# CRITICAL CONCEPTS (Numeracy)

*The Critical Concepts listed below should be deeply understood at the end of each grade level. It is important to note, however, that these concepts only represent a portion of the curriculum being taught at each grade level.*

### Kindergarten

*Number sense: size of a number/quantity*

- Subitizing: recognizing a quantity without having to count
- Cardinality: the last number that you say is the quantity- not the name of the number
- Partitioning: breaking a number into parts example: 5 is 3 and 2; 4 and 1 etc
- Sequencing: being able to put numbers into order
- Conservation: recognizing that the quantity doesn’t change when you change the arrangement

### Grade 1

*Addition and Subtraction to 20*

- Understanding number to 20: sequencing, quantity etc
- Skip counting by 2’s and 5’s: counting multiples- vocabulary
- Strategies to add and subtract facts to 20: making 10, doubles, near doubles

### Grade 2

*Addition and Subtraction to 100*

- Solid understanding with facts to 20
- Skip counting by 2,5, and 10
- Skip counting by 10 starting at any number- very important
- Addition up to 100 (24+53; 27+48)
- Subtraction (56-34; 83-48)

### Grade 3

*Addition and Subtraction to 1000*

*Equations: finding an unknown value example x+7 = 13 ; also equations such as 6+7 = 3+x*

### Grade 4

*Multiplication: 2 digit x 1 digit and 3 digit x 1 digit*

- Multiplication facts
- Area model
- Distributive property

*Fractions and decimals*

- Decimals to the hundredths (0.12)
- Comparing fractions with common denominators
- Benchmarks of 0, 1/2, 1 (placing fractions on number lines using these benchmarks)
- Recognition that fractions must have equal sized pieces

### Grade 5

*Multiplication 2 digit x 2 digit*

- Area model
- Distributive property

*Division 3 digit ÷ 1 digit*

- 2 methods: repeated subtraction, decomposition

*Fractions*

- Building equivalent fractions, comparing and ordering fractions

*Area and perimeter*

- Finding area (relating to multiplication, and perimeter-putting a fence around the outside)

### Grade 6

*Fractions, decimals, ratio, percent*

- Improper fractions- also called fractions greater than 1, and mixed numbers
- Discounts, %

*Factors and multiples*

- GCF greatest common factor, factor trees
- Multiples

### Grade 7

*Integers*

- Addition, subtraction, multiplication, division with integers (positive and negative numbers)

*Equations*

- 2 step equations such as 3x – 4 = 8

*Proportional reasoning*

- Discounts
- Ratios
- Finding missing parts: eg 3% of 1800

### Grade 8

*Fractions*

- Addition, subtraction, multiplication, division using fractions

*Equations*

- Including integer coefficients eg -2x + 3 = -9

*Pythagorean theorem*

- c^2 = a^2 + b^2 for right triangles

### Grade 9

*Order of operations*

- Exponents
- Exponent laws

Example a^m x a^n = a ^(m+n)

*Polynomials: gathering like terms and simplifying*

Example 2x + 6 – (3x – 9)

*Equations: Solving multi-step equations with rational coefficients*