Activities Middle Mathematics

8/3/2019 Activities Middle Mathematics

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© Dorothea Scanlon 2011

Table of Contents

Mathematics Learning Centres ........................................................................................................ 2How to use this book .......................................................................................................................... 2Lesson structure ................................................................................................................................. 3Resources ............................................................................................................................................ 4Assessment .......................................................................................................................................... 4

Planning .............................................................................................................................................. 6Icon board ........................................................................................................................................... 8Topic Focus: Number –Numbers...................................................................................................... 9Topic Focus: Number – Number Patterns ..................................................................................... 13Topic Focus: Number –Addition and Subtraction Number Facts .............................................. 15Topic Focus: Number - Addition .................................................................................................... 17Topic Focus: Number - Subtraction ............................................................................................... 19Topic Focus: Number - Multiplication........................................................................................... 21Topic Focus: Number -Division ...................................................................................................... 25Topic Focus: Number – Using Brackets and the Four Processes ................................................ 27Topic Focus: Number – Money....................................................................................................... 29

Topic Focus: Number – Money and Decimals............................................................................... 31Topic Focus: Number -Fractional Numbers ................................................................................. 33Topic Focus: Measurement - Time ................................................................................................. 35Topic Focus: Measurement – Length ............................................................................................. 39

Topic Focus: Measurement – Volume, Mass, Capacity ............................................................... 43Topic Focus: Space- Location, Position and Orientation ............................................................. 45Topic Focus: Space – Shape-2D ...................................................................................................... 47Topic Focus: Space – Shape – 3D ................................................................................................... 49Topic Focus: Chance and Data - Chance....................................................................................... 51Topic Focus: Chance and Data – Collecting, Displaying & Interpreting Data.......................... 531-100 Number Chart ........................................................................................................................ 55Australian Money............................................................................................................................. 58MAB – Base 10 Materials ................................................................................................................ 58Common Shapes ............................................................................................................................... 593D Nets .............................................................................................................................................. 60



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Mathematics Learning Centres

Mathematics learning centres foster many flexible, empowering and creative teaching and learningstrategies. They support and provide:

ü Ease of teacher demonstration and instruction during whole class, small group or individualsessions.

ü Students with ‘scaffolding’ to develop and extend their mathematics learning. ü Independent group and individual participation. ü Students with choice and opportunities to explore mathematics concepts through

engagement and stimulation in a variety of multi-sensory activities. ü To have fun and develop a positive attitude to mathematics learning in a non-threatening

environment.

How to use this book

This book presents fun, interesting and straightforward mathematics learning centre activities thatwill empower teachers to work smarter not harder during the planning, implementation andassessment of mathematics lessons. They are based around the Level 3 outcomes as defined by the

national curriculum statements in ‘Mathematics- a Curriculum Profile for Australian Schools’.Activities are best used and adapted for students between the ages of 8 and 11 years. Or inextension or support programs for those students who are working with in the level 3 nationaloutcomes. The book is split into two major areas Establishing & Maintaining Mathematics LearningCentres and Activities and Lesson Plans. The first section guide teachers through the process of establishing and maintaining effective mathematic learning centres. With the next section providingthe activities that teachers can plan and implement into their mathematics planning andimplementation. Each section outlines and presents:

Establishing & Maintaining Mathematics Learning Centres:

ü An overview of lesson structures

ü Planning overview and weekly proformaü Assessment checklist and overview.ü Mathematics icons

Activities & Lesson Plans:

ü Activities created with a ‘thinking curriculum’ in mind provide a variety of learningopportunities that enable students of all abilities to develop and strengthen mathematicsskills and knowledge.

ü Detailed teacher notes to give an overview about each lesson.ü Activities matched to Mathematics- a curriculum profile for Australian schools.ü Lessons are organised into strands of Number, Space, Measurement, Chance and Data withthe Working Mathematically integrated into these lessons although outcomes are not

included.

