Mathematics
PRE-SCHOOL 3
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Measurement
Understand and apply the tools and concepts of measurement
1. Length
a.
Identify attributes of real objects; longer, shorter
2. Mass
a.
Identify attributes of real objects and situations; heavier, lighter
3. Volume and Capacity
a.
Identify attributes of real objects; full, empty
4. Time
a.
Identify events in their daily routine; before, after, bedtime, story time, today, tomorrow
5. Temperature
a.
Identify attributes of real objects; hotter, colder
Shape and Space
Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Properties of Shape
a.
Begin to sort 2D shapes
b. Begin to describe and sort real life 3D shapes according to attributes such as size or form
2. Position and movement
a.
Begin to explore the paths, regions and boundaries of their immediate environment (inside, outside) and their
position (under, beside, next to down, in, in front of, on)
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Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Is aware that a graph is a source of data collection using real objects
b. Sort objects by attribute (e.g. colour)
2. Chance and probability
a. Begin to discuss and identify outcomes that will happen, won’t happen and might happen
Mathematics
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Pattern
a.
Begin to find simple patterns
b. Begin to create a simple pattern, using real objects
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a.
Count and order numbers to 10
b. Read and write numbers to 5
c.
Estimate quantities to 5
d. Use 1:1 correspondence
e.
Begin to model number relationships to 5
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Mathematics
PRE-SCHOOL 4
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Measurement
Understand and apply the tools and concepts of measurement
1. Length
a. Identify attributes of real objects; longer, shorter
2. Mass
a. Identify attributes of real objects and situations; heavier, lighter
3. Volume and Capacity
a. Identify attributes of real objects; full, empty
4. Time
a. Identify events in their daily routine; before, after, bedtime, story time, today, tomorrow, days of the week
5. Temperature
a. Identify attributes of real objects; hotter, colder
Shape and Space
Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Properties of shape
a. Begin to sort and label 2D shapes
b. Sort and describe real life 3-D shapes according to attributes such as size or form
2. Position and Movement
a.
Explore the paths, regions and boundaries of their immediate environment, (inside, outside, above, below) and their
position (next to, behind, in front of, up, down)
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Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Sort and begin to label real objects into sets by similar attributes (e.g. colour and shape)
b. Begin to create graphs using real life objects
2. Chance and probability
a. Discuss and identify outcomes that will happen, won’t happen and might happen
Mathematics
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Pattern
a. Find and describe simple patterns
b. Create and describe a simple pattern using real objects
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a. Count and order numbers to 20
b. Read and write numbers to 10
c. Model number relationships to 5
d. Estimate quantities to 10
e. Use 1:1 correspondence
f. Begin to explore the conservation of number through the use of manipulative
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Mathematics
KINDY
Subject: MATHEMATICS
Strand
Data Management
Measurement
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Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Is aware of the concept of graphing data
b. Sort and label into sets by one or more attributes
c. Is able to interpret a pictograph or bar graph
d. Create a graph of real objects and compare quantities using number words
e. Discuss and compare data represented in a teacher-generated Venn diagram
2. Chance and probability
a. Is introduced to the vocabulary of probability; impossible, certain
Understand and apply the tools and concepts of measurement
1. Length, Perimeter and Area
a. Compare lengths and know words like ‘longest, shortest, tallest
b. Estimate, compare and measure objects using non-standard units
c. Explore the concept of area (how much space is being taken up; more/less)
2. Mass
a. Compare weights and know words like ‘heavy, heavier, light and lighter’
b. Use a balance to compare weights of objects
c. Estimate and begin to compare and measure objects using non-standard units
3. Volume & Capacity
a. Compare and order capacities of objects and know words like ‘this holds more’ etc
b. Estimate and begin to compare and measure capacities using non-standard units
4. Time
a. Know morning, afternoon and evening and activities they do at these times
b. Name and order days of the week and understand there are 12 months in a year
c. Become familiar with the calendar
d. Order events with respect to time and how long they take and know terms like ‘this takes more time/less time’
e. Can tell the time to the hour on analogue and digital clock, and
f. Begin to match the time between analogue and digital
5. Temperature
a. Know and use terms like hotter & cooler
Mathematics
Shape and Space
Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and angle
a. Recognize straight and curved line
2. 2D and 3D Shape
a. Sort and label 2D shapes using correct mathematical vocabulary; (sides, corners, circle, square, rectangle, triangle)
b. Describe, compare 2D shapes according to attributes such as size or form (e.g. big, small, triangle, circle, square,
rectangle)
c. Create a picture using 2D shapes
d. Introduced to 3D shapes e.g. cube/box, sphere/ball
3. Transformation/Symmetry
a.
Introduced to symmetry
b. Create simple symmetrical designs
c.
Begin to find and explain symmetry in their immediate environment
4. Location and Position
a.
Give and follow simple directions related to movement and position
b. Explore and describe the paths, regions and boundaries of their immediate environment (inside, outside, above,
below) and their position (next to, behind, in front of, up, down)
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Pattern
a. Find and describe simple patterns
b. Create simple patterns using real objects
c. Create and extend patterns
d. Recognize and extend patterns in numbers; skip counting, 2’s, 10’s
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a.
Count, compare and order numbers to 20
b. Read and write and model numbers to 20
c.
Use the language of mathematics; more, less, number names, total
d. Use 1:1 correspondence
e.
Introduce ordinal numbers to describe the position of things in a sequence
f.
Explore the conservation of number through the use of manipulative
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Mathematics
g.
h.
i.
j.
k.
l.
m.
n.
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Model number relationships to 10 (e.g. show me one more than 3, take 2 away from these cubes, number bonds)
Introduce the use of mathematical vocabulary and symbols of addition and subtraction (add, plus, subtract, take
away, minus, equals, makes, all together)
Introduce how to describe the meaning of addition and subtraction
Estimate quantities to 20
Introduce using pictorial representations to solve simple word problems
Introduce the use of number lines and hundreds charts
Begin to select and explain an appropriate method for solving a problem
Introduce the concept that the position of a digit gives it value and begin to understand what each digit represents
including zero (place value) with numbers greater than 10
Mathematics
GRADE 1
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Sort and label objects into sets by one or more attributes
b. Create a pictograph or bar graph from a set of real objects
c. Able to interpret a pictograph or bar graph
d. Begin to interpret a graph by comparing qualities; more, fewer, less than, greater than
e. Discuss and compare data represented in simple Venn diagram using student information
f. Begin to collect data using tally marks
2. Chance and probability
a. Begin to discuss, identify, predict and place outcomes in order of likelihood; impossible, unlikely, likely, certain
Measurement
Understand and apply the tools and concepts of measurement
1. Length, Perimeter and Area
a. Estimate, compare and measure lengths using non-standard and standard units of measurement (cms)
b. Explore the concept of area using non-standard units
2. Mass
a. Compare weights and know words like ‘heavy, heavier, light, lighter’
b. Use a balance to compare weights of objects
c. Estimate, compare and measure objects using non-standard units
d. Begin to use gram, kilogram
e. Compare and order weight of objects to a kilogram
3. Volume and capacity
a. Compare and order capacities of objects and know words like ‘this holds more’ etc
b. Estimate, compare and measure capacities using non-standard units
c. Compare and order the capacity of containers to a litre
4. Time
a. Use a calendar to determine the date and to identify the sequence of days of the week and months of the year
b. Estimate time elapsed to 1 minute
c. Calculate and record time elapsed to 1 hour
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Mathematics
d. Identify and compare lengths of time; minute and hour
e. Order events with respect to time and how long they take and know terms like ‘this takes more time/less time’
f. Tell and record the time to the hour and half hour both digital and analogue
g. Begin to read and write the time to a quarter hour
5. Temperature
a. Understand hot and cold and begin to connect this to using a Celsius thermometer
Shape and Space
Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Understand line encloses space
2. 2D and 3D Shape
a. Use what they know about 2D shapes to see and describe 3D shapes
b. Sort and label 2D and 3D shapes using appropriate mathematical vocabulary (sides, corners, circles, sphere, square, cube)
c. Create 3D shapes
3. Transformation/Symmetry
a. Find and explain symmetry in their immediate environment
b. Create and explain simple symmetrical designs
c. Begin to combine and transform 2D shapes to make another shape
4. Location and position
a. Give and follow simple directions related to movement and position
b. Use mathematical vocabulary to describe position, direction and movement (e.g. ! turn, whole turn, left, right,
forward, backward)
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a.
Explore, describe and extend patterns in number by 2’s, 5’s, 10’s and odd and even numbers to 100
2. Number sense and numeration
a.
Recognise patterns and rules for addition (e.g. 4+3=7, 3+4=7) up to 20
b. Recognise patterns and rules for subtraction (e.g. 12-3=4, 12-4=3) up to 20
c.
Model the relationship between addition and subtraction
d. Introduce the operation of multiplication as repeated addition
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Mathematics
Number
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Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a.
Read, write, count, model, compare, order numbers to 100
b. Can position one and two digit numbers on a number line and 100’s chart
c.
Use the language of mathematics; more, less, number names, total
d. Use 1:1 correspondence
e.
