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