National Curriculum Primary School Learning Outcomes in ... · Addition and subtraction: use formal...

$: National Curriculum Primary School Learning Outcomes in ... · Addition and subtraction: use formal algorithm up to 5-digits; develop formal algorithm for proper fractions with like$
For Use in 2019-2020

National Curriculum Primary School Learning Outcomes in Mathematics

Standard 2 to Standard 6

Learning Outcomes for Middle and Upper Division Mathematics

Strand: Numbers and Number Operations

Counting and Sequencing

Count and sequence numbers, reading and writing numbers in a variety of ways.

Standard 2:

Count up to 10,000: start and end at any two given numbers.1.13

Read, write and match numbers up to 10,000 using numerals and words.1.14

Standard 3:

Read and write numbers up to 100,000 using numerals and words.1.15

Standard 4:

Read and write numbers up to 1,000,000.1.16

Standard 5:

Read and write numbers up to 10,000,000.1.17

Standard 6:

Read and write numbers up to 1,000,000,000.1.18

Place Value

Use place value to understand our number system and other systems.

Standard 2:

Use place value to sequence a set of numbers: ascending and descending; order up to 10,000.

2.6

Standard 2:

Express numbers up to 10,000 in usual and expanded form.2.5

Standard 3:

Express numbers up to 100,000 in usual and expanded form.2.7

Give the value of a number based on position: for example, in 9,341 the 3 has a value of 300.2.8

Standard 4:

Use place value to recognize difference between two numbers: for example, 8,537 is 400 less than 8,937 because the hundreds place values differ by 4.

2.9

Use place value to recognize the advantage of a positional number system over a character based system in a historical comparison of relevant number systems.

2.10

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Standard 5:

Express large numbers using scientific notation.2.11

Use place value to express numbers in bases other than 10: use bases smaller and larger than 10.

2.12

Standard 6:

Express small numbers using scientific notation: every place value is 10x smaller than the place value to the left.

2.13

Use place values to convert between bases: to and from base 10 (bases smaller and larger than base 10); between two bases other than base 10

2.14

Integers

Use and work with integers to show both size and direction.

Standard 2:

Introduce situations in which students encounter the concept of directed number: temperature, elevation.

3.4

Standard 3:

Extend number line to show negative numbers.3.5

Standard 4:

Use number line to sequence directed numbers: integers in ascending and descending order.3.6

Use objects / pictorials to represent and solve problems involving small negative integers.3.7

Standard 5:

Use number line to show positive and negative numbers: integers, decimals and fractions.3.8

Standard 5:

Use negative numbers to solve problems.3.9

Standard 6:

Use negative numbers in the solution of word problems.3.10

Solve problems involving absolute value.3.11

Fractions and Decimals

Work fluently with fractions and decimals.




Standard 2:

Express decimal numbers in usual and expanded form: tenths.4.7

Recognize equivalent forms of common fractions and decimals.4.8

Standard 2:

Compare and sequence fractions and decimals: use models and number line to judge size; fractions with like denominators and equivalent fractions with different denominators; recognize simplified form of proper fractions.

4.6

Standard 3:

Compare and sequence fractions and decimals: fractions with unlike denominators; decimals up to hundredths.

4.9

Recognize equivalent forms of given fractions and decimals: include equivalent forms of improper fractions and mixed numbers; introduce percent as fraction with denominator of 100.

4.10

Standard 4:

Compare and sequence mixed numbers, decimals and percents: fractions with like and unlike denominators; decimals up to thousandths.

4.11

Standard 4:

Write equivalent forms of given fraction: introduce use of LCM / LCD; write mixed numbers as improper fractions and vice versa; reduce fractions to simplest form.

4.12

Standard 4:

Use percent to represent common everyday situations.4.13

Standard 5:

Recognize equivalent forms of decimal, fraction, percent.4.14

Standard 6:

Solve problems involving fractions, decimals and percents.4.15

Number Operation Concepts

Understand meanings of number operations and how they relate to one another.

Standard 2:

Use inverse property of operations to complete or rewrite sentences.6.7




Standard 3:

Express repeated multiplication as powers.6.8

Standard 4:

Express repeated division as roots.6.9

Standard 5:

Investigate associative, distributive and commutative properties.6.10

Number Operations and Computation

Compute fluently with basic operations using integers, fractions and decimals.

Standard 2:

Addition and subtraction: develop formal algorithm up to 3-digit numbers with and without regrouping; use objects / pictorials to show addition and subtraction of simple fractions and decimals (concrete).