Begin to use ordinal numbers to describe the position of things in a sequence
f.
Explore the conservation of number through the use of manipulative
g. Use mathematical vocabulary and symbols of addition and subtraction (e.g. add, sum, +)
h. Introduce how to describe the meaning of addition and subtraction
i.
Estimate quantities to 50
j.
Solve simple word problems using pictorial representations
k. Read, write, model addition and subtraction from 10 then 20
l.
Automatic recall of addition and subtraction facts to 10
m. Add and subtract double digit numbers without regrouping
n. Select and explain an appropriate method for solving a problem
o. Begin to explain and model place value including zero as a place holder
p. Begin to round any 2 digit number to the nearest 10
q. Begin to use number lines and hundreds charts
r.
Begin to use strategies to solve addition and subtraction problems.
s.
Introduce addition with regrouping
2. Fractions
a.
Introduce vocabulary of half, whole, equal parts, quarter
b. Introduce to concept of whole, half quarter of a concrete object
c.
Introduce the concept of fractions of a group e.g. whole, half, quarter
Mathematics
GRADE 2
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Collate data using tally marks accurately
b. Display data in a graph (pictograph, bar, column)
c. Interpret a graph by comparing qualities; more, fewer, less than, greater than
d. Design a simple survey
e. Discuss, compare and create sets from data using Venn diagrams
f. Begin to use the scale on the vertical axis of a bar graph to represent large quantities
g. Introduce Venn diagrams as a way of recording information
2. Chance and Probability
a. Discuss, identify, predict and place outcomes in order of likelihood; impossible, unlikely, likely, certain
Measurement
Understand and apply the tools and concepts of measurement
1. Length, Perimeter, Area
a.
Estimate, measure and label length with non-standard units
b. Estimate and measure perimeter with non standard units
c.
Begin to use standard tools to measure length
d. Estimate, measure, label and compare using formal methods and standard units of measurement for length: m, cm
e.
Explore the concept of area using standard units
2. Mass
a.
Estimate, measure and label mass with non standard units
b. Begin to use appropriate tools to measure mass (g, kg)
c.
Estimate, measure, label and compare mass using formal methods and standard units of measurement: g, kg
d. Use a balance to compare weights of objects
e.
Compare and order weight of objects to a kilogram
3. Volume & Capacity
a.
Estimate, measure and label volume & capacity with non standard units
b. Begin to use appropriate tools to measure volume
c.
Estimate, measure, label and compare using formal methods and standard units of measurement for volume:
litres (mL, L)
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Mathematics
Measurement
Understand and apply the tools and concepts of measurement
1. Length, Perimeter, Area
a.
Estimate, measure and label length with non-standard units
b. Estimate and measure perimeter with non standard units
c.
Begin to use standard tools to measure length
d. Estimate, measure, label and compare using formal methods and standard units of measurement for length: m, cm
e.
Explore the concept of area using standard units
2. Mass
a.
Estimate, measure and label mass with non standard units
b. Begin to use appropriate tools to measure mass (g, kg)
c.
Estimate, measure, label and compare mass using formal methods and standard units of measurement: g, kg
d. Use a balance to compare weights of objects
e.
Compare and order weight of objects to a kilogram
3. Volume & Capacity
a.
Estimate, measure and label volume & capacity with non standard units
b. Begin to use appropriate tools to measure volume
c.
Estimate, measure, label and compare using formal methods and standard units of measurement for volume:
litres (mL, L)
d. Compare and order the capacity of containers to a litre
4. Time
a.
Use a calendar to count & record days, weeks and months
b. Read and write time to the hour, 1/2 hour and ! hour (analogue and digital)
c.
Begin to read and write the time to the minute using intervals of 10 minutes and 5 minutes on 12-hour clocks.
(analogue)
d. Begin to estimate time elapsed to 2 or 3 minute
e.
Calculate and record time elapsed to 1 hour
f.
Identify and compare lengths of time second, minute and hour
5. Temperature
a. Estimate and use thermometer to measure temperature in degrees Celsius
Shape and Space
Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Understand whole turns, quarter turn, half turn
b. Understand north, south, east, west on a compass
2. 2D and 3D Shape
a. Use geometric vocabulary of 2D and 3D shapes (e.g. edge, face, corner/vertex)
b. Name and describe the mathematical features of common 3D shapes (e.g. cube, cylinder, cone, sphere, prism,
pyramid)
c. Sort, describe and model regular and irregular polygons, triangles, hexagons, trapeziums
3. Transformation/Symmetry
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Mathematics
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a. Analyze patterns in number systems to 100
b. Understand and use number patterns to solve problems (e.g. 6+?=10)
c. Model with manipulative, the relationship between multiplication and addition (repeated addition)
d. Begin to model numbers as an array
2. Number sense and numeration
a.
Understand and use relationship between addition and subtraction up to 100 (e.g. 55+5=60, 5+55=60)
b. Use manipulative to identify patterns and rules for multiplication and division (e.g. 4x3=12, 3x4=12, 12!4=3,
12!3=4)
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a. Read, write, count, model, compare, order numbers to 1000
b. Use the language of mathematics; more, less, number names, total
c. Count in 2’s, 3’s, 5’s, 10’s and explore other numbers
d. Use ordinal numbers to describe the position of things in a sequence
e. Begin to explore odd and even numbers
f. Count forward to 1000 in 2’s, 5’s, 10’s
g. Automatic recall of addition and subtraction facts to 10 then 20
h. Model addition equations to 1000 without regrouping
i. Use mathematical vocabulary and symbols of addition and subtraction (e.g. add, sum, +)
j. Round off any 2-digit number to nearest 10 then 100
k. Add and subtract double digit numbers without regrouping
l. Can explain and model place value including zero as a place holder to 1000
m. Can select and explain an appropriate method for solving +, -, word problems
n. Introduce addition with regrouping
o. Use and describe a strategy to solve subtraction problems using correct mathematical language
p. Estimate answers using rounding and approximation of quantities to 100
q. Read, write and model simple multiplication and division problems
r. Begin to use mathematical vocabulary and symbols of multiplication and division: times, divide, factor, product,
quotient, x
s. Begin to select and explain an appropriate method for solving x and word problems
t. Solve word problems using pictorial representations
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Mathematics
2. Fractions
a. Use mathematical vocabulary and symbols of fractions; numerator, denominator, equivalence
b. Can read and write the symbols for " and !
c. Can use the correct math language to describe a " and !
d. Understand and model the concept of equivalence to 1; two halves=1, three thirds= 1
e. Model addition and subtraction of fractions with the same denominator (e.g. "+", !=!+!)
f. Use the concept of fractions of a group
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Mathematics
GRADE 3
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Design own survey, collect data and use tally marks accurately
b. Display data in an appropriate graph (pictograph, bar, column)
c. Use teacher generated information to create a line graph and a point graph
d. Interpret and compare a variety of graphs
e. Begin to use the scale on the vertical and horizontal axis of a bar graph to represent large quantities
f. Discuss, compare and create sets from data that has subsets using Venn diagrams
g. Is aware of the concepts/words mode and median and range at a simple level
2. Chance and probability
a. Begin to discuss, identify, predict and place outcomes in order of likelihood; impossible, very unlikely, unlikely,
equally likely, likely, very likely, certain
b. Begin to suggest situations that are fair or unfair (e.g. fairground games)
c. Possible outcomes are given a simple numerical scale 0-1 (impossible, ! or a one in two chance, certain)
d. Is able to put possible outcomes on a simple scale
Measurement
Understand and apply the tools and concepts of measurement
1. Length, Perimeter and Area
a.
Estimate, measure, label and compare using formal methods and standard units of measurement for length: m, cm
b. Use appropriate tools and units to measure length to the nearest centimeter
c.
Estimate and measure perimeter with non standard and standard units
d. Explore the concept of area using non-standard and standard units
2. Mass
a.
Estimate, measure, label and compare mass with non standard units
b. Use appropriate tools to measure mass (g, kg)
c.
Apply correct knowledge of appropriate unit needed to measure objects
d. Estimate, measure, label and compare mass using standard units of measurement (g, kg)
e.
Use a balance to compare weights of objects
f.