ü Lessons cover national level 3 outcomes.ü Learning centres task cards that suggest activities that stimulate and develop all student

abilities, learning and thinking styles.

Resources:

ü 1-100 Numbers Chartü Australian Coins and Notesü MAB Base 10 diagrams

ü 2D Shapesü 3D Netsü Grid paper



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Lesson structure

For optimal mathematics learning it is suggested that lessons be structured using the organisationalstructure of whole, part, whole. The concept of ‘whole’ suggests the whole class engaging incollaborative learning activities as opposed to ‘part’ which refers small group or individual

participation. Therefore, lessons are planned and implemented according to the following structure:Ø Setting the scene & activity introduction:

To set the scene for mathematics learning the whole class begins learning together and participatesin 5 minute ‘energising activities’. ‘Energisers’ relate to concepts being introduced and investigateduring the lesson. After the initial scene is set class teachers lead whole class discussions anddemonstrations that ‘tune’ students into mathematical concepts and processes. Learning activitiesare then explained. Students are directed to their activity with the use of an Icon Board.Ø Learning centre activities, focussed teaching & classroom roving: This aspect of the mathematics lesson takes up the majority of lesson time. Students spilt intogroups or work individually to actively engage in learning centre activities. While studentsindependently complete their learning centre the teacher conducts focused teaching and learninggroups and general classroom roving.

• Learning centre activities: A variety of different learning centres can run simultaneously

during this time. Depending on the needs of students or classroom dynamics teachersmay choose to structure learning centre engagement in a variety of ways. These include:

§ Students not participating in ‘Teaching Group’ complete an activity sheet thenselect an activity from the selection on the task card.

§ Students not participating in ‘Teaching Group’ complete an activity sheet thenseparate into pre-determined groups to complete a pre-determined activity fromthe task card. For example, group 1 moves to the computer to complete the ICTactivity while group 2 works at a set of tables to complete the Creating &Making’ activity.

§ The activity sheet is used as a pre-determined or individual choice learningcentre.

• Focussed teaching and learning groups: These are generally known as ‘Teachinggroups’. Teachers draw out a small group of students to provide them with either extrateaching support or extension. This time can also be used to conduct assessmentactivities.

• Classroom Rove: When focussed teaching sessions are complete teachers conductgeneral roving of the room. Teacher move around the room from individual to individualor group to group to observe student learning. Informal assessment such as anecdotalnote taking is a useful tool to record observations.

Ø Share-time: To conclude the lesson students and the teacher again meet as a whole class for ‘share time’. ‘Share time’ enables all students to celebrate successes, discuss concerns, reflect

upon learnings and further draw upon or seek clarification about the mathematical concepts and processes investigated and employed during the lesson.



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Resources

Concrete mathematics resources should be made available to students at all times. This may be asimple as creating a ‘tool box’ using a large plastic container or tub to, creating mathematicsresource shelves or trollies. Resources readily available should include:

Calculators Plastic counters Bottle tops M.A.B.

Unifix Buttons Rulers Counting FramesIcy-pole sticks Dice container Number Charts Writing & Drawing tools

Hands on concrete materials can also be created quickly easily and at low cost. Make or collect thefollowing:

• Number Flash Cards – Cut coloured card into rectangles and handwrite numbers or alternatively use a desktop publishing program to print them out.

• Luck dip number boxes – Enlarge the Number Chart (pg 56) and cut out each number place into a washed take away food tub.

• Raffle ticket books or pre-used numbered ticket stubs

• Any old or used ticket tubs with numbers on them that are clearly readable

Note: For maximum use and longevity laminate number charts and flash cards.

Assessment All activities in this book are linked to the National Curriculum Outcomes. Assessment should bean ongoing process. Ongoing assessment assists in the process of planning and curriculumimplementation. Student assessment can be easily integrated into the structure of the mathematicslesson therefore, making it non-threatening for students. Assessment can be formal with the use of standardised testing kits or informal. Informal assessments can include student checklists or anecdotal notes of any observations that occurred. The following is an example of a completed

assessment checklist using the proforma provided in this book.

