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### Year 5 (NCEA) Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 5
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Reasoning Simple addition up to the number 20
Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20.
3 Calculations Subtraction up to the number 10
Objective: On completion of the lesson the student will be able to calculate the answer to take away or subtraction number sentences up to the number 10.
4 Calculation-multiplication The multiplication sign
Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems.
5 Calculation sharing/division Strategies for division
Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.
6 Calculation-larger numbers The numbers 100 to 999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99.
8 Multiplication Multiples and factors of whole numbers
Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.
9 Length Using the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
10 Volume Introduction to volume. using the cubic centimetre as a standard unit
Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo
11 Problems Solve and record division using known facts and sharing
Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems.
12 Place value The numbers 1000 to 9999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
13 Fractions Using fractions 1/2, 1/4, 1/8 to describe part of a whole
Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.
14 Fractions Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection
Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.
15 Time, months Months and seasons of the year
Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season.
16 Time, days of week Days of the week
Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary.
17 Time, duration Duration
Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.
18 Time, minutes Analogue – Telling time – minutes in the hour
Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock.
19 Time, units Units of time
Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.
20 Time, a.m. p.m. AM and PM time
Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time.
21 Time, quarter to, past Quarter past and quarter to
Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.
22 Time, minutes past the hour Minutes past
Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.
23 Time, minutes to the hour Minutes to
Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.
24 3-D shapes Viewing 3-D shapes.
Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.
25 Lines and angles Mapping and grid references
Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.
26 Lines and angles Main and intermediate compass points
Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location.
27 Lines and angles Informal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
28 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
29 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
30 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
31 Data Pie and bar graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs.
32 Geometry-angles Measuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
33 Calculations Subtraction by Comparison
Objective: On completion of the lesson the student will be able to calculate take away or subtraction number sentences by comparison methods.
34 Calculations Subtraction up to the number 20 and beyond
Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences.
35 Subtraction Subtraction up to the number 99
Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences.
36 Subtraction Subtraction with borrowing
Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method
37 Subtraction Subtraction of two-digit numbers Involving comparison.
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.
38 Multiplication Multiplication – important facts.
Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
40 Subtraction Subtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
41 Multiplication Multiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
42 Division Division with and without a remainder.
Objective: On completion of the lesson the student will understand division with and without a Remainder.
43 Division Dividing two and three digit numbers by a single digit number.
Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.
44 Counting and numeration The numbers 10 000 to 99 999
Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.
45 Counting and numeration Addition to 9999 and beyond
Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.
46 Subtraction Subtraction involving four digit numbers and beyond using the renaming method.
Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers.
47 Counting and numeration Seven digit numbers
Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers.
48 Multiplication Multiplication by 2 and 3 digits
Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.
49 Division Divide whole numbers by a 2 digit divisor
Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.
50 Fractions Comparing and ordering fractions
Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.
51 Fractions mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
52 Fractions Improper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
53 Fractions Fractions 1/5, 1/10, 1/100
Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.
54 Fractions Finding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
55 Fractions Multiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
56 Fractions Reducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
57 Fractions Comparing and ordering fractions greater than (>) 1
Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.
58 Fractions Subtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
59 Fractions Adding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
60 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
61 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
62 Fractions Multiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
63 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
64 Decimals Introduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
65 Decimals Comparing and ordering decimals to two decimal places
Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.
66 Decimals Decimals with whole numbers 10th and 100th
Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.
67 Decimals Adding decimals to two decimal places
Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)
68 Decimals Subtracting decimals to two decimal places
Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)
69 Decimals Using decimals – shopping problems
Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.
70 Decimals Using decimals to record length
Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.
71 Decimals Rounding decimals
Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.
72 Decimals Decimals to three decimal places
Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths.
73 Decimals Adding decimals with a different number of decimal places
Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.
74 Decimals Subtracting decimals with a different number of places
Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.
75 Decimals Multiplying decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.
76 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
77 Decimals Multiplication of decimals by decimals to two decimal places
Objective: On completion of the lesson the student will be able to multiply decimals to two digits.
78 Percentages Introduction to percentages, including relating common fractions to percentages
Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.
79 Percentages Changing fractions and decimals to percentages using tenths and hundredths
Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.
80 Percentages Changing percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
81 Multiplication Multiplying 2-digit numbers by multiple of 10
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.
82 Multiplication Multiplying 3 and 4-digit numbers by multiples of 100
Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.
83 Multiplication Multiplying 2-digit numbers by 2-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.
84 Multiplication Multiplying 4-digit numbers by 3-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication.
85 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
86 Division/repeat subtraction Repeated subtraction with divisors less than 20 with no remainders
Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20.
87 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders
Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders.
88 Division/repeat subtraction Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders
Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders.
89 Division/repeat subtraction Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders
Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders.
90 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with remainders
Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders.
91 Division/repeat subtraction Repeated subtraction with divisors greater than 20 with remainders as fractions
Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions
92 Division/repeat subtraction Repeated subtraction with divisors less than 35 with some remainders
Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders.
93 Division/repeat subtraction Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders
Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders.
94 Division/repeat subtraction Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders
Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders.
95 Division/repeat subtraction Using divide, multiply and subtraction in the bring down method
Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method.
96 Sign word problems Solving Word Problems by recognising Sign Words
Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.
97 Length Using the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
98 Length Read and calculate distances on a map using the formal unit kilometre
Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map.
99 Length Compare and convert formal units of measurement
Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.
100 Area Introduction to the square centimetre.
Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.
101 Area Introducing the rules for finding the area of a rectangle and a parallelogram.
Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.
102 3-D shapes Constructing models.
Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms.
103 Volume Using the cubic centimetre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting.
104 Volume Introducing the formula for volume.
Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.
105 Volume Using the cubic metre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat
106 Volume Solving Problems about Volume – Part 1.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.
107 Capacity Using the cubic cm and displacement to measure volume and capacity
Objective: On completion of the lesson the student will know a way to find volume and capacity.
108 Capacity Using the cubic cm as a standard unit of measurement for volume and capacity
Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.
109 Capacity The relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
110 Capacity Converting between volume and capacity using kilolitres and litres
Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity.
111 Capacity Estimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
112 Weight/mass The kilogram
Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.
113 Weight/mass The gram and net mass
Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.
114 Time, digital, analogue Comparing analogue and digital time
Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.
115 Time, digital O’clock and half past using digital time
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock.
116 Time, analogue O’clock and half past on the analogue clock
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.
117 Time, 24-hour 24 hour time
Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time.
118 2-D shapes Using the prefix to determine polygons
Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.
119 2-D shapes Spatial properties of quadrilaterals
Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.
120 Angles Measure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
121 2-D shapes Recognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
122 Tessellating 2-D shapes Use grids to enlarge/reduce 2D shapes
Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.
123 3-D shapes Recognise and name prisms according to spatial properties
Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.
124 3-D shapes Recognise and name pyramids according to spatial properties
Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.
125 Exam Exam – Year 5
Objective: Exam