Compare and order weight of objects to more than a kilogram
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Mathematics
3. Volume and Capacity
a. Estimate measure label and compare units of measurement: volume and capacity … mL & L
b. Use appropriate tools to measure volume
c. Begin to record volume using correct notation
d. Use appropriate tools and units to measure volume and capacity e.g. “would you measure the capacity of the
swimming pool in L or mL?”
e. Volume of a container is independent of its shape
4. Time
a. Use a calendar to count & record days, weeks and months, seasons
b. Read and write time to the hour, 1/2 hour and " hour (analogue and digital)
c. Read and write time to 5 minutes before and after the hour (analogue and digital)
d. Estimate, read and write the time to the minute using intervals of 10 minutes and 5 minutes on 12-hour analogue and
digital clocks.
e. Estimate up to 5 minutes elapsed and measure/calculate time elapsed to 12 hours
f. Identify and compare lengths of time second, minute and hour
g. Begin to convert number of minutes to hours and vice versa
5. Temperature
a. Estimate, and use a thermometer to measure temperature in degrees Celsius
Shape and Space
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Understand the vocabulary of and identifies and labels acute, right and obtuse angles
b. Begin to measure and construct angles (obtuse, acute and right) using a protractor
c. Begin to understand and identify lines (parallel, perpendicular and intersecting) line segments, rays and angles
2. 2D and 3D Shape
a. Use geometric vocabulary of 2D and 3D shapes (e.g. edge, face, vertices)
b. Introduce Euler’s Rule
c. Understand, name and describe the mathematical features of common 3D shapes (e.g. cube, cylinder, cone, sphere,
prism, pyramid)
d. Sort, describe and model regular and irregular polygons, triangles, hexagons, trapeziums
e. Classify, sort and label types of triangles and quadrilaterals
3. Transformation/Symmetry
a. Create symmetrical patterns
b. Understand lines of reflective symmetry and create symmetrical patterns
c. Turn a 2D net into a 3D shape and vice versa
Mathematics
d. Combine and transform 2D shapes to make another shape (Tangrams)
e. Understand tessellations
4. Location and Position
a. Locate features on a grid using coordinates in a quadrant
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a. Find patterns in number tables
2. Number sense and numeration
a. Solves multiplication and division equations using <, >, =, #
b. Solves fraction and decimal equations using <, >, =, #
c. Use manipulatives to model the relationship between multiply and divide, divide and subtract, multiply and add and
vice versa
d. Count forwards and backwards in 2’s, 5’s, 10’s, 50’s, 100’s, 1000’s
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a. Read, write, compare numbers to 100 000
b. Identify even and odd numbers
c. Identify place and value of numbers to 100 000
d. Manipulate numbers up to 100 000 in expanded, standard and word form
e. Add up to 3 digit numbers without regrouping
f. Add up to 3 digit numbers with regrouping
g. Subtract up to 3 digit numbers without regrouping
h. Subtract up to 3 digit numbers with regrouping
i. Automatic recall of addition and subtraction facts to 10 then 20
j. Identify, solve and create number patterns
k. Use <, >, =, # with whole numbers
l. Estimate number to 1,000
m. Can explain and model place and value including zero as a place holder
n. Understand, solve and create number sentences using + and o. Able to use skip counting of answers to 10x tables
p. Use multiplication facts up to 10x
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Mathematics
q. Create, write and solve multiplication problems 2 digit by 1 digit in vertical format
r. Know and use division facts up to 10x
s. Identify factors of multiples of 10x tables
t. Use simple equations
u. Use estimating strategies and then solve
v. Solve connected word problems choosing from a variety of strategies
2. Fractions
a. Adding/subtracting fractions with common denominators
b. Adding/subtracting mixed fractions and improper fractions
c. Reading fractions correctly
d. Regularly using correct terminology for fractions (numerator, denominator, mixed, improper,)
e. Use <, >, =, # symbols with fractions
f. Convert simple improper fractions to mixed numbers
3. Decimals
a. Understand place value up to hundredths
b. Reading decimals correctly
c. Use <, >, =, # symbols with simple decimals
d. Order decimals to 1 whole
e. Round decimals to closest whole number
f. Adding and subtracting decimals using regrouping
g. Begin to change numbers from simple decimal to fraction form: 50%=1/2
4. Percentages
a. Begin to understand percent and its relationship to fractions and decimals
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Mathematics
GRADE 4
Subject: MATHEMATICS
Strand
Data Management
Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Design a survey and systematically collect and organize and record the data in displays; pictograph, bar graph,
column graph, line graph, point graph)
b. Label graphs with titles, axes, keys, and scales
c. Interpret information represented in various graphs
d. Introduce students to a spreadsheet, using simple formulas to manipulate data and to create graphs
e. Discuss, compare and create sets from data that has subsets using Venn diagrams
f. Use scale on vertical axis
g. Use and understand mode and median
h. Is aware of the concept/word range and mode
2. Chance and probability
a. Discuss, identify, predict and place outcomes in order of likelihood; impossible, very unlikely, unlikely, equally
likely, likely, very likely, certain
b. Suggest situations that are fair or unfair (e.g. fairground games)
c. Construct own situations which are ‘fair’ and ‘unfair’
d. Introduced to a broader numerical scale 0-100 or 0%-100%
e. Aware that prediction of outcomes in a survey is an estimate as only a sample of the population is used
f. Aware that there are a number of possible events for a given situation (eg in a classroom ! students may have blue
eyes, blond hair, ! have neither, ! has blue eyes, ! has blond hair)
Measurement
Understand and apply the tools and concepts of measurement
1. Length, Perimeter and Area
a.
Accurately use measuring tools with simple scales
b. Estimate, measure, label and compare using formal methods and standard units of measurement for length: (m, cm)
for perimeter and area
c.
Use appropriate tools and units to measure length to the nearest centimeter
d. Develop procedures for finding area
e.
Begin to understand and calculate the surface area of solid figures
f.
Calculate the area of composite shapes by separating them into simple parts
g. Introduce strategies for calculating area of irregular polygons (shapes consisting of squares and rectangles)
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Mathematics
2. Mass
a. Accurately use measuring tools with simple scales
b. Select and use appropriate standard units of measurement when estimating, describing, comparing & measuring (gm, kg)
c. Use a balance to compare weights of objects
d. Compare and order weight of objects to more than a kilogram
e. Understand that a tonne is the next largest measure after kg
3. Volume and Capacity
a. Select and use appropriate standard units of measurement when estimating, describing, comparing and measuring
b. Develop procedures for finding volume and capacity
c. Calculate volume of solid figures using using V=LxWxH
d. Record volume using correct notation
e. Compare and order the capacity of containers to a litre
4. Time
a. Read and write the time to 1 minute before and after the hour (analogue and digital)
b. Convert number of minutes to hours and vice versa
c. Introduce the use of, and construct timetables (12 hour clock) and timelines
d. Introduce 24 hour clock
e. Introduce world time zones
5. Temperature
a. Estimate and measure using a thermometer, the temperature in degrees Celsius above and below zero
Shape and Space
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Classify sort and label all types of triangles (scalene, isosceles, equilateral, right angle) and quadrilaterals (rhombus,
trapezoid, parallelogram, square, rectangle)
b. Begin to measure and construct angles (obtuse, acute, right) using a protractor
c. Understand and use the geometric vocabulary for circles; diameter, radius, circumference
d. Understand and construct points, lines, rays and segments; parallel, perpendicular, intersecting
e. Introduce using a compass to make a circle
2. 2D and 3D Shape
a. Describe, classify and model 3D shapes
b. Use the geometric vocabulary of 2D and 3D shapes; parallel, face, edge, vertex
c. Create simple tessellations
Mathematics
3. Transformation/Symmetry
a. Turn a 2D net into a 3D shape and vice versa
b. Create Tessellations
4. Location and Position
a. Name, read and plot coordinates in four quadrants
Pattern and Function
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a. Model and explain number patterns
b. Introduce the use of real life problems to create a number pattern, following a rule
2. Number sense and numeration
a. Begin to model exponents as repeated multiplication
b. Understand and use the relationship between addition and multiplication
c. Understand and use the relationship between multiplication and division (inverse function)
d. Understand and use the relationship between division and subtraction
3. Algebra
a. Begin to develop, explain and model simple algebraic formulas in more complex equations: x + 1=y
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a. Read, write, model, compare, order numbers to 100 000 000
b. Understand place and value through to 100 000 000
c. Read numbers up to 100 000 000
d. Manipulate numbers up to 100 000 000 in expanded, standard and word form
e. Solve addition equations using 4 digit numbers without and with re-grouping
f. Solve subtraction equations using 4 digit numbers without and with re-grouping
g. Estimate number to 1,000
h. Understand, solve and create number sentences using + and i. Recalls and uses multiplication tables through to 12x12
j. Know and use division facts up to 12x12
k. Create and solves multiplication equations using 3 digit by 2 digit numbers
l. Begin to use division equations using multiples of 10 and other 2-digit divisors
m. Begin to read and write addition and subtraction equations using negative numbers (thermometer)
n. Begin to read and write exponential notation
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Mathematics
o. Select the most appropriate and efficient method of solving a problem; mental estimation, mental arithmetic, pencil
and paper, calculator
p. Share problem solving strategies with others
2. Fractions
a. Read, write and model addition and subtraction of fractions with related denominators
b. Use the mathematical vocabulary of fractions: proper, improper, mixed numbers
c. Read, write and model proper fractions, improper fractions and mixed numbers
d. Compare and order fractions
e. Model equivalency of fractions: 2/4=1/2
f. Simplify fractions
g. Convert mixed numbers to improper fractions
h. Convert improper fractions to mixed numbers
3. Decimals
a.
Begin to read, write and model multiplication and division of decimals by multiples of 10
b. Begin to round decimals to a given place or whole number
4. Percentages
a.