Assessment Check List Class Junior 1

Strand: MeasurementLevel: 2

Students Outcome: Measuring 1.21 Refers to familiar recurring phenomena when describing time.Indicators:

ü Order events within today and place regular activities in typical order.ü Understand that clocks are used to tell the time of day and link specific times on clock

to recurring daily phenomena.ü Understand that clocks are used to reflect the passage of time, linking the movement of

hands or changing of numbers to the passage of time.

Student Name

Beginning Consolidating Established

Comment

Jonh Green 5/8/07 Completed ‘What Did you do Yesterday’ – Ordered some events in correct sequence.

Petra Hope 5/8/07 Orders all events appropriately and is able to tello’clock times.



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Assessment Check List Class

Strand:Level:

Students Outcome:

Indicator:Student Name

Beginning Consolidating Established

Comment



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Planning Detailed documentation of practice is a key feature in the establishment and maintenance of effective mathematics learning centres and mathematics learning. The following details should beclearly outlined in planning documents:

• Focus/foci for lessons.

• Assessment outcomes.

• Activity/ies description.• Student grouping and activities they are expected to complete.

• List of students for focused teaching group and what skills will be taught.

• List of resources.The following is an example of detailed classroom planning with the aid of teaching notes andactivity ideas:

Focus: Ordinal Number Year Level: Prep

(Fig 1) Student Outcome:

Number Level 1: 1.11 Count and order: Counts and estimates collections, orders two or more collections, orders thingswithin collections

Indicator: Use terms first, second, third to indicate position in a sequence

(Fig 2) Mathematical Concepts:

• Ordinal number language e.g. First, second, third

• One-to –one correspondence

• Counting collections

• Ordering and creating sequence

(Fig 3) Resources:

Mathematics tool box coloured paper pencils & markers copies of ordinal number activity sheet & task cardsGlue Mathematical Words & Symbols Card.

(Fig 4)Whole Class Shared Maths

Energiser Activity: Students participate in races such as running, hopping, skipping, sack, walking/tossing balloons etc. Awardstudents with a place in the race using ordinal number i.e. First, Second, Third, Fourth etc.

Discuss: Language of ordinal number that was used in the energising activity. Explain: Activity sheet and learning centre activities. Demonstrate: How to record and write ordinal numbers in numerals and words.

(Fig 5) Independent Maths: Students select one of the following activities:

• Ordinal Number activity sheet

• Use a desktop publishing program to create a poster displaying a line of animals and label the order they are placed.

• Play board game and record the order each person finished.

• Draw counting materials (unifix, teddy counters, buttons) out of a container. Create a poster to show what order theywere drawn out.

• Make a ‘great presents’ book. On each page draw and write presents that would be appropriate to give someone ontheir 1st, 3rd 6th 10th 16th and 35th birthday

(Fig 6)Teaching Group

Angela, Michael, Connor, Aimee & Nickos

(Fig 7)Teaching Group Focus

• Ordering and creating sequence

• Ordinal number language e.g. First, second, third

(Fig 8) Share time:

Students discuss with a partner a fact they know about ordinal number. For example the winner or leader in a line is alwaysthe 1

st.

Helpful Hint : Enlarge the weekly planning proforma (over leaf) to allow for ease of planning andmaximum space.



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Insert planning proforma this page



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Icon board An icon board containing pictorial icons, student groups and student name tags should beestablished and updated for each mathematics lesson. The icon board is a reference for students whoneed further clarification about what is expected of them during the lesson. The board shoulddisplay what mathematical activity students will engage in and which students will participate in

focussed teaching sessions. The following is an example of how the board can be organised. Page 3contains a set of icons that may be used to create the icon board.

