Grade 3 Math Outcomes

NUMBER & PLACE VALUE

CONCEPTUAL UNDERSTANDING

  • The base 10 place value system is used to represent numbers and number relationships.
  • Numbers are a naming system.
  • Numbers can be used in many ways for different purposes in the real world.

Knowledge

  • Use the language of mathematics to count, order and compare numbers up to 10,000 for example on a number line.
  • Recognise, model, read, write and order numbers to represent quantities in real-life situations up to 10,000.
  • Estimate quantities up to 1,000
  • Round numbers to the nearest 10, 100, or 1000
  • Model numbers up to 10,000 using the base ten place value system by regrouping. E.g. 9,999 (9 thousands, 9 hundreds, 9 tens and 9 ones)

OPERATIONS

CONCEPTUAL UNDERSTANDING

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

Select and use the appropriate mental, written and inventive strategies for addition and subtraction involving up to three digit numbers, and multiplication and division up to double digit and single digit numbers up to 20 e.g 16x4.

Knowledge

  • Addition and subtraction facts involving double and single digits numbers e.g 27-4 or 74-8

Addition & Subtraction e.g. 346+182

Strategies:

  • Estimation
  • Using manipulatives
  • Place value (300+100+40+80, 6+8)
  • Rounding (346+(200) -12)
  • Making tens and compensating (350+182 -6)
  • Use of algorithm*

*delay until invented strategies are secure.

Without Regrouping e.g. 347-132

  • Place value (340-130)(7-2)
  • Reversibility (adding up) 132+?= 347

With regrouping e.g. 373-146

  • Take tens then ones (373-100=273)( 273-40=233)(233-6=227)
  • Compensating (373-150=223) (223+4=227)
  • Reversibility (adding up) 373+__ =146

Multiplication & Division

Knowledge

  • Efficiently recall multiplication and division facts to 10.

Strategies e.g. 14x7

  • Uses knowledge of multiplication and division facts.
  • Place value(10x7)+(4x7)
  • Compensation (10x4) - (3x4)
  • Using area models.
  • Algorithms for double and single digit numbers (as checking and when using numbers flexibly is secure)

PROPORTIONS & RATIOS

CONCEPTUAL UNDERSTANDING

  • Fractions are ways of representing whole- part relationships.

Knowledge

  • Read, use and model fractions ½, ¼, ⅓ up to 1/10th in real-life situations.
  • Order fractions with like denominators.

Strategies: (Note: using visual representations)

  • Use number knowledge to find fractions of whole numbers, E.g. ¾ of 12 is 9
  • Recognize and generate simple equivalent fractions, E.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent using materials.
  • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers, E.g. 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
  • Compare two fractions with the same numerator or the same denominator with the symbols >, =, or <, and justify the conclusions, E..g. by using a visual fraction models.


SHAPE & SPACE

CONCEPTUAL UNDERSTANDING

Van Hiele Level 1

  • Classify shapes
  • Know the properties of shapes
  • Identify shapes by describing their parts
  • Think about all shapes with a class of shape e.g. all rectangles not just the common ones.
  • Understand what makes a rectangle a rectangle or a square a square.

Knowledge

Shape:

  • Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
  • Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
  • Identify symmetry in the environment including tessellations.

Shapes: cubes, cylinders, cones, spheres, polygons, quadrilaterals, rectangular prisms, square-based pyramids.

Space:

  • Create and interpret simple grid maps to show position and pathways using coordinates.
  • I can use scales, legends, and directions to interpret information contained in basic maps.

MEASUREMENT

CONCEPTUAL UNDERSTANDING

  • Objects and events have attributes that can be measured using appropriate tools.
  • Relationships exist between standard units that measure the same attributes.

Knowledge

Measure and estimate lengths in standard units.

  • Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and litres (l).

Geometric Measurement:

  • Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
  • Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Time

  • Tell time to the minute and investigate the relationship between units of time

PATTERN & FUNCTION

CONCEPTUAL UNDERSTANDING

  • Functions are relationships or rules that uniquely associate members of one set with members of another set.
  • By analysing patterns and identifying rules for patterns it is possible to make predictions.

Knowledge

  • Describe, continue, and create number patterns resulting from performing addition or subtraction and multiplication and division.

DATA HANDLING & CHANCE

CONCEPTUAL UNDERSTANDING

  • Information can be expressed as organized and structured data
  • Objects and events can be organized in different ways.
  • Some events in daily life are more likely to happen than others.

Knowledge

Data Handling

  • Design a survey and systematically collect, organize and display data in pictographs and bar graphs
  • Select appropriate graph form(s) to display data interpret range and scale on graphs.
  • Interpret range and scale on graphs.
  • Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
  • Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Chance

  • Conduct chance experiments, such as tossing a coin or rolling a dice, identify and describe possible outcomes (possible, likely, unlikely, fair, unfair) and recognise variation in results.