Read, write and model simple percentages
b. Interchange fractions, percentages and decimals
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Mathematics
GRADE 5
Subject: ATHEMATICS
Strand
Data Management
Measurement
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Students should be able to:
Understand and apply strategies used to manage/handle data and consider probability
1. Data collection and representation
a. Design a survey and systematically collect, organize and record the data in displays
b. Choose an appropriate graph type to display information (pictograph, bar graph, column graph, line graph, point graph, pie
graph)
c. Interpret and understand information represented in different graphs
d. Label graphs with titles, axes, keys, and scales
e. Compare same information represented in different graphs
f. Introduce students to a spreadsheet, using simple formulas to manipulate data and to create graphs
g. Discuss, compare and create sets from data that has subsets using Venn diagrams
h. Use scale on vertical and horizontal axis
i. Use and understand mode, median, range and mean
j. Create and manipulate an electronic database for their own purposes (Excel)
2. Chance and probability
a. Discuss, identify, predict and place outcomes in order of likelihood; impossible, very unlikely, unlikely, equally likely,
likely, very likely, certain
b. Suggest situations that are fair or unfair (e.g. fairground games)
c. Construct own situations which are ‘fair’ and ‘unfair’
d. Use a broader numerical scale 0-100 or 0%-100%
e. Is aware prediction of outcomes in a survey is an estimate as only a sample of the population is used
f. Understand that a number of possible events possible outcomes for 1 situation. (in a classroom ! students may have blue
eyes, blond hair, ! have neither, ! has blue eyes, ! has blond hair)
Understand and apply the tools and concepts of measurement
1. Length, Perimeter and Area
a. Use measuring tools, with simple scales, accurately
b. Estimate, measure, label and compare using formal methods and standard units of measurement for length: (m, cm) for
perimeter and area
c. Understand that the accuracy of a measurement depends on the situation and precision of the tools
d. Compare perimeters of different shapes (p=16 could be 4x4 or 2x8)
e. Develop formula for finding area
f. Calculate the surface area of solid objects using formula
g. Estimate and record areas in square metres and centimeters
Mathematics
h. Calculate the area of composite shapes by separating them into simple parts
i. Explain that the area of squares and rectangles can be found by multiplying length by breadth and be able to calculate areas
of irregular polygons
j. Use decimal notation in measurement 3.2 cm, 1.47 km
k. Convert between units of length (mm to cm, m to km)
2. Mass
a.
Use measuring tools with simple scales
b. Estimate, measure, label and compare, using formal methods and standard units of measurement, objects of different mass
(g, kg)
c.
Use a balance to compare weights of objects
d. Compare and order weight of objects to more than a kilogram
e.
Understand that a tonne and milligram are the largest and smallest measures used.
f.
Use the abbreviations for milligrams, grams, kilograms and tonnes
g. Use decimal notation in measurement 3.2 g, 1.47kg
h. Convert between units of mass (g to kg and vice versa)
3. Volume & Capacity
a.
Select and use appropriate standard units of measurement when estimating, describing, comparing and measuring
volumes and capacities
b. Calculate volume and capacity by using the formula V=LxWxH
c.
Record volume using correct notation
d. Compare and order the capacity of containers to any given volumetric measure
e.
Convert between units of volume (mL, L)
4. Time
a. Begin to use a calendar as a planning tool
b. Read and write the time using the 12 and 24hr clock
c. Use and construct timetables and timelines
d. Use world time zones
e. Convert number of minutes to hours and vice versa, convert minutes to seconds
5. Temperature
a. Read thermometer to measure temperature in degrees Celsius (above and below zero)
Shape and Space
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Lines and Angle
a.
Classify, sort, measure and label all types of triangles and quadrilaterals: scalene, isosceles, equilateral, right-angled,
rhombus, trapezium, parallelogram, kite, square, rectangle
b. Understand and use the vocabulary of lines, rays and segments: parallel and perpendicular
Mathematics
c.
Understand, measure and construct types of angles: obtuse, acute, straight, reflex, right
d. Understand, measure and construct circles calculating diameter, radius, circumference
e.
Use a pair of compasses to construct circles, parallel lines, perpendicular lines
f.
Understand that an angle is a measure of rotation
2. 2D and 3D Shape
a. Use the geometric vocabulary of 2-D and 3-D shapes: parallel, face, edge, vertex
b. Introduce and identify symmetry and congruency within 2D shapes
c. Describe, classify and model 3-D shapes
d. Introduce reducing and enlarging shapes to scale
e. Construct a 3D shape from a 2D net
3. Location and position
a. Read and plot coordinates in 4 quadrants
b. Introduce the language and notation of bearing to describe position
4. Transformation/Symmetry
a.
Create tessellations
b. Begin to recognize tessellations in everyday environment
Pattern and Function
Number
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Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a.
Model, explain and use number patterns
b. Use real life problems to create a number pattern, following a rule.
c.
Begin to write own rules for patterns Introduce exponents and
2. Number sense and numeration
a. Understand and use the relationship between multiplication and division
b. Understand and use the relationship between division and subtraction
c. Model exponents as repeated multiplication
d. Introduce exponents and roots as inverse functions: 92, !81
e. Use real-life problems to create a number pattern, following a rule
f. Model and explain number patterns (function tables)
3. Algebra
a. Develop, explain and model simple algebraic formulas in more complex equations: x + 1 = y, where y is any even whole
number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes
1. Whole number
a.
Read, write and model numbers, using the base 10 system, to millions and beyond
b. Automatically recall and use basic number facts (addition to 20, multiplication /division to 10x10)
Mathematics
c.
d.
e.
f.
g.
Understand place and value through to 100 000 000
Solve addition and subtraction equations using 4 digit numbers with re-grouping
Solve complex equations using 4 digit numbers involving 2 different processes
Recall and use multiplication tables and division facts through to 12x12
Use written methods for short multiplication and division by a single digit integer of two-digit then three digit then four
digit integers,
h. Use written methods for long multiplication at first for two digit by two digit integer calculations then for three digit by
two digit calculations
i.
Extend division to informal methods of dividing by a two digit divisor
j.
Use estimation and other strategies to check that their answers are reasonable
k. Round numbers to nearest ten, hundred, thousand
l.
Read, write and model addition and subtraction of integers (positive and negative numbers)
m. Read, write and model exponential notation
n. Select the most appropriate and efficient method of solving a problem
o. Share problem solving strategies with others
p. Is aware of the order of operations using BEDMAS (Brackets, Exponents, Division, Multiplication, Addition,
Subtraction)
2. Fractions
a. Read, write and model addition and subtraction of fractions with related denominators
b. Use the mathematical vocabulary of fractions: proper fractions, improper fractions, mixed numbers
c. Read, write and model proper fractions, improper fractions and mixed numbers
d. Compare and order fractions
e. Model equivalency of fractions by converting to common denominators and explaining method and reasoning
f. Simplify fractions by canceling common factors
g. Convert improper fractions to mixed numbers and back
h. Recognize equivalence between decimal and fraction forms of one half, one quarter, one tenth and one hundredth
3. Decimals
a. Understand and use decimal notation for tenths, hundredths and thousandths in context
b. Locate on a number line and order, a set of decimal numbers or measurements
c. Round a number with one or two decimal places, to the nearest integer or tenth
d. Read, write and model the addition and subtraction of decimals to the thousandths
e. Read, write and model multiplication and division of decimals (with reference to money) by whole numbers
f. Analyze and solve problems using a variety of skills and strategies
4. Percentage & Ratio
a. Understand that percentage means the number of parts per 100 and that it can be used for comparisons
b. Find percentages of whole number quantities using a calculator
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Mathematics
c. Recognize approximate proportions of a whole and use fractions and percentages to describe them
d. Calculate percentages using pencil and paper
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Mathematics
GRADE 6
Subject: MATHEMATICS
Strand
Statistics and Probability
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Students should be able to:
Understand and apply strategies used to manage and manipulate data and probability. Develop an awareness and
understanding of the concepts and skills involved in collecting, collating and analysing data
1. Data collection and representation
a. Specify the problem and plan: formulate questions in terms of the data needed, and consider what inferences can be
drawn from the data; decide what data to collect (including sample size and data format) and what statistical evidence
is needed
b. Choose appropriate graph type to display information (pictograph, bar graph, column graph, line graph, point graph,
pie graph)
c. Examine critically, and justify their choice of mathematical presentation of problems involving data
d. Label graphs with titles, axes, keys, and scales
e. Interpret and understand information represented in different graphs
f. Compare same information represented in different graphs
g. Introduce students to a spreadsheet, using simple formulas to manipulate data and to create graphs
h. Use scale on vertical and horizontal axis
i. Construct and interpret tables and graphs using graphing software
2. Chance and probability
a. Describe and order the likelihood of events in everyday situations using appropriate everyday language (e.g.
