of 5 | 5 + 5 | 10 |
| 3 rows of 4 | 4 + 4 + 4 | 12 |
| 4 rows of 5 | 5 + 5 + 5 + 5 | 20 |
Equal shares
Halves, thirds and fourths describe equal shares of a whole. Half of = 2 equal shares, a third of = 3 equal shares and a fourth (or quarter) of = 4 equal shares. The shares must be the same size, but they can look different: a square can be halved by a vertical, horizontal or diagonal line. More shares mean smaller shares.
A rectangle.
3 for thirds.
Make 3 equal parts.
Do the parts have the same area?
Worked examples and common mistakes
Example: Is 17 odd or even? Odd, since the ones digit is 7. Example: Write the equation for 3 rows of 6: 6 + 6 + 6 = 18. Common mistakes: counting a pair as one, drawing unequal parts as 'halves' and thinking a bigger number of shares is a bigger piece. Fold paper to prove shares are equal.
Check your understanding: model answers
1. Even, since it ends in 4. 2. 3 + 3 + 3 + 3 + 3 = 15. 3. Draw two lines to make three equal parts.
✨ Key Takeaways
- Even numbers can be paired; odd numbers have one left over.
- Arrays show repeated addition.
- Halves, thirds and fourths are equal shares.
- More shares make smaller shares.
💬 Questions for Discussion & Reflection
- Is 24 even or odd?
- Write an addition equation for 5 rows of 3.
- Split a rectangle into thirds.
Print graph paper for arrays →