MATHS OVERVIEW-YEAR 3 TERM 1, 2013
YEAR LEVEL / CONTENT DESCRIPTORSYear 3 / Number & Algebra
DURATION / ACMNA051 Investigate the conditions required for a number to be odd or even and identify odd and even numbers
ACMNA052 Recognise, model, represent and order numbers to at least 10 000
ACMNA053 Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
ACMNA054 Recognise and explain the connection between addition and subtraction
ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
ACMNA056 Recall multiplication facts of two, three, five and ten and related division facts
ACMNA058 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
ACMNA059 Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents
ACMNA060 Describe, continue, and create number patterns resulting from performing addition or subtraction
Term 1
LINKS TO OTHER LA’s
Measurement & Geometry
ACMMG061 Measure, order and compare objects using familiar metric units of length, mass and capacity
ACMMG062 Tell time to the minute and investigate the relationship between units of time
ACMMG063 Make models of three-dimensional objects and describe key features
ACMMG066 Identify symmetry in the environment
ACMMG064 Identify angles as measures of turn and compare angle sizes in everyday situations
Statistics & Probability
ACMSP067 Conduct chance experiments, identify and describe possible outcomes and recognise variation in results
ACMSP068 Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording
ACMSP069 Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies
ACMSP070 Interpret and compare data displays
DEVELOPING INQUIRING & REFLECTIVE LEARNERS
☐COMMUNITY CONTRIBUROR ☐LEADER AND COLLABORATOR ☐EFFECTIVE COMMUNICATOR
☐ACTIVE INVESTIGATOR ☐DESIGNER AND CREATOR ☐QUALITY PRODUCER
Achievement Standard
By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model andrepresent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.
Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.
Proficiency Strands
Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of datacollections and data displays
MAG Planning Term 1 Year 3
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES3.1.1
Odd and Even Numbers / ACMNA051 Investigate the conditions required for a number to be odd or even and identify odd and even numbers. / There are many ways to represent numbers. How do they look the same? How are they different? / What makes 5 a special number?
Choose two of these numerals.
1 2 3 4 5 6 7 8 9 0 / • recognise and explain number patterns, eg odds and evens, numbers ending with five
• model odd and even numbers using arrays and other collection-based diagrams [L] / What numbers are in the pattern 2,4,6,8,….. and also in the pattern 5,10,15,20….? Do children realise that all multiples of 10 will be in both patterns because they are even numbers and that multiples of 5 will not be in the 2’s pattern because they are odd numbers? / Can the student give a definition of an odd /even number? Can the student identify odd and even numbers, and give reasons why they are odd/even? Can the student identify a four digit number, for example: 4327 as odd or even, with an explanation? /
- Counters / straws
- Hundreds Board
- Odd or even - investigation sheet
- 1-100 cards
- Calculator
- Individual whiteboards and washable pens
- FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.2
Numbers to 10 000
(1) / ACMNA052 Recognise, model, represent and order numbers to at least 10 000 / Numbers tell us how much and how many / What real life situations might this number describe?
Option 1 100
Option 2 1000
Students choose one options but will still benefit from class discussion / First Steps in Mathematics – Number Course Book
Diagnostic Task – Up to and over 100 page 16
Diagnostic Task – Up to and through the 100s
page 16 (modify this task for Up to and over 1000) / Make up a four-digit PIN number and say why it is easy to remember. The emphasis here is on being able to communicate the reason to someone else. You could possibly make restrictions such as not using birth years / • represent numbers up to four digits using numerals, words, objects and digital displays
• make the largest and smallest number from four given digits (U) (F) [CCT]
• identify the number before and after a given two-, three- or four-digit number
• use place value to compare and explain the relative size of four-digit numbers (R) (U) [CCT]
• use the symbols for ‘is less than’ and ‘is greater than’ to show the relationship between two numbers / • Number Board
• Sticky notes
• Place value chart
• Tiny 100, 10 , 1
• Flip chart
• Digits
• Place value arrows
• Calculator
• FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.3
Place Value
(1) / ACMNA053 Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems. / Number benchmarks are useful for relating numbers and estimating amounts / How many years old is someone who is 1 000 days? Are you older or younger than this? / First Steps in Mathematics – Number Course Book
Diagnostic Task – Lollies/Candies/Sweets / Display my number – Using base ten materials. Give students a number e.g. 256. Ask them to use the material to show how many different ways you can model the number (e.g. 256 ones, 25 tens and 6 ones, 2 hundreds 1 ten and 15 ones etc.) / • apply an understanding of place value and the role of zero to read, write and order numbers up to four digits
• interpret four-digit numbers used in everyday contexts (U) / • Tiny - Hundreds, Tens and Ones
• Place Value Chart - Thousands
• Rubber bands to bundle the tiny hundred frames.