Figure 1.Figure 2 – ICT Icon

Figure 3. Teaching Groups Icon Figure 4 – Sharetime icon

Figure 5. Create & Construct Icon Figure 6 Play, Do, Make Icon

Figure 6 Group work icon Figure 7 Individual work icon



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Teacher Notes:

Topic Focus: Number –Numbers

Student Outcomes:

Count and Order – 3.11 Counts, orders, estimates and describes with whole numbers, common fractions and decimal fractions for money or measurements (two places).

Indicator: Use multiples –equivalent groups- to count and compare collections.

Use place value to read, write, say and interpret whole numbers, oral or writtenUse place value to assist in estimation.

Mathematical Concepts:

• Reading and writing numbers in numerals and words.

• Place value.

• Rounding numbers to nearest 10 or 100.

• Odd and even numbers.

• Extended form.

• Creating pictorial representations of numbers. Setting the Scene:

Five Minute Energiser Number Who Am I? – Select a number between 0- 9999 write in down but don’t show anybodyelse. Students try to guess the number by asking questions that can only receive a yes no answer.For example students could ask, ‘is it a 3 digit number?’, ‘is it odd or even?’, ‘does it have a 0 init?’ etc.Tunning In and Activity Introduction:

Discuss: Which questions were most successful in giving information about the number and why? Revise: Place value, identifying odd and even numbers, making and drawing MAB number models. Introduce: Rounding numbers to their nearest 10 or 100. Sharetime

Students share the numbers they have rounded to the nearest 10 or 100 and discuss the strategies

they used to do so.



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Numbers Learning Centres Number Mind-Map.Create a mind-map displaying information about a number of your choice. The number should beone that you are confident with but that also challenges you. Your mind-map should include thefollowing information:

Your number in numerals and words.Your number in extended form e.g 678 = 6 hundreds + 7 tens +8 ones.A picture of your number.Round your number to its nearest 10 or 100.A number pattern your number appears in.

Number Trivia Cards.Create a set of trivia cards about numbers. Questions could be about the number’s place value, theycould be MAB pictures, they could be true or false questions or multiple choice.

Number Table

Insert a 4 column and 10 row table into a publishing document. Type in the headings below andlook at the completed example. To finish to table roll a dice to create a number (up to 4 digits) andthen write the number in numerals, words, round it to its nearest 10 or 100, write it in extended for and insert .

Numerals Words Round Number to Nearest 10 or 100

Extended Form

457 Four hundred andfifty seven

460 4 hundreds 6 tens0 ones

Round the Number

Select a ticket from the lucky dip numbers and round it to its nearest 10 or 100. Record your number and answer.



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Teacher Notes:

Topic Focus: Number – Number Student Outcomes:


Indicator: Use multiples –equivalent groups- to count and compare collections.

Use place value to read, write, say and interpret whole numbers, oral or writtenUse place value to assist in estimation.


• Reading and writing numbers in numerals and words.

• Place value.

• Rounding numbers to nearest 10 or 100.

• Odd and even numbers.

• Extended form.

• Creating models and pictorial representations of numbers. Teaching Tips:

•

MAB Picture – Another idea is to cut out a one, ten, hundred and thousand block pictures (pgand scan the MAB pictures into a computer and then save each one as a picture file. Studentscan then insert them instead of creating a picture and taking a digital photo of it.

Setting the Scene:

Five Minute Energiser

• Number Models – Play in groups of three, one player uses MAB to make a number, while theother two verse each other to guess the number. The player who guess correct wins.

Tunning In and Activity Introduction:

Discuss: What strategies students used to figure out the number. Revise and demonstrate: How to make numbers using MABs; draw visual representations of them;and how to write numbers in numerals, words and extended form.

Sharetime: Students share a fact about place value, rounding or making models of numbers that they learnttoday or yesterday.



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Number Learning Centre Activities.

Place Value Challenge No of Players: 2-5Equipment:

Dice (2 or more)1 minute sand timer or stop watch.How to play:One person is ‘The Adjudicator’, the others are the contestants. The adjudicator rolls the four diceand starts the clock. The contestants have one minute to use the four dice to create as many numbersas they possibly can. Numbers can be single, double, three, four or 5 digit numbers it is up to thewhole team to decide how many to use. No number can be repeated unless they appear twice withinthe roll. The Adjudicator calls stop when time has run out. The contestants must be able to readtheir numbers to the Adjudicator and the contestant with the most numbers wins.