7.6

Standard 2:

Multiply and divide whole numbers: develop formal algorithm.7.7

Standard 3:

Multiplication and division: use formal algorithm with whole numbers up to 5-digits; develop formal algorithm for simple fractions; extend formal algorithm for multiplication and division of whole numbers to decimals (tenths).

7.9

Standard 3:

Addition and subtraction: use formal algorithm up to 5-digits; develop formal algorithm for proper fractions with like denominators; add and subtract decimals with and without regrouping; add and subtract with negative numbers (do concrete).

7.8

Standard 4:

Multiply and divide integers, fractions and decimals.7.11

Standard 4:

Use ratio to compare quantities.7.12

Standard 4:

Add and subtract: develop formal algorithms for working with integers, especially negative values; add and subtract fractions with unlike denominators; add and subtract decimals (positive and negative); expand powers with same base to add or subtract.

7.10




Standard 5:

Perform computation which combine operations: use parenthesis; order of operations; use associative, commutative, distributive properties to simplify operations.

7.13

Multiply and divide using exponents: develop formal rules to handle indices.7.15

Standard 5:

Identify and work with ratios in real-life problem solving: include working with scales, conversions, percents; simplify ratios.

7.14

Standard 6:

Solve problems involving proportions.7.17

Standard 6:

Combine operations that require conversions between types of fractions and decimals.7.16

Estimates and Approximations

Make reasonable estimates and approximations

Standard 2:

Use rounding-off to the nearest hundreds to estimate solutions to computations.8.4

Standard 3:

Estimate size of fraction: is about the same as, is smaller than, is bigger than.8.5

Standard 4:

Round-off decimals to the nearest tenth.8.6

Standard 5:

Round-off decimals to the nearest hundredth and thousandth.8.7

Standard 6:

Use appropriate rounding-off to record solutions to problems: level of accuracy.8.8

Mental Math

Use mental math techniques creatively.

Standard 2:

Develop multiplication facts: patterns for 2-digit multiplicands with multipliers 0, 1, 2, 3, 5, 9, 10.

9.4




Standard 3:

Use variety of techniques to do mental multiplication and division: move decimal point to the left or right when multiplying or dividing by 10; multiply by 'half and double': for example, 12x6=12x3x2=36x2=72; use multiplication facts for 0 - 12.

9.5

Standard 4:

Use variety of techniques for adding a series of small numbers: re-arrange; use benchmark sums, for example, numbers that sum to multiples of 10; use rounding-off, for example 547+98 = 547+100-2 = 647-2 = 645.

9.6

Standard 5:

Use variety of techniques to simplify multiplication: use factors, for example, 32x6 = (30x6)+(2x6) = 180+12=192); multiply by reciprocal (patterns for fractions with denominator of 7, 9, 11).

9.7

Standard 6:

Use shortcuts for multiplying by specific numbers.9.8



Strand: Patterns and Relationships

Number Patterns

Understand and work with patterns (repeating, increasing, decreasing, and numerical).

Standard 2:

Use tables and charts to identify, describe and represent patterns or sorting rules.10.6

Standard 3:

Use representations of patterns to solve problems.10.7

Standard 4:

Use pattern rules to predict subsequent element(s) in a series or sequence of numbers.10.8

Standard 5:

Describe patterns represented in graphs and series of abstract symbols.10.9

Standard 6:

Describe rule used to complete a pattern based on abstract symbols.10.10

Special Group Numbers

Explore number patterns to discover properties of special number groups.

Standard 2:

Investigate patterns when multiplying by 2, 3, 5, 8, 10.11.5

Standard 2:

Explore patterns for special number groups: for example, perfect squares, prime and composite numbers; use symbols for union and intersection.

11.4

Standard 3:

Investigate patterns when multiplying by 4, 6, 7, 9, 11, 12.11.6

Standard 3:

Explore LCM and HCF: use Venn diagram to present multiples and factors.11.7

Standard 4:

Investigate patterns with fractions: especially sevenths, ninths, elevenths.11.9

Standard 4:

Explore divisibility rules for division by single digits.11.8




Standard 4:

Investigate growing, shrinking and repeating patterns involving translations.11.10

Standard 5:

Explore rational and irrational numbers.11.11

Standard 5:

Investigate arithmetic progressions.11.12

Standard 6:

Investigate number patterns based on single operations.11.13

Investigate geometric progressions.11.14

Relations, Functions and Graphs

Understand relations, functions and graphs.