impossible, very unlikely, unlikely, equally likely, likely, very likely, certain)
b. Describe the likelihood of events in everyday situations using appropriate mathematical terminology (1 in 4 chance,
50:50 chance)
c. Utilize graphic organizer (tree diagrams) to identify possible outcomes
d. Predict and record possible outcomes of an event
e. Explain the differences between predicted results and actual results of an experiment
f. Use samples to make predictions about a larger population from which the sample comes
g. Understand a number of possible events for 1 situation (e.g. in a classroom ! students may have blue eyes, blond
hair, ! have neither, ! has blue eyes, ! has blond hair)
Mathematics
Geometry and
Trigonometry
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Understand and apply the tools and concepts of measurement enhancing spatial awareness and giving insight into the
realms of construction and navigation
1. Length, Perimeter and Area
a. Select and use the appropriate device and unit to measure lengths or distance
b. Estimate with a reasonable degree of accuracy and then measure and record lengths or distances including kilometers
c. Convert between units of length (mm to cm, m to km)
d. Calculate lengths or distances using decimals to 3 decimal places
e. Compare perimeters of different shapes ( p=16 could be 4x4 or 2x8)
f. Construct a square metre using a variety of lengths and widths
g. Understand and show that the perimeter of shapes can be the same regardless of the length of sides
h. Estimate and calculate areas in square metres and centimetres
i. Use the abbreviations for square metres and square centimeters
j. Explain that the area of squares and rectangles can be found by multiplying length by width and be able to calculate
k. Calculate the area of irregular shapes composed of squares and rectangular sections
l. Calculate the area of composite shapes by separating them into simple parts
m. Develop and use the formula for the area of a triangle
n. Apply knowledge of length, perimeter and area through practical problem-solving activities
2. Mass
a. Estimate the mass of familiar things
b. Select and use the appropriate device and unit to measure mass
c. Compare the mass of different objects
d. Use the abbreviations for milligrams, grams, kilograms and tonnes
e. Convert between milligrams, grams, kilograms and tonnes to 3 decimal places
f. Apply the knowledge of mass to practical problem solving situations
3. Volume and capacity
a.
Understand the concept of kilolitre
b. Use the abbreviations for millilitres, litres and kilolitres
c.
Construct 3D objects using cubic centimetre blocks and measures volume by counting the number of blocks
d. Use the abbreviations for cubic centimeter and cubic metres
e.
Estimate the volume of rectangular prisms using cubic centimeters
f.
Calculate the volume of rectangular prisms by multiplying the length by the width by the height
g. Select and use the appropriate device and unit to measure capacity
h. Calculate capacity using milliliters and litres to 3 decimal places
i.
Compare and order the capacity of containers to a more than a litre
Mathematics
j.
Convert between units of volume (mL, L, kL)
4. Time
a. Tell the time using analogue, 24 hour and digital clocks
b. Convert between analogue, 24 hour and digital time
c. Convert from one time unit to another time unit
d. Calculate the duration of an event using starting and finishing times
e. Use a stopwatch to time events accurately to hundredths of a second
f. Use world time zones
g. Understand the terminology of AD, BC (e.g. 400BC) and CE ( Common Era) BCA (Before Common Era)
h. Read and construct a time line including AD and BC and /or CE and BCE
5. Temperature
a. Determine and record temperature variations
b. Estimate and read maximum and minimum temperatures in Celsius
c. Calculate and interpret average temperature
Geometry and
Trigonometry
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Use symbols for ‘is parallel to ll’ and is perpendicular
b. Identify and draw perpendicular lines
c. Name and label lines, rays and line segments
d. Use compass to bisect angles
e. Use common conventions to indicate right angles, equal angles and parallel lines
f. Classify and identify angles as right, acute, obtuse, reflex, straight or a revolution
g. Construct, label and name angles using letters of the alphabet
h. Estimate and measure angles in degrees using protractor and geometry software
i. Construct an angle of a given size using a protractor
j. Prove and use the fact that the sum of the interior angles of a triangle is 180 degrees
k. Recall the definition of a circle and the meaning of related terms, including centre, radius, chord, diameter,
circumference, tangent, arc, sector and segment; understand that the tangent at any point on a circle is perpendicular
to the radius at that point, explain why the perpendicular from the centre to the chord bisects the chord; understand
that inscribed regular polygons can be constructed by equal division of a circle
l. Prove and use the fact that the sum of the interior angles of a quadrilateral is 360 degrees
m. Calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and
use the angles of regular polygons
Mathematics
n. Understand the meaning of the term congruence
o. Recognise congruence in lines, shapes and solids
p. Apply understanding of angles to spatial sense and geometric reasoning activities (movement of the hands of a clock)
2. 2D and 3D Shape
a. Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium
and rhombus; classify quadrilaterals by their geometric properties
b. Visualise and sketch simple solids from different views
c. Construct a model of simple 3D object from drawings of different views. Use appropriate terms in describing 3D
objects including base, edge, surface, vertex and face
d. Construct a model of a simple solid from an isometric drawing
e. Identify and name the properties of rectangular prisms and triangular prisms
f. Identify and name the properties of square based and triangular based pyramids
g. Use formal names for prisms
h. Identify iscoceles, scalene and equilateral triangles
i. Compare and describe the side and angle properties of iscoceles, equilateral and scalene triangles
3. Transformation/Symmetry
a. Rotate shape clockwise and anti clockwise
b. Rotate a shape about a point (e.g. 90 degrees)
c. Identify and name shapes that have rotational symmetry
d. Use both pen and paper and geometry software to construct a shape that has rotational symmetry
e. Translate shapes over a given distance (e.g. 5 squares to the left)
f. Reflect a complex shape or design on a line
g. Recognise tessellations in everyday environment
h. Make enlargements and reductions of 2D shapes, pictures and maps using pen and paper or geometry software
i. Discuss similarities and differences of the same object or scene represented in different sizes
j. Introduce drawing software to create tesselations
4. Location and Position
a. Use a coordinate grid to make simple 2D shapes
b. Read and interpret maps, plans, scale drawings and diagrams that have been drawn to scale
c. Read and write scales in words and through diagrams
d. Recognise and use cardinal and intermediate points on a magnetic compass
e. Use a magnetic compass to find north and hence the direction associated with the other three major compass points
f. Follow a simple orienteering course
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Mathematics
Algebra and Discrete
Numbers
Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a. Build a simple numerical or geometric pattern using materials (e.g. match stick patterns)
b. Complete the pattern for a numerical or geometric series
c. Explain how the answers in a series of values are determined
d. Determine and record a rule, in words, to describe the pattern presented in a table
e. Generate common integer sequences (including sequences of odd or even integers, squared integers, powers of 2)
2. Number sense and numeration
a.
Find the first terms of a sequence given a rule arising naturally from a context (e.g. the number of ways paying in
cents using only 1c and 2c coins)
3. Algebra
a.
Express simple functions, at first in words and then in symbols
b. Calculate the missing number in a series of values
c.
Apply a rule to a table to calculate the missing values
d. Calculate the value of a missing number in a number sentence (e.g. 7x ?=42)
e.
Distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite
unknown numbers in equations, (x+1 =65) defined quantities or variables in formulae, (V=IR) general, unspecified
and independent numbers in identities (3x+2=5x or 3(a+b)=3a+3b)
f.
Set up simple equations (e.g. find the angle a in a triangle with angles a, a+10, a+20) solve simple equations by
using inverse operations or by transforming both sides in the same way (5x=7)
g. Use formulae from mathematics and other subjects (e.g. area of a triangle, area of a circle)
Number
Understand and apply basic and advanced properties of the concepts of number and problem solving processes and
the skills of estimation and calculation
1. Whole number
a. Recognise the existence of different number systems
b. Provide examples of the use of number in everyday life
c. Read, write and model numbers, using the base 10 systems, to millions and beyond
d. Place numbers in descending and ascending order
e. Compare numbers and use symbols <, >, =, "
f. Round to the nearest 10, 100, 1000, 10 000 and 100 000
g. Use written methods for short multiplication and division by a single digit integer of two-digit then three digit then
four digit integers
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Mathematics
h. Use written methods for long multiplication at first for two digit by two digit integer calculations then for three digit
by two digit calculations
i. Choose appropriately between mental, written and calculator methods for addition and subtraction problems
j. Use a variety of checking procedures, including working the problem backwards, and considering whether the result
is of the right order of magnitude
k. Give solutions in the context of the problem to an appropriate degree of accuracy, recognizing limitations on the
accuracy of data and measurements
l. Use rounding and a mental strategy to multiply a 2 digit number by a 2 digit number to obtain an approximate answer
(e.g. 67 x 53=70 x 50=3500)
m. Explore algorithms for long multiplication and understand them
n. Multiply a 2 digit number by a 2 digit number using the extended form (long multiplication)
o. Divide a number with 3 or more digits by multiples of 10 (including remainders)
p. Select and use appropriate operations to solve contextual word problems.
q. Solve complex equations using 4 digit numbers involving 2 different processes
r. Add, subtract, multiply and divide integers and then any number; multiply or divide any number by powers of 10, and
any positive number by a number between 0 and 1; find the prime factor decomposition of positive integers (e.g.
