# 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

• 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

• 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)

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

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

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)

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

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

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

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