Number Flip it Chart?

Construct a ‘Number Flip It’ chart to make different numbers.You will need:A3 Coloured Poster CardA4 paper.Markers, stapler, glue, scissors etc.Method:On your A3 paper write the heading ‘Flip it Number Chart’.Decide if your flip it chart will be made up of two, three, four or five digit numbers.Cut your A4 paper in quarters.Take 10 pieces of the cut paper and staple them together in a row along the top.Write the number 0-9 in the flip pad, (each page should contain a different number).

Create an identical flip pad for each place value column.Stick all the flip pads in a row on the A3 paper. Make sure they are as close as possible.Flip the different pads to create new numbers.Use your chart to: Read and write numbers in words or numerals.

Make the number you have created with MAB.Round it to the nearest 10 or 100.

MAB Picture.Use MAB to create a picture scene. Take a digital photo of your picture scene and insert it into a

publishing document. Add up how much your picture is in total value. On your page insert howmany ones, ten, hundreds and thousands were in your picture.

Number QuadrantsComplete the following number quadrants. Choose a number to place in the middle of thequadrants.Quadrant 1- Make your number using MAB then draw the picture in the quadrant.Quadrant 2- Write your number in extended form.Quadrant 3 – Round it to the nearest 10 or 100.Quadrant 4-Write facts about the number. – Is it odd or even, how many digits is it made up of,what number comes before and after it etc.



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Teacher Notes:

Topic Focus: Number Patterns

Student Outcomes:

Number Patterns 3.12 – Identifies, continues and invents whole number patterns involving the four operations, including where successive terms in a sequence can be linked by an addition or

subtraction strategy.

Indicators: Describe a rule that could be used to generate a sequence involving an addition or subtraction strategy which may involve more than adding a constant amount.Describe a rule that could be used to generate a multiplying or repeated additionsequence.Continue or fill in number sequences based on an addition or subtraction strategyinvolving more than adding a constant amount.Follow a rule to generate a number sequence based on addition or subtractionstrategy.Use patterns in digits to make predictions.


• Skip counting

• Creating sequence• Predicting, creating and describing counting patterns.

• Repeated addition and subtraction.Setting the Scene:

Five Minute Energiser Pattern Hunt- Go on a hunt for all the patterns in and around the classroom that you can find. Takedigital photos of these or a written list.Tunning In and Activity Introduction:

Classify: Classify the patterns that were discovered into groups of number, shape or other. Explain: Number patterns and their relation to multiplication, repeated addition and subtraction.

Demonstrate: How to create and identify number patterns with alternate amountsSharetime: Share the strategies that you used to solve your number patterns.



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Number PatternsFill and Find.Complete these counting patterns and describe their rule.5, 10, 15, 20 -------------------1006, 12, 18, 24--------------------72

4, 8, 12, 16----------------------602, 4, 6, 8, 10---------------------381, 3, 5, 7, 9--------------------------312, 5, 8, 11, 14----------------------353, 8, 13, 18, 23--------------------43101, 98, 95, 92--------------------62143, 139, 135, 131, ----------------91

Dice Patterns.Select one of the numbers below to start your number pattern. Roll a dice to find out what you willadd on or subtract to create your number pattern.

67 54 221 1 0 8 5 7 88 54 186 754 653 11 21 38

Roll the dice twice to create an alternate number pattern.

Our House.Generally streets and roads are numbered odds on one side and evens on the other. Why do youthink this is?Use a desktop publishing program to create your poster.If you live in a street or road use your house as a start and create a poster to show the number

pattern on your side of the street or road.If you live in a crescent, court, avenue or other does the same rule apply to you? If yes complete the

above activity. If no, create a poster showing the house numbers in your street.