• MAB materials – thousands hundreds tens ones
• Digits 0-9
• Place Value Arrows
• FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.4
Connecting
Addition &
Subtraction / ACMNA054 Recognise and explain the connection between addition and subtraction. / Doing and undoing – understanding the process and being able to work backwards / Draw pictures to match the number sentences
8 – 2 = 6
6 + 2 = 8 / • Students can consistently apply a given rule (addition and subtraction of numbers to 10); and describe the inverse operation.
• Students can describe the rule (e.g. -2; +10) by looking at the relationship between numbers in the recording table. / Use the function machine as per normal but do not tell the students the rule, only the ‘function machine worker’. When the students’ card is outputted, the students then need to work out what the rule is that was applied to their number. / Write an addition number fact on the board such as 8 + 7 = 15. Ask a student to tell you what the subtraction fact would be reverse of this addition fact. For 8 + 7 = 15, the reverse subtraction fact is 15 – 7 = 8.
Continue with examples to 20. / • Function Machine – Arrows add +1, +2 and subtract 1,2
• Numerals 1 - 100
• Recording table and rules
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.5
Addition
Strategies / ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation. / A critical aspect of mathematical thinking is the recognition that knowing one thing about a number can provide other information about that number. / Use 3 ten frames and display 10 and 15.
Ask students to record similarities such as • they are both less than
• they are both more than
• You can say both numbers when you count by
Ask students to record differencies
• 10 is often shown in counting books but 15 is not
• 10 can be shown by using one ten frame but 15 can not
• 10 is 1 more than 9, but 15 is / • Students choose efficient strategies for addition and subtraction
• Students record mental strategies, eg ‘I added 20 to 159 to get 179, then I added 3 more to get 182.’or use an empty number line [L] / Write the number 42 on the board and tell children that it is the answer to some number sentences. Explain that they are allowed to use any of the following calculator keys: + - = and any of the digit keys to find number sentences that equal 42. They record their findings. Note if children use + and – in the same number sentence or if they use combinations of more than two numbers, for example, 12+20+10=42. / Give the students a two digit addition number story, for example:
38+27=
Ask students to add the numbers together, showing the strategies and the steps they have used to get their answer. Note if students can select an appropriate strategy and explain how they have applied the strategy to the number problem / • Addition and Subtraction strategy practice cards
• Subitisation dot cards 1-10 and Numerals 1-100
• Red tens frames
• Bundling sticks
• Place value arrows
• Number line 1-100
• Partitioning part-part-whole cards
• Mini- whiteboard and washable pens
• Double ten frames
• Playing cards
• FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.6
Subtraction Strategies / ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation / There are many different ways to add and subtract numbers / Review of year 2 strategies / • identify and choose efficient strategies for addition and subtraction, including:
• the jump strategy, eg 23 + 35; 23 + 30 is 52, 53 + 5 = 58
• the split strategy, eg 23 + 35; 20 + 30 + 3 + 5 = 5the compensation strategy, eg 63 + 29; 63 + 30 is 93, subtract 1 to obtain 92
• using patterns to extend number facts, eg 500 – 200; since 5 – 2 = 3, so 500 – 200 is 300
• bridging the decades, egg 34 + 26; 34 + 6 is 40, 40 + 20 is changing the order of addends to form multiples of 10, eg 16 + 8 = 4; add 16 to 4 first
Students are asked to subtract 9, 8 and 7 from a two digit number, explaining the strategies they use. / In pairs, students choose a two-digit number without repeating any digit or using zero, for example: 38. The student reverses the order of the digits to create a second number, for example: 83. The student subtracts the smaller number from the larger and records this as a number sentence. The answer is used to start another reversal subtraction. Play continues until zero is reached. Students discuss strategies used and any patterns they have observed. / Students are given a calculation such as 160-24=136 and are asked to create a number of problems where this calculation would be needed. Students share and discuss responses. / • Addition and Subtraction strategy practice cards
• Subitisation dot cards 1-10 and Numerals 1-100
• Number line 1-100
• Partitioning part-part-whole cards
• Who has game - subtraction of 9 from two-digit number
• Hundreds Boards – routine and non-routine
• Mini- whiteboard and washable pens
• Counters
• FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.7
Money / ACMNA059 Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents.