Standard 2:

Use graphs and charts to show mathematical relationships: for example, arithmetic properties.

12.4

Standard 3:

Identify instances of arithmetic properties and use rules in computation.12.6

Standard 3:

Use mathematical relationships to solve problems.12.5

Standard 4:

Use graphs and charts to show variation or change over time: include Venn diagrams for 2 sets.

12.7

Standard 5:

Use graphs to represent linear relationships between two variables: first quadrant.12.8

Standard 6:

Use a table of values to graph and interpret linear relations.12.9

Use graphs to investigate region represented by an inequality.12.10

Equations and Inequalities

Apply equations and inequalities in one variable to solve problems.




Standard 2:

Translate word statement into expressions using letter or symbol to represent unknown number.

13.2

Standard 3:

Use equations to describe simple word problems.13.3

Standard 3:

Use strategies to maintain equivalence: change subject of formula.13.4

Standard 4:

Solve equations in one variable: understand role of variables in equations: whole number coefficient and solution.

13.5

Standard 5:

Use an equation to represent a generalization arising from some relationship.13.6

Use an equation to solve a word problem.13.7

Solve equations with 2 or 3 variables, for example, if v+2=7 and v+2+w= 10 then v=5 and w=3; or If p+q=r, and p=3, q=4 then r=7.

13.8

Standard 6:

Substitute given values to evaluate an expression.13.9

Standard 6:

Solve simple equations and inequalities.13.10



Strand: Measurement

Measurement Applications

Apply measurement systems, techniques, tools and formulas moving fluently between related units.

Standard 2:

Estimate, measure, compare and record measures including fractional parts for metricand customary units: length, weight, volume, time, temperature.

15.9

Standard 2:

Estimate and determine elapsed time given the durations of events.15.10

Standard 3:

Recognize the need for larger and smaller units of measurements: length, weight, volume, time; compare units used in everyday items (packages, industry).

15.15

Standard 2:

Convert measurements from one system to another: length, weight, volume, time, temperature.

15.12

Standard 2:

Calculate perimeter of irregular shapes using metric and customary units.15.14

Standard 2:

Measures angle in degrees and name such angles (acute, right, obtuse, straight, scalene).15.11

Derive simple formulas for determining the area of common shapes.15.13

Standard 3:

Solve problems involving differences in temperature (positive and negative).15.17

Standard 4:

Measure lengths, weights, volumes, time, temperature with metric and customary unitsand convert among them: select appropriate unit and instrument.

15.19

Standard 3:

Use angles to describe rotation and properties of shapes and figures.15.16

Calculate area of composite and irregular shapes using metric and customary units.15.18

Standard 4:

Solve problems involving the relationship between a 12-hour clock and a 24-hour clock.15.20



Strand: Measurement

Standard 4:

Calculate surface area of common regular objects using metric and customary units identifying the appropriate units for the object in question.

15.21

Derive simple formulas for determining volume of common shapes.15.22

Standard 5:

Compare and sort lengths and weights within and between metric and customary units selecting appropriate unit for various items introduced.

15.23

Understand difference and relationship between weight and mass: through experiments.15.24

Standard 5:

Investigate how changing dimensions of a figure affect perimeter, area and volume.15.25

Standard 6:

Solve problems involving perimeter, area, surface area and volume.15.26



Strand: Spatial Relationships and Shapes

Properties of Shapes

Discover, analyze and use characteristics and properties of two- and three dimensional geometrical shapes to identify, describe, sketch and model.

Standard 2:

Construct triangles and quadrilaterals.16.10

Standard 3:

Construct circles and other polygons.16.13

Standard 2:

Classify triangles based on angle sizes.16.11

Sketch and match simple figures: match figure to given net or side, bottom and top views.16.12

Standard 3:

Draw right-prisms: parallel faces to include triangles, squares, rectangles, circles.16.17

Draw faces of 3-dimensional figures.16.18

Standard 3:

Describe circle based on the attributes of center, radius, diameter.16.14

Identify arcs and sectors.16.15

Identify rotational symmetry.16.16

Standard 4:

Sketch spheres and cones.16.19

Construct pyramids.16.20

Standard 5:

Recognize ratio between circumference and diameter of any circle.16.23

Standard 5:

Construct 2-dimensional shapes from specific dimensions for sides, diagonals, diameter, radius, altitude, angles.