True or False –Number Pattern Facts.Answer these questions with either true or false and explain why?12 is in the 3s counting pattern.54 is in the 7s counting pattern.13 is in the even numbers counting pattern.45 is in the fours counting pattern.91 is in the eights counting pattern.89 is in the 4s counting pattern.76 is in the 6s counting pattern.

452 is in the 3s counting pattern.654 is in the 6s counting pattern.99 is in the 9s counting pattern.101 is in the 11s counting pattern.



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Teacher Notes:

Topic Focus: Number –Addition and Subtraction Number Facts

Student Outcomes:

Mental Computation 3.15 – Estimates and calculates mentally, including adding (sum to 100) and subtracting two-digit numbers and multiplying numbers to 10. Indicator: Remember basic addition facts and some multiplication facts and calculate mentally

basic multiplication facts they don’t recall. Equations 3.13 – Uses understanding of whole and fractional numbers, relationships and operations to construct and complete simple statements of equality.

Indicator: Use addition/subtraction and multiplication/division relationships to solve missingnumber problems.Use patterns in sequences of number equations to generate new equations.


• Automatic response of numbers to 20.

• The relationship between addition and subtraction.

• Mental computation of numbers up to 100

Teaching Tips:

• Round the World in 25 – Change the number in the title to the number of students in your class.Setting the Scene:


• Round the world in 25 – Students stand in a circle, select two students to begin. Call outautomatic response equations to students, the first to answer moves along to the next student.The student who can travel around ‘the world’ and beat their opponents is the winner.


Explain: The addition and subtraction relationship when completing number facts to 100.

Demonstrate: How to complete fact families and number sequences.Sharetime:

Share the strategies you used to complete number fact equations.



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Number Facts to 100Addition & Subtraction Automatic Response – Numbers to 20How many equations can you complete in one minute. Keep repeating to better your previous score.6+4= 3+7= 9+1= 5+5= 8+2= 9+6= 11+9= 9+9= 6+6= 12+8= 7+4= 2+3=5+6= 4+4= 1+19= 8+6= 12+5= 12+3= 17+3= 9+9= 3+3= 1+9= 2+8= 2+6=

4+16= 11+7= 17+2= 14+5= 15+4= 14+3= 2+16= 14+3= 12+3= 14+1= 6+12= 15+2=10-2= 8-7= 5-2= 7-3= 9-4= 2-1= 6-4= 7-7= 8-5= 3-3= 7-2= 11-1=4-4= 7-6= 9-1= 7-1= 6-3= 3-2= 8-2= 9-6= 10-5= 12-6= 12-5= 17-7=18-6= 15-7= 17-3= 18-9= 20-6= 19-4= 20-7= 18-7= 14-7= 18-3= 16-9= 18-11=

Paper Doll Number Fact FamiliesHold a piece of A4 paper portrait way up and then fold it into quarters. Draw an outline of a personon the front page making sure the arms extend to the end of the page, like the diagram below andthen cut around its outline. Unfold to see your family write a different number fact on each of thedolls and decorate. E.g 14+6=20 6+14=20 20-14=6 20-6=14See how many different families you can make.

Number Fact Poster.Use a desk top publishing program to create a poster displaying all the number facts to 100 that youknow. Create and solve some new ones.

Number Fact Patterns.Complete the following equations.1+9= 13-7= 11+8=10+9= 23-7= 21+8=20+9= 33-7= 22+8=30+9= 43-7= 23+?=31

40+9= 53-7= ??+8=50+9= 63-7= ??+?=5160+9= 73-7= ??+?=6170+9= 83-7= ??+?=?80+9= 93-7= ??+?=?90+9= 103-7= ??+?=?Create your own number sequence patterns.



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Teacher Notes:

Topic Focus: Number - Addition

Student Outcomes:

Applying Numbers 3.14 – Makes a suitable choice of operation for situations involving wholenumbers, amounts of money and familiar measurements.