Proficiency Strand:
Problem Solving – modelling authentic situations. / Numbers tell how many or how much / How many ways can $1 be represented? / • Change from $1 – ask the student to select a Catalogue items up to $1 and calculate the change from $1 using the coin strips.
• Four ways to show money: Ask students to show four different ways to make up to $15 using notes and coins. / The total on the cash register is $25.75. What combination of notes and coins could you give? List some possible combinations. Present your findings with pictures. / Catalogue buys: Provide small groups of students with supermarket catalogues that display items that cost under $10. In pairs students cut out and paste items they can buy for $20. Students record the quantities and use calculators to check their calculations. More able students could work out the change they would receive from $20. / • Collection of play coins and notes
• Shop items: cereal boxes, egg cartons, empty plastic drink bottles, yoghurt containers.
• Catalogue items up to $1
• Catalogue items – mixed dollar and cents.
• A collection of catalogues from supermarkets and toy shops.
• Money to $1 for number line
• Coin Strips
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.8
Metric Units / ACMMGO61 Measure, order and compare objects using familiar metric units of length, mass and capacity. / Applying appropriate techniques, and tools to determine measurement / Describe three things that weigh less than a shoe. Tell how you know they weigh less than a shoe / Observe students as they participate in each section of the Activity Process. Ask students to journal their understandings about measurement from these activities.
Note students’ understanding of
• Use of comparative language
• Ability to estimate objects that are 1m, 1L and 1 kg .
• Using scales to check predictions
• Accuracy when measuring. / • Ask students to estimate and measure how many arbitrary units make a metre, for example: felt pens, paperclips, hand spans, unifix cubes. Record the estimate and the actual measure.
• Repeat above for capacity and mass. / Record all the things that we measure in metres. Make a list and add to it when another suggestion is made / • Metre ruler
• Streamers
• Balance scale
• Kitchen scale
• 1kg mass – for example 1kg rice.
• Measuring jug (1litre)
• Empty grocery items – 1kg and 1 litre
• Early Years FISH Kit
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.9
Time to Minute / M-MG3. Tell time to the minute and investigate the relationship between units of time.
Proficiency Strand:
Understanding – using appropriate language to communicate times / Time is about repeating events / Recording events which are regularly repeated / • Give each student a piece of paper and black pen. Simply ask them to “to draw a clock”. Later discuss the clock with each student (tell me about your clock; how do clocks work? What time does your clock show? etc.) to gain further insights. Annotate these for future reference.
• Ask students to draw in where the hour hand should be at these times: 12:50; 4:25; 9:30; 8:00; 8:45 / Problem – the hands of a clock make an angle that is less than a quarter of a turn. What time might it be? / Ask students to record times (analogue and digital) on the Individual whiteboard clock : 6:00; 1:10; 3:30; 11:55; 7:40: 10:25 / • Class clock – analogue and digital time:
• Class clock with second (sweep) hand or
Individual whiteboard clocks and pen
TOPIC / CONTENT DESCRIPTOR / KEY IDEA / Pre-ASSESS / ASSESSMENT / INVESTIGATION / STUDENT JOURNAL / RESOURCES
3.1.10
Data / ACMSP068 Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording.
ACMSP069 Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies
ACMSP070 Interpret and compare data displays / Selecting and using appropriate statistical methods to analyze data / How could you sort a group of toys and make a graph to show how many toys are in different groups? / Use the IDEAL tally chart to collect data on another topic of interest, for example: favourite icecream or favourite game. Provide a 10x10 grid to students and ask them to create a column graph to display the information. Ask questions about the data: most popular, least popular, difference between, how many chose… etc. / If two more children came into our class, how might this change our graph? Draw the new column graph using your new data. If I child left, how might it change the graph? / Collect data about topics of interest to children, for example: favourite game, favourite icecream, and favourite flavour of corn chip. / • 10x10 floor grid
• Paper squares to fit grid squares
• 10x10 paper grid
• FISH Kit
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