8000= 2 x 5)
s. Begin to use the order of operations using BEDMAS (Brackets, Exponents, Division, Multiplication, Addition,
Subtraction)
2. Fractions
a. Continue, create and describe patterns involving fractions (!, #, 3/4, 1)
b. Convert fractions to lowest terms
c. Convert improper fractions to mixed numbers
d. Add and subtract simple fractions by changing one denominator (2/3 +1/6)
e. Demonstrate understanding of addition and subtraction of fractions through everyday problem solving
f. Convert simple decimals to fractions (0.125=125/1000=1/8)
g. Convert fractions to decimals (3/4= 75/100=0.75)
3. Decimals
a.
Provide examples of the use of decimals in everyday life
b. Explain the place value of tenths, hundredths and thousandths
c.
Read and write decimals to thousandths, in both numerals and words
d. Write decimals in expanded form (e.g. 1.25=1 unit+2 tenths+5 hundredths or 1+0.2+0.05)
e.
Round off to the nearest whole number, tenth or hundredth, estimate answers to problems involving decimals
f.
Compare and order decimals; descending and ascending
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Mathematics
g. Use symbols <, >, =, " to compare decimals
h. Add or subtract decimal numbers that have a different number of decimal places
i.
Multiply and divide decimal numbers including money by 10, 100, and 1000
j.
Multiply and divide decimal numbers, including money, by single digit numbers in everyday contexts
k. Multiply and divide tenths, hundredths and thousandths by a single digit to terminating numbers
4. Percentage and Ratio
a.
Explain the use of percentages in everyday life
b. Express simple fractions and decimals as percentages (50%=50/100=1/2)
c.
Express everyday percentages as fractions and decimals (10%, 20%)
d. Compare quantities using ratio
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Mathematics
GRADE 7
Subject: MATHEMATICS
Strand
Statistics and Probability
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Students should be able to:
Understand and apply strategies used to manage data and probability. Develop an awareness and understanding of
the concepts and skills involved in collecting, collating and analysing data
1. Data collection and representation
a. Specify the problem and plan: formulate questions in terms of the data needed, and consider what inferences can be
drawn from the data; decide what data to collect (including sample size and data format) and what statistical evidence
is needed
b. Understand the purpose of taking a sample population
c. Explain the difference between a random sample and a biased sample (e.g. examine surveys in the media)
d. Plan a range of ways to collect data
e. Record data using spreadsheets, and use simple formulae to create graphs using graphing software
f. Construct and interpret pie graphs using graphing software
g. Find the mean, median, mode and range from given data
h. Interpret information from data, graphs and tables
i. Review and evaluate as they work and at conclusion
2. Chance and probability
a. Describe and order the likelihood of events in everyday situations using appropriate everyday language (e.g.
impossible, very unlikely, unlikely, equally likely, likely, very likely, certain)
b. Describe the likelihood of events in everyday situations using appropriate mathematical terminology (1 in 4 chance,
50:50 chance)
c. Assign numbers and percentage to chance
d. Utilize graphic organizer (tree diagrams) to identify possible outcomes.
e. Make own probability generator (e.g. spinner to show P= 2/5 chance of red)
f. Predict and record possible outcomes of an event
g. Test predictions
h. Explain the differences between predicted results and actual results of an experiment
i. Use samples to make predictions about a larger population from which the sample comes
j. Understand a number of possible events e.g. 4 possible outcomes for 1 situation
k. Identify risk and consequences of taking chances
l. Demonstrate an understanding of what constitutes gambling (lotto, poker machines)
m. Identify some of the social consequences of gambling
Mathematics
Geometry and
Trigonometry
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Understand and apply the tools and concepts of measurement enhancing spatial awareness and giving insight into the
realms of construction and navigation
1. Length, Perimeter, Area
a. Convert between all units
b. Use the formula; Distance=speed x time to solve problems
c. Demonstrate the understanding of the relationship between perimeter and area through practical problem solving
activities (e.g. investigating floor plans of sports fields)
d. Use appropriate strategies and devices to estimate and accurately measure the area of a shape
e. Use appropriate units of measurement
f. Calculate the area of complex composite shapes by separating them into simple parts
g. Use scale in ratio form to calculate either original size or drawing size (explores different methods of estimating the
area of an irregular shape, cube house)
h. Calculate the area of a circle using A= ! r 2
i. Calculate the area of composite shapes which include circles
j. Apply knowledge of length, perimeter and area through practical problem-solving activities
2. Mass
a.
Estimate and compare the mass of familiar things
b. Convert between mg, g, kg & tones to three decimal places
c.
Choose appropriate units and tools to measure weight of a variety of objects
d. Identify the relationships between milligrams, grams, kilograms and tonnes
e.
Apply the knowledge of mass of 1 litre of water = 1 kilogram to practical problem solving activities
3. Volume and Capacity
a. Convert between all units
b. Use the symbols cL3, mL3, kL3
c. Demonstrate the understanding of volume through practical problem solving activities
d. Estimate the volume of rectangular prisms using cubic centimeters
e. Develop and use formula through practical problem solving activities
f. Develop and use formula for volume of rectangular prisms; V=LxWxH
g. Demonstrate awareness that capacity is related to volume (e.g. through displacement activities)
h. Calculate capacity using milliliters and litres to 3 decimal places
4. Time
a. Understand time zones around the world and daylight saving time
b. Calculate the duration of an event using starting and finishing times Explain ways in which time is measured in other
cultures (e.g. moon cycles)
Mathematics
c. Use Speed=Distance/Time to answer problems
d. Construct and interpret time lines using appropriate scale (including AD and BC) and CE (Common Era) and BCE (
Before Common Era)
5. Temperature
a. Demonstrate awareness of Celsius, Farenheit & Kelvin temperature scale
b. Use online resources to compare current temperatures in different parts of the world
Shape and Space
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Use the terms lines, points, rays, segments, intersections, parallel and perpendicular when constructing diagrams,
bisecting lines and angles with a compass
b. Bisect angles using a compass
c. Construct triangles when only the lengths of sides are given
d. Recall the definition of a circle and the meaning of related terms, including centre, radius, chord, diameter,
circumference, tangent, arc, sector and segment; understand that the tangent at any point on a circle is perpendicular
to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord; understand
that inscribed regular polygons can be constructed by equal division of a circle
e. Use understanding of angles to determine compass bearings and true bearings
f. Draw a 2D shape given a description of its side and angle properties, using geometric software or a ruler, protractor
and set square
2. 2D and 3D Shape
a. Identify 2D shapes within patterns across cultures and in nature
b. Classify solids in terms of their geometric properties. (ie faces, edges, vertices, cross section)
c. Draw 3D solids
d. Identify and names properties of polyhedra (e.g. tetrahedron, pentagonal prism, hexagonal prism)
e. Construct complex solids from nets (Hexagonal based pyramid)
f. Draw oblique and isometric projections of cubes using paper or drawing software
g. Recognise the properties of quadrilaterals
h. Construct, name and classify scalene, iscoceles and equilateral triangles
i. Determine unknown angles in quadrilaterals and triangles
3. Transformation
a. Enlarge and reduce shapes using a scale
b. Create tessellations using rotation, translation and reflection using drawing software
Mathematics
4. Location and Position
a. Draw environmental and geometric objects from different perspectives
b. Describe and draw what is seen and not seen from different views of 3D objects (e.g. pyramids and prisms)
c. Draw 3D objects using solid lines for visible edges using interactive geometry software
d. Use both pen and paper and geometry software to construct a shape that has rotational symmetry
e. Translates shapes over a given distance (e.g. 5 squares to the left)
f. Recognise that a location can be represented on maps or plans using different scales
g. Recognise tessellations in everyday environment
h. Use a scale to calculate the distance between two points on a map
i. Read, write and use scales in words in problem solving
j. Produce scaled plans and respond to the question ‘what scales are used in commercial applications (e.g. buildings,
orienteering maps, atlases)
k. Evaluate maps and scales in terms of scale, use of symbols, appropriateness for task, clarity of purpose and accuracy
etc
l. Use coordinate grids to make more complex 2D shapes (e.g. making a picture)
m. Explain a pathway to a location on a model, map or plan using distance, direction, angle multiples of 45 degrees,
compass points and coordinates
n. Follow simple directions to move from point to point on a given path, using maps, a magnetic compass and written
and oral instructions
o. Develop a simple orienteering course
Algebra and Discrete
Numbers
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Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Patterns in numbers
a. Extend and describe the rule for numeric and geometric patterns, 1 series (e.g. 7, 36, 181, 906 is the previous number
times 5 plus 1)
b. Construct a number sentence to match a problem that is presented in words and that requires finding an unknown
c. Use inverse operations to solve a number sentence
d. Use index notation for simple integer powers, and simple instances of index laws; substitute positive and negative
numbers into expressions such as 3x2+4 and 2x33
e. Use systematic trial and improvement methods with ICT tools to find approximate solutions of equations where there
is no simple analytical method
f. Generate common integer sequences (including sequences of odd or even integers, squared integers, powers of 2)
g. Find the first terms of a sequence given a rule arising naturally from a context (e.g. the number of ways paying in
cents using only 1c and 2c coins);or from a regularly increasing spatial pattern
Mathematics
2. Algebra
a.