Indicator: Suggest a story question that relates to a given number sentence.

Equations 3.13 – Uses understanding of whole numbers and fractional numbers, relationships and operations to construct and complete simple statements of equality.

Indicator: Use addition/subtraction and multiplication/division relationships to solve missingnumber problems.

Written Computation – 3.16 Uses understood written methods to add and subtract any whole

numbers and amounts of money and to multiply and divide whole numbers by whole numbers to 10. Indicator: Add columns of whole numbers and subtract one number from another.

Give a reasonable explanation of their written method for adding or subtractingnumbers works by referring to place value.

Calculators 3.17 Uses a calculator for operating on whole numbers, amounts of money and measurements.

Mathematical Concepts:• Language of addition.

• Vertical and horizontal addition of three digit numbers.

• Manipulate materials to solve addition picture, number and word problems.

• Recording addition number and word problems.

• Trading. Teaching Tips:

• Luck Dip MAB Addition – Use the MAB diagrams to create cards representing three, two andsingle digit numbers.

Setting the Scene:

Five Minute Energiser • Bingo Addition: Students create a 5 by 5 grid and add numbers 1-20 in each box. Teacher calls

out addition sum to 20 and students mark off the answer if it exists on their grid. The firststudent to get four in a row is the winner.


Brainstorm: All the strategies that students used when adding the answers for addition bingo. Introduce and demonstrate: Vertical addition with trading. – Estimate and record estimation first.Use MAB materials to complete problem and write a number problem to accompany it.Sharetime: Students share the strategies that they found to be the easiest use to solve addition problems. Ask students if there were different strategies for different types of sums. Ask students if their

estimations were accurate and why?



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Addition Learning CentresLuck Dip MAB AdditionPick two cards from the MAB lucky dip box and add them together. First estimate and record your estimation. Then record your addition number problems appropriately and write a number story toaccompany it.

Race to a HundredPlay in pairs or a group of three. Each player takes a turn to roll the dice and makes the number theyrolled using MAB you will need to trade as your number gets higher. The first to reach 100 or moreis the winner.

Bulls-eye!Players select 10 counters and flick them onto the target. The numbers on the target represent

points. Each player adds their points and the player with the most points is the winner.

Create your own bulls-eye target and allocate point to it. Use it to play a game.Addition Grids

+ 346 543 672 989

453

567

765

865

Try creating your own addition grids.

+ 5 17 34 99

14

76

61114

+ 34 88 97 150

56

76

5390

+ 16 44 63 98

188

236

270480



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Teacher Notes:

Topic Focus: Number - Subtraction

Student Outcomes:


Indicator: Suggest a story question that relates to a given number sentence.


Indicator: Use addition/subtraction and multiplication/division relationships to solve missingnumber problems.


numbers and amounts of money and to multiply and divide whole numbers by whole numbers to 10. Indicator: Add columns of whole numbers and subtract one number from another.

Give a reasonable explanation of their written method for adding or subtractingnumbers works by referring to place value.

Calculators 3.17 Uses a calculator for operating on whole numbers, amounts of money and measurements.

Mathematical Concepts:• Vertical and horizontal subtraction of three, two and single digit number.

• Estimating before solving subtraction problems.

• Manipulate MAB and other materials to solve subtraction number and word problems.

• Recording subtraction number problems appropriately and creating subtraction number stories.

• Regrouping

Teaching Tips:

• The Weekend Footy ResultsTo extend this activity allow students to explore the sports section of the newspaper to find other

game results and then work out the difference in these results.Setting the Scene:


• Tell me what you know about subtraction- Students sit in a circle and take turns to tell the classsomething they know about subtraction. Record student answers,


Discuss: Answers given about subtraction and address any misconceptions. Demonstrate: How to estimate, use MAB to solve vertical subtraction problems using regrouping,record problems appropriately and write a word problem to accompany the number problem.Sharetime: Ask students to share something about subtraction they found hard or easy and ask them to explain

why? If students encountered a difficulty ask them what they did to solve this problem.



