TERM TWO LEARNING OBJECTIVES
NUMBER KNOWLEDGE & FRACTIONS
NA3-5: Know fractions and percentages in everyday use.
Understand the meaning of the digits in a fraction, how the fraction can be written in numerals and words, or said, and the relative order and size of fractions with common denominators (bottom numbers) or common numerators (top numbers).
Know fundamental concepts are that fractions are iterations (repeats) of a unit fraction, for example 3/5 = 1/5 + 1/5 + 1/5 and 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3.
Know that the numerator (top number) is a count and the denominator tells the size of the parts, for example in 5/3 there are five parts. The parts are thirds created by splitting one into three equal parts. This means that fractions can be greater than one, for example 4/3 = 1 1/3, and that fractions have a counting order if the denominators are the same, for example 1/3, 2/3, 3/3, 4/3,...
Know the size of the denominator also affects the size of the parts being counted in a fraction. For example, thirds of the same whole are smaller than halves of the same whole. So fractions with common numerators have an order of size based on the size of the parts, for example 2/7 < 2/5 < 2/3 (< means “less than”).
Know simple common fraction-percentage relationships, including 1/2 = 50%, 1/4 = 25%, 1/10 = 10%, 1/5 = 20%, and use this knowledge to work out non-unit fractions as percentages, for example 3/4 = 75%.
Level 3 - Student Achievement Objectives
I can identify fractions and percentages in everyday use.
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
The effects of operations for addition and subtraction with fractions and decimals are the same as those with whole numbers.
The real-world actions for addition and subtraction of whole numbers are the same for operations with fractions and decimals.
Different real-world interpretations can be associated with division calculations involving fractions (decimals).
Fractions with unlike denominators are renamed as equivalent fractions with like denominators to add and subtract.
The product of two fractions can be found by multiplying numerators and multiplying denominators.
Level 4 - Student Achievement Objectives
I can add and subtract fractions with related denominators e.g. 1/5 + 3/10 = 5/10 = 1/2
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
A fraction describes the division of a whole (region, set, segment) into equal parts.
The bottom number in a fraction tells how many equal parts the whole or unit is divided into. The top number tells how many equal parts are indicated.
A fraction is relative to the size of the whole or unit.
A decimal is another name for a fraction and thus can be associated with the corresponding point on the number line.
A percent is another way to write a decimal that compares part to a whole where the whole is 100 and thus can be associated with the corresponding point on the number line.
Percent is relative to the size of the whole.
Level 4 - Student Achievement Objectives
I can find a fraction of a number e.g. 5/6 of 24 = ロ
I can find the whole given the fraction of the number e.g. 4/7 of ロ = 24
I can find a percentage of a quantity e.g. 20% of 70 = ロ
I can find the whole given the percentage e.g. 30% of ロ = 15
I can find what percent one number is of another e.g. ロ% of 76 = 19
I can multiply and divide decimals with tenths using place value partitioning e.g. 4 x 1.3 = (4 x 1) + (4 x 0.3); 4.8 ÷ 3 = (3 ÷ 3) + (1.8 ÷ 3)
NA4-4: Apply simple linear proportions, including ordering fractions.
Benchmark fractions like 1/2 (0.5) and 1/4 (0.25) can be used to estimate calculations involving fractions and decimals.
Level 4 - Student Achievement Objectives
I can compare and order fractions including halves, thirds, quarters, fifths and tenths.
I know how to write equivalent fractions e.g. 1/4 = 3/12 = 25/100
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
Decimal place value is an extension of whole number place value.
The base-ten numeration system extends infinitely to very large and very small numbers (e.g., millions & millionths).
A comparison of a part to the whole can be represented using a fraction.
A percent is a special type of ratio where a part is compared to a whole and the whole is 100.
Level 4 - Student Achievement Objectives
I know fractions, decimals and percentage conversions for halves, thirds, quarters, fifths, eighths, and tenths, e.g. 3/4 = 0.75 = 75%.
NA5-1: Reason with linear proportions.
This means students will explore linear proportions in a variety of contexts. Linear proportions apply to situations which can be modelled using equivalent fractions, that is, a/b = c/d where a,b,c, and d are integers (usually whole numbers).
Level 5 - Student Achievement Objectives
I can solve problems involving linear proportions by using equivalent fractions/ratios.
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
This means students will understand calculations involving fractions, decimals, percentages and integers.
Students should be able to explain the calculation steps (procedures) they followed and justify those steps by describing the quantities involved.