16.21

Investigate relationships between interior angles and exterior angles in a triangle.16.22

Standard 5:

Construct compound 3-dimensional figures.16.24




Standard 6:

Investigate relationship between interior and exterior angles of quadrilaterals and other polygons.

16.25

Identify similar and congruent figures.16.27

Standard 6:

Apply Pythagoras theorem to right-angle triangles.16.26

Construct polyhedral using nets (2-dimensional patterns).16.28

Representation of Shapes

Use representational systems (Eg. coordinate system) to give location, describe spatial relationships, and explore symmetry and transformations.

Standard 2:

Make and test predications regarding transformations of plane geometric shapes.17.10

Standard 2:

Plot points using the first quadrant of the coordinate system.17.11

Standard 3:

Use coordinates to find position on a globe or map.17.12

Standard 4:

Use rectangular grid and ordered pairs to plot simple shapes and investigate vertical and horizontal distance and area.

17.14

Standard 3:

Formal transformations: translation, reflection, rotation.17.13

Standard 4:

Investigate tessellations of geometrical shapes.17.15

Plot on a rectangular grid the results of a reflection and translation.17.16

Standard 6:

Plot on a rectangular grid the results of a rotation.17.19

Standard 5:

Plot points on all four quadrants of a coordinate grid.17.17

Interpret scale drawings.17.18




Standard 6:

Apply concepts, properties, and relationships of adjacent, corresponding, vertical, alternate interior, complementary, and supplementary angles: figure out a missing angle.

17.21

Standard 6:

Bisect lines and angles: use of a Geometry Set.17.20



Strand: Data Handling and Probability

Data Collection and Organization

Collect, organize and display relevant data to answer questions related to real life situations.

Standard 2:

Use diagrams and set notation to describe data sets: differentiate between discrete and continuous data.

18.9

Standard 2:

Determine data inclusion using simple deductive reasoning and/or basic logic: use simple truth tables where appropriate.

18.10

Standard 3:

Use graphs to compare two sets of data: construct graphs with a variety of axes, scales and legends.

18.11

Identify data as qualitative or quantitative.18.12

Standard 4:

Understand precision, accuracy and error in measurement.18.14

Standard 4:

Represent data using a variety of graphical forms.18.13

Standard 5:

Construct circle graphs: discuss when circle graphs are appropriate.18.15

Apply Venn diagrams to three sets.18.16

Standard 6:

Determine appropriate data display method for given situation.18.17

Construct box plots.18.18

Collect and represent data from simple random samples.18.19

Data Analysis

Analyze, describe and summarize data using appropriate statistical methods and measures.

Standard 2:

Investigate measure of central tendency: median, mode.19.8

Standard 2:

Investigate characteristics of data sets: shape, distribution; use stem and leaf graphs.19.7




Standard 3:

Investigate measure of central tendency: mean.19.9

Investigate measure of dispersion: range19.10

Standard 4:

Interpret frequency tables, charts, and graphs.19.11

Compute mean, median, mode, range for a set of data.19.12

Standard 5:

Describe patterns in data including clusters, gaps and outliers.19.13

Interpret circle graphs and Venn diagrams.19.14

Standard 6:

Use scatter plot to determine trend.19.16

Standard 6:

Interpret data from box-plots (box-and-whisker plots).19.15

Standard 6:

Investigate how extremes and other factors affect measures of central tendency.19.18

Standard 6:

Discuss appropriateness of measures of central tendency.19.17

Interpret data from simple random samples.19.19

Probability

Investigate inferences and apply probability concepts in the solution of problems.

Standard 2:

Do experiments to determine simple probability: use tables to represent the sample space.20.5

Investigate arrangements of x items from a set of n items: differentiate permutations and combinations.

20.6

Standard 3:

Use tables and Venn diagrams to answer basic probability questions: apply probability concepts to real-life activities and games.

20.7

Derive and apply simple formula for probability: express probability as a fraction between 0 – 1 (inclusive).

20.8




Standard 4:

Use lists, tree diagrams, and tables to determine the possible combinations from two disjoint sets when choosing one item from each set.

20.9

Derive probability of complementary events.20.10

Standard 5:

Determine probability from data given in tables and graphs.20.11

Compare theoretical and experimental probability in real-life situations.20.12

Standard 6:

Make predictions based on data patterns.20.13

Use tree-diagrams to determine probability of multiple events.20.14


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