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Subtraction Learning CentresReverse SubtractionHere are the answers, what are the questions? Write a list of the possible number or word problems.14 27 32 48 53 167 89 150 7 11 535 765 965

The case of the Missing Counters.I had a jar full of counters and now I only have 25 left. Write as many equations as you can to showhow many were taken away. Write word problems to match your number sentences. Remember theamount that was in the jar can be different each time.

Develop a Computer Generated Subtraction Game.Use a desktop publishing program to develop a game that is based around subtraction. Your gamecan be a set of quiz questions, board game, card game or another exciting game. Print your gameand play it with friends.

The Weekend Footy Results

On the weekend a round of footy was played. 16 teams played a game each and the results were asfollows:

Dragons v’s Crows 115 to 67.Saints v’s Dolphins 97 to 48.Bears v’s Lions 134 to 89.Bullants v’s Reds 67 to 23.Trains v’s Trucks 146 to 37Storm v’s Allstars 94 to 55.Magic v’s Troopers 61 to 9.Spies v’s Tigers 142 to 78.

Find the difference in scores between all games.



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Teachers Notes:

Topic Focus: Number - Multiplication

Student Outcomes:


Indicator: Select an appropriate multiplication to deal with repeated addition.


Indicator: Use the relationship between multiplication and division to solve missing number problems.


numbers and amounts of money and to multiply and divide whole numbers by whole numbers to 10. Indicator: Multiply by single digit numbers.Calculators 3.17 Uses a calculator for operating on whole numbers, amounts of money and measurements.


• Creating equal and unequal groups

• Recognition of multiplication symbol (x) and language (groups of, lots of, times)

• Repeated addition

• Counting rows and arrays

• Skip countingTeaching Tips:

• Find your group: Use the BLM on page 50 to cut up for this activity. Setting the Scene:


• Find your group Give students each a card that they need to hold in-front of themselves. Theyneed to move around the room silently to make groups of three. The set comprise of a

multiplication algorithm, the answer a repeated addition picture.Tunning In and Activity Introduction:

Explore: Give students a calculator and ask them to complete a variety of repeated additionalgorithms e.g. 5+5+5+5+5= Mention to the students that it is taking a while to key in all of thenumbers can anybody think of a quicker way to solve these problems.

Discuss: Multiplication and its relationship to repeated addition. Demonstrate: How to estimate, use materials to solve multiplication problems, how to solvemultiplication with remainders and how to record them.Sharetime: Students share a strategy that they found useful to solve multiplication problems.



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Multiplication Learning Centre Activities.

Cows in the Meadow.On the weekend I visited a farm and saw cows grazing in a meadow. The meadow was split intosmaller fields. In each field an equal amount of cows was grazing all except one field which had an

uneven amount. Create a poster to display what the meadow may have looked like. Write a number sentence and word problem to accompany your picture.

Multiplication Cards.Use the cards on the sheet as a starting point and then add to this deck by creating your own cards.Use a piece of card to split into three columns and eight equal rows. In the first column write your number problem, in the second the answer and in the final column a repeated addition picture.

Singles, Pairs, Tripples or DozensSome objects naturally occur or come in equal collections. For example, socks come in pairs andeggs are sold in dozens.

Create a slide show to display more than one collection of these objects. On each slide include thename to describe the collection, how many objects it takes to create that collection. Use collectionto create a multiplication picture, repeated addition number problem and multiplication number andword sentence.Helpful Hint:1= single2= pair or twin set3= triple6= half dozen12= dozen

Old School DaysA school is made up of 10 equal classes and 1 that is not. Create a poster to display what the classesmay look like.Include a multiplication number problem and word story.Estimate how many students attend this school and then give an answer.



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Teacher Notes:

Topic Focus: Number - Multiplication

Student Outcomes:


Indicator: Select an appropriate multiplication to deal with repeated addition.




numbers and amounts of money and to multiply and divide whole numbers