Level 5 - Student Achievement Objectives
I can estimate multiplication and division problems that involve decimals
I can multiply decimals using a range of strategies
I can divide decimals using a range of strategies
I can add and subtract fractions with unrelated denominators e.g. 5/8 + 1/6 = 15/24 + 4/24 = 19/24
I can multiply fractions e.g. 3/4 x 2/5 = (3 x 2) / (4 x 5) = 6/20 = 3/10
I can divide fractions e.g. 1/2 ÷ 3/8 = 1/2 x 8/3 = 8/6
I can multiply and divide integers e.g. -2 x 3 = -6; -8 ÷ -2 = 4
I can find a percentage of a quantity e.g. 56% of 38 = ロ
I can find the whole given the percentage e.g. 56% of ロ = 21.28
I can find what percent one number is of another e.g. ロ% of 38 = 21.28
MEASUREMENT
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
This means students will recognise that length, area, volume and capacity, weight, angle, and temperature are the characteristics (attributes) of objects people most commonly measure in everyday life.
Measurement involves quantifying an attribute using units. Units of measure have characteristics including being a part of the attribute they measure and uniformity (same size). When measuring, the units need to fill a length, space, time etc., with no gaps or overlaps (this is known as tiling).
Students should be familiar with common units in the metric system
Level 4 - Student Achievement Objectives
I can use measurement instruments involve reading linear scales
I can understand that the marks on a linear scale show the endpoint of units and that scales always have a baseline (zero).
I can apply additive and multiplicative number strategies to measurement problems that involve whole numbers of units.
GM3-2: Find areas of rectangles and volumes of cuboids by applying multiplication.
This means students will begin by measuring the areas of rectangles and other shapes using square units.
This is because square units of the same size tessellate, that is join together with no laps or overlaps. That means that the measurement is consistent whereas the use of a non-tessellating unit would give variable results due to gaps and overlaps.
Volume is measured in cubes of the same size. At Level Three students should apply whole number multiplication to make the process of counting squares or cubes more efficient.
Level 4 - Student Achievement Objectives
I can begin to measure the area of rectangles and other shapes using square units
Apply whole number multiplication to make the process of counting squares or cubes more efficient.
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
Measurement involves a selected attribute of an object (length, area, mass, volume, capacity) and a comparison of the object being measured against a unit of the same attribute.
The longer the unit of measure, the fewer units it takes to measure the object.
A given time of day can be represented in more than one way.
For most money amounts, there are different, but finite combinations of currency that show the same amount; the number of coins in two sets does not necessarily indicate which of two sets has the greater value.
Length measurements in feet and inches can be added or subtracted where 1 foot is regrouped as 12 inches.
Level 4 - Student Achievement Objectives
I can select the appropriate unit of measure
I can estimate and measure with accuracy
I can measure length of an object
I can measure the area of a shape
I can measure temperature on a scale including negative numbers
I can measure weight on a scale to the nearest tenth of a unit
I can measure volume/capacity of an object
I can measure angles using a protractor
I can read analogue and digital times
GM4-2: Convert between metric units, using whole numbers and commonly used decimals.
Measurements can be represented in equivalent ways using different units.
Algorithms for operations with measures are modifications of algorithms for rational numbers.
Measurement involves a selected attribute of an object (length, area, mass, volume, capacity) and a comparison of the object being measured against a unit of the same attribute.
Level 4 - Student Achievement Objectives
I can convert between units of measure using whole numbers and decimals
I can convert between am/pm and 24hr time
I can convert between analogue and digital time
GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
Measures of area, volume, capacity and temperature can each be compared using ideas such as greater than, less than, and equal.
Angles can be compared using ideas such as greater than, less than, and equal.
A large number of objects in a given area can be estimated by finding how many are in a subsection and multiplying by the number of subsections.
Measurement involves a selected attribute of an object (length, area, mass, volume, capacity) and a comparison of the object being measured against a unit of the same attribute.
Length, area, volume, and mass/weight measurements can be estimated using appropriate known referents.
A large number of objects in a given area can be estimated by finding how many are in a sub-section and multiplying by the number of sub-sections.
The longer the unit of measure, the fewer units it takes to measure the object.
Level 4 - Student Achievement Objectives
I can find the perimeter of rectangles, parallelograms and triangles
I can find the area of a rectangle using the formula Area = base x height
I can find the area of a triangle using the formula Area = 1/2 (base x height)
I can find the area of parallelograms using the formula Area = base x height
I can find the volume of cubes and cuboids using the formula Volume = base x height x depth
GM4-4: Interpret and use scales, timetables, and charts.
A given time of day can be represented in more than one way.
For most money amounts, there are different but finite combinations of currency that show the same amount; the number of coins in two sets does not necessarily indicate which of the two sets has the greater value.
Times in minutes and seconds can be added and subtracted where 1 minute is regrouped as 60 seconds.
Time duration for events can be compared using ideas such as longer, shorter, and equal.
The numbers used to make an estimate determine whether the estimate is over or under the exact answer.
Level 4 - Student Achievement Objectives
I can read and interpret timetables and charts
I can understand and use scale diagrams
I can solve problems involving time
I can solve problems involving temperature