Numeracy

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