## CONCEPTUAL UNDERSTANDING

• The base 10 place value system can be extended to represent magnitude and numbers in two directions.

## Knowledge:

• Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
• Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
• Read, write, and compare decimals to thousandths.
• Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
• Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• Use place value understanding to round decimals to any place.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.

## CONCEPTUAL UNDERSTANDING

• The operations of addition, subtraction, multiplication and division are related to each other and are used to process information to solve problems of whole and part whole numbers.

## Knowledge:

• Selects and uses the appropriate mental, written and inventive strategies for addition and subtraction, multiplication and division of multi digit numbers and with decimals to 100th.

Knowledge:

• All multiplication/division facts
• All basic facts knowledge within 100

Strategies

• Using standard algorithm
• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
• Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

## CONCEPTUAL UNDERSTANDING

• Fractions and decimals are ways of representing whole-part relationships.
• Ratios are a comparison of two numbers or quantities.

## Knowledge:

Read, write, and compare decimals to thousandths.

## Fractions:

Strategies:

• Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd)
• Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = ⅓.
• For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
• Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

## Decimals:

Strategies:

• Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

## CONCEPTUAL UNDERSTANDING

Van Hiele Level 2.

• students begin to think about the properties of shapes without focusing on one particular object E.g. if all 4 angles are right angles it must be a rectangle.
• Use logical reasoning “Why?” “What if?”
• Students analyse the relationships between properties e.g. if a quadrilateral has 4 right angles, it also has diagonals of the same length.

## Knowledge:

Shape: Classify two-dimensional figures into categories based on their properties.

• Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
• Classify two-dimensional figures in a hierarchy based on properties.

Space: Graphing Coordinate Planes:

• Graph points on the coordinate plane to solve real-world and mathematical problems.
• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
• Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

## Knowledge:

• Convert like measurement units within a given measurement system.
• Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Geometric measurement:

• Recognize volume as an attribute of solid figures and understand concepts of volume measurement.A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
• A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
• Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
• Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
• Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
• Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

TIme:

• Determines time world wide

## Knowledge:

• Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction
• Use equivalent number sentences involving multiplication and division to find unknown quantities

## INTRODUCTION TO ALGEBRA

• Explain square numbers and triangular numbers
• Represent patterns using tables, graphs, words, and symbolic rules
• Select appropriate methods to analyze linear patterns
• Solve for x
• Represent pattern rule by using a function machine
• Predict the nth number
• Record the rule of a pattern (growing, linear) as a simple algebraic formula
• Use brackets and order of operations to solve number sentences
• Follow the rules of a function by plugging outcomes back into the function (iteration)
• Begin simple graphing of functions using the cartesian plane
• Use functions to solve problems

## Knowledge:

### Data Handling:

• Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations of fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

### Chance:

• List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions
• Recognise that probabilities range from 0 to 1