Express simple functions, at first in words and then in symbols; explore the properties of simple polynomial
functions
b. Distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite
unknown numbers in equations, (x+1 =65) defined quantities or variables in formulae, (V=IR) general, unspecified
and independent numbers in identities (3x+2=5x or 3(a+b)=3a+3b) and in functions they define new expressions or
quantities by referring to known quantities
c.
Understand that the transformation of algebraic expressions obeys and generalizes the rules of arithmetic; simplify
or transform algebraic expressions by collecting like terms, by multiplying a single term over a bracket and by
taking out single term common factors
d. Use the conventions of co-ordinates in a plane; plot points in all four quadrants
e.
Investigate pattern rules in solving problems
f.
Investigate and analyses graphs showing relationship between variables
g. Set up change to Uses simple equations (e.g. find the angle a in a triangle with angles a, a+10, a+20) solve simple
equations by using inverse operations or by transforming both sides in the same way (5x=7)
h. Predict future trend from linear graphs
i.
Construct a number sentence to match a problem that is presented in words and that requires finding an unknown
j.
Number
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Use formulae from mathematics and other subjects (e.g. area of a triangle, area of a circle); substitute numbers into a formula
Understand and apply basic and advanced properties of the concepts of number and problem solving processes and
the skills of estimation and calculation
1. Whole Number
Develop an understanding of number systems across time and place
a. Recognise, use and write in words numbers beyond 1 000 000
b. Identify place value of numbers over 1 000 000
c. Compare numbers and use symbols ( ), >,<, =, !
d. Write numbers up to 1 000 000 in expanded form (e.g. using powers of 10) Recall all positive integer complements to
100, recall all multiplication facts to 10x10 and use them to derive quickly the corresponding division facts
e. Use power or index (exponents) notation
f. Write numbers over 100 000 in ascending and descending order
g. Identify large numbers in everyday use (e.g. comparing populations)
h. Identify factors, common factors, prime factors, highest common factor and lowest common multiple
i. Use arrays and divisibility rules
j. Identify triangular numbers and cubic numbers
Mathematics
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l.
m.
n.
o.
Apply square root to square numbers and uses the symbol " , !
Solve a given 2 step number or word problem
Multiply a 3 digit number by a 2 digit number using long multiplication
Divide a number with 3 or more digits by a single digit or multiples of 10 with a remainder expressed as a decimal
Understand the order of operations using BEDMAS (Brackets, Exponents, Division, Multiplication, Addition,
Subtraction)
p. Use and explain appropriate strategies in problem solving (e.g. working backwards, trial and error)
q. Identify the operations required to solve more complex problems within their experience (e.g. banking;
deposit/withdrawal)
r. Recognise the existence of negative numbers (e.g. profit and loss)
s. Use a calculator, when appropriate, to solve problems
t. Use the function keys for reciprocals, squares, square roots, powers, fractions (and how to enter as a decimal); use the
constant key
u. Understand the calculator display, interpreting it correctly, and knowing not to round during the intermediate steps of
a calculation
v. Recall the cubes of 2,3,4,5 and 10 and the fraction to decimal conversion of familiar simple fractions
2. Fractions
a. Compare the size of fractions with different denominators
b. Compare and order mixed numbers and improper fractions in ascending and descending order
c. Add and subtract fractions with different denominators, including improper fractions and whole numbers
d. Multiply fractions including whole numbers and mixed numbers, canceling using common factors
e. Convert fractions to frequently used decimals and percentages
3. Decimals
a.
Round off decimals to 3 places
b. Divide decimals by a whole number
c.
Use notation for recurring decimals
d. Multiply decimal numbers by decimal numbers (e.g. 0.2x0.3=0.06)
e.
Divide decimals using a calculator (e.g. calculating averages)
f.
Convert decimals to fractions
g. Use decimals in problem solving in everyday contexts
h. Convert percentages to fractions and decimals
i.
Convert fractions and decimals to percentages
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Mathematics
4. Percentages
a. Express fractions of quantities as percentages (e.g. 20 out of 25 is 4/5 is 80%)
c. Find simple percentages of quantities using both pen and paper and calculator
d. Find discount as a percentage of a given amount of money
e. Solve practical problems using percentage decrease and percentage increase
5. Ratio
a.
Compare quantities using ratios in problem solving
b. Recognise where fractions or percentages are needed to compare proportions; identify problems that call for
proportional reasoning, and choose the correct numbers to take as 100%, or as a whole
c.
Solve word problems about ratio and proportion, including using informal strategies and the unitary method of
solution
d. Develop a range of strategies for mental calculation; derive unknown facts from those they know; add and subtract
mentally numbers with up to 2 decimal places; multiply and divide numbers with no more than one decimal digit,
using factorisation where possible
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Mathematics
GRADE 8
Subject: MATHEMATICS
Strand
Statistics and Probability
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Students should be able to:
Understand and apply strategies used to manage and manipulate data and probability. Develop an awareness and
understanding of the concepts and skills involved in collecting, collating and analysing data
1. Data collection and representation
a.
Understand the purpose of taking a sample population
b. Explore a process for statistical inquiry by: formulating key questions to explore (e.g. social and environmental
issues)
c.
Explain the difference between a random sample and a biased sample (e.g. examine surveys in the media)
d. Plan a range of ways to collect data
e.
Classify data as a categorical or quantitative (discrete or continuous) gather data from secondary sources, include
printed tables and lists from ICT based sources
f.
Organize and displaying data in table and graph form (e.g. spreadsheets, rainfall of the local area compared with
another area, space given to male and female sports in newspapers)
g. Record data using spreadsheets, and use simple formulae to create graphs using graphing software
h. Present results of surveys; describe initial questions, data collection process, preferences, conclusions; and comment
on how they might be improved
i.
Interpret information from data, graphs and tables
j.
Analyze data and make general comments on its distribution, correlation
k. Construct and interpret pie graphs using graphing software
l.
Find and use the mean, median, mode and range from given data
m. Review and evaluate as they work and at conclusion
2. Chance and probability
a.
Describe and order the likelihood of events in everyday situations using appropriate everyday language Describe the
likelihood of events in everyday situations using appropriate mathematical terminology (1 in 4 chance, 50:50
chance)
b. Assign numbers and percentage to chance
c.
Utilize graphic organizers (tree diagrams, matrix diagrams) to identify possible outcomes
d. Make own probability generator (e.g. spinner to show P= 2/5 chance of red)
e.
Predict and record possible outcomes of an event
f.
Test predictions
g. Explain the differences between predicted results and actual results of an experiment
Mathematics
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Geometry and
Trigonometry
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Use samples to make predictions about a larger population from which the sample comes
Understand a number of possible events eg 4 possible outcomes for 1 situation
Identify risk and consequences of taking chances
Demonstrate an understanding of what constitutes gambling (lotto, poker machines)
Identify some of the social consequences of gambling
Investigate experimental and theoretical probabilities eg.What is the probability of an astrologer’s prediction being
accurate?
Write formulae to determine probability:-and consider: what type of event has a 50:50 chance of happening?
Consider birth of a boy or a girl
Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1
Understand that if they repeat an experiment, they may-and usually will-get different outcomes, and that increasing
sample size generally leads to better estimates of probability and population characteristics
Understand and apply the tools and concepts of measurement enhancing spatial awareness and giving insight into the
realms of construction and navigation
1. Length, Perimeter and Area
a. Convert between units of area (e.g. cm2 to mm2, m2 to km2, mm2 to cm2, cm2to m2, m2 to km2, m2 to ha2)
b. Establish ‘pi’ as the ratio of the circumference to the diameter of a circle by practical means
c. Calculate the perimeter of polygons and circles using the appropriate formulae
d. Estimate area of objects with a reasonable degree of accuracy using various strategies
e. Calculate the area of polygons using appropriate formulae (e.g. rectangles, triangles, parallelograms, trapezium)
f. Use different methods to approximate the area of a circle (e.g. sectors into a parallelogram or rectangle)
g. Apply knowledge of perimeter, circumference and area through practical and are through practical problem-solving
activities
h. Find loci, both by reasoning and by using ICT to produce shapes and paths
2. Mass
a. Convert between units of mass to three decimal places
b. Recognise that the units for volume, mass and capacity are related as follows; 1000cm3 or 1L of pure water has a
mass of 1kg and apply this knowledge to practical problem solving activities
c. Solve problems involving capacity, mass and volume
3. Volume and Capacity
a. Convert between cL,mL, L, kL
b. Convert between units of capacity and units of volume (ie 1 cm3 + 1mL3 , 1000 cm3=1L, 1m3=1kL)
c. Calculate the volume of prisms using Volume=area of base x height, and use appropriate units (e.g. mm3, cm3 and m3)
Mathematics
d.
e.
4. Time
a.
b.
Calculate capacity using milliliters and litres to 3 decimal places
Apply knowledge of volume through practical problem-solving activities
Use a standard time zone map to answer questions related to time differences
Use bus, train and plane timetables to plan a journey, calculating departure and arrival, time, and the time taken for
sections of the journey considering time zones and international dateline
c. Convert between analogue, 24 hour and digital time
d. Solve problems by using the relationship of Speed=Distance/Time
e. Use a stopwatch to time events accurately to hundredths of a second
f. Construct and interpret time lines using appropriate scale (including AD and BC and CE and BCE)
5. Temperature
a. Demonstrate awareness of Celsius & Farenheit temperature scale
b. Use online resources to compare current temperatures in different parts of the world
Shape and Space
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Understand the mathematics of shapes and spaces and can apply basic and advanced concepts of geometry
1. Line and Angle
a. Determine angle properties relating to straight lines, intersecting lines, parallel lines and a transversal by using
geometry software
b. Use the angle properties of parallel lines to determine unknown angles: corresponding, alternative, allied and
vertically opposite
c. Calculate unknown interior and exterior angles of a triangle
d. Determine the sum of interior angles of any n-sided polygon using triangles
e. Understand, recall and use Pythagoras theoram
2. 2D and 3D Shape
a. Identify faces, edges of polyhedra and looks at relationships (e.g. Eulers formula)
b. Develop nets to construct complex 3D objects (e.g. soccer ball)
c. Use ICT to investigate nets of more complex objects (e.g. crystals)
d. Critique the use of 2D shapes and 3D objects in common applications (e.g. packaging ‘why are milk cartons square in
cross section, architecture ‘how are triangles used for strength in building’)
e. Use isometric graph paper to draw 3D constructions
f. Use 2D representations of 3D shapes and analyse 3D shapes through 2D projections and cross-sections, including
plan and elevation
3. Transformation
a. Identify rotational symmetry
Mathematics
b. Construct a mirror image of designs using a line of symmetry
c. Use line and rotational symmetry to classify polygons and polyhedra
d. Create a complex tessellating shape by using translation, rotation or reflection to modify a simple shape
e. Identify functional and aesthetic uses of tessellations in social contexts (e.g. paving, works of M C Escher)
f. Perform 2 step geometrical transformations using grid paper or drawing software
g. Describe various transformations
4. Location and Position
a. Use a Cartesian grid to plot points and lines and develop a relationship to describe the lines
b. Use bearings and distance to describe a position (e.g. street directories, treasure maps)
c. Recognise that enlargements preserve angle but not length; identify scale factor of an enlargement as the ratio of the
lengths of any two corresponding line segments and apply this to triangles; understand the implications of
enlargement for perimeter; use and interpret maps and scale drawings; understand the implications of enlargement for
area and for volume
d. Understand that one coordinate identifies a point on a number line, two coordinates identify a point on a plane and
three coordinates identify a point in space; use axes and coordinates to specify points in all four quadrants; locate
points with given coordinates; find the coordinates of points identified by geometrical information; find the
coordinates of the midpoint of the line segment AB given points A and B, then calculate the length
Discrete Number and
Algebra
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Understand the nature of patterns and functions and can apply the basic and advanced concepts of algebra
1. Algebra understanding
a. Describe patterns ad relationships in society (e.g. time of year and demand for electricity)
b. Describe geometric patterns in words and adds to the pattern
c. Construct a table of values for a pattern
d. Use spreadsheets to make a number machine to look at rules for linear expressions
e. Evaluate an algebraic expression by substituting numbers for unknowns
f. Write a rule to describe a pattern and use pronumerals (e.g. 4n+3, 2x+1)
g. Use patterns to solve a problem (e.g. constuction of taxi fares, flag fall + rate/km)
h. Define and give examples of a pronumeral, term, like terms, constant term and coefficient, expression and equation
i. Collect like terms in expressions with 1 and 2 pronumerals
j. Use index notation to collect like items
k. Use the distributive law to expand brackets and simplify
2. Algebra solving
a.
Solve simple linear equations by inspection or trial and error
b. Undo algebraic expressions using inverse operations
Mathematics
c.
d.
e.
f.
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n.
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p.
q.
r.
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t.
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Solve linear equations containing 2 or more operations
Solve worded problems by constructing equations and solving them
Graph the values from a given table or a grid
Plot and describe points in the four quadrants of the Cartesian plane
Describe the pattern formed when a graph is drawn from a table of values (ie write the rule)
Describe and model a situation. Make connections and analyse it (e.g. look at a fun run fundraiser in relation to
sponsorship rates, models the different rates, graphs and analyses)
Distinguish the different roles played by letter symbols in algebra, knowing that letter symbols represent definite
unknown numbers in equations, defined quantities or variables in formulae, general, unspecified and independent
numbers in identities and in functions they define new expressions or quantities by referring to known quantities
Understand that the transformation of algebraic expressions obeys and generalizes the rules of arithmetic; simplify
or transform algebraic expressions by collecting like terms, by multiplying a single term over a bracket and by
taking out single term common factors, and by expanding the product of two linear expressions including squaring a
linear expression; distinguish in meaning between the words ‘equation’, ‘formula’, ‘identity’, and ‘expression’
Use index notation for simple integer powers, and simple instances of index laws; substitute positive and negative
numbers into expressions such as3x2+4
Set up simple equations, solve simple equations by using inverse operations or by transforming both sides in the
same way
Use linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the
equation; solve linear equations that require prior simplification of bracket, including those that have negative signs
occurring anywhere in the equation and those with a negative solution
Use formulae from mathematics and other subjects; substitute numbers into a formula, derive a formula and change
its subject
Set up and use equations to solve word and other problems involving direct proportion, and relate their algebraic
solutions to graphical representations of the equations
Generate points and plot graphs of simple quadratic functions
Use the conventions for coordinates in the plane, plot points in all four quadrants; recognize that equations of the
form y=mx+c correspond to straight line graphs of functions in which y is given explicitly in terms of x or implicitly
Link a graphical representation of an equation to algebraic solution; find an approximate solution of a pair of linear
simultaneous equations by graphical methods, then find the exact solution by eliminating one variable; consider the
graphs of cases that have no solution or an infinite number of solutions
Find the gradient of lines given by equations of the form y=mx+c (when values are given for m and c); investigate
the gradients of parallel lines and lines perpendicular to these lines
Solve simple linear inequalities in one variable and represent the solution set on a number line
Mathematics
u.
v.
w.
x.
y.
z.
Number
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Has some understanding of systematic trial and improvement methods with ICT tools to find approximate solutions
of equations where there is no simple analytical method
Generate common integer sequences (including sequences of odd or even integers, squared integers, powers of 2,
powers of 10, triangle numbers)
Find the first terms of a sequence given a rule arising naturally from context; find the rule (and express it in words)
for the nth term of a sequence
Generate terms of a sequence using term-to-term and position-to–term definitions of the sequence; use linear
expressions to describe the nth term of an arithmetic sequence, justifying its form by referring to the activity or
context from which it was generated
Express simple functions, at first in words and then in symbols; explore the properties of simple polynomial
functions
Construct linear functions arising from real-life problems and plot their corresponding
Understand and apply basic and advanced properties of the concepts of number and problem solving processes and
the skills of estimation and calculation
1. Whole number
a. Research a different culture’s number system, past and present and compares it to the Hindu-Arabic system used
today
b. Round off numbers in multiples 10 and to 1 or 2 significant figures
c. Use index notation to express powers of numbers (positive indices only) and links this to the calculator using the
power key (negative roots)
d. Recognise the link between squares and square roots, cubes and cube roots and uses the correct notation
e. Estimate using 1 and 2 figure working and apply this to problem solving
f. Use the calculator to perform calculations including exponents
g. Explore common uses of positive and negative signs (e.g. temperatures, loss and gain, north and south)
h. Add and subtract directed numbers using a number line
i. Understand and use rules for adding and subtracting directed numbers
j. Use the terms square, positive and negative square root (knowing that the square root sign denotes the positive square
root) cube, cube root, use index notation for small integer powers and index laws for multiplication and division of
positive integer powers
k. Understand and use rules for multiplying and dividing directed numbers
l. Combine operations with directed numbers using order of operations (BEDMAS)
m. Use the calculator to combine operations with directed numbers
Mathematics
2. Fractions
a. Add and subtract mixed numbers
b. Multiply and divide fractions
c. Find the reciprocals of numbers
d. Use the calculator to perform operations on fractions
e. Solve real-life problems involving fractions
f. Determine sets of equivalent fractions
3. Decimals
a.
Round numbers correctly to a given number of decimal places including when using a calculator
b. Add, subtract, multiply and divide decimal numbers to three decimal places
c.
Multiply and divide decimal numbers by whole and decimal numbers
d. Use decimals in problem solving
4. Ratio
a.
Express information as a ratio
b. Simplify ratios
c.
Find equal ratios
d. Use equal ratios (proportion) to solve real life problems
e.
Use ratio to divide quantities (e.g. divide $120 in the ratio 2:3)
f.
Apply ratio to scale diagrams
g. Express information as a rate (a runner sprints 100 metres in 12 seconds expressed as a rate 8.3m/s)
h. Use ratio to solve real life problems
5. Percent
a.
Express one quantity as a percentage of another
b. Find percentages of quantities
c.
Find a percentage of a quantity when given another. (find 80% of a quantity if 15% is 30)
d. Calculate percentage change
e.
Use percentage to calculate profit and loss
f.
Calculate tax or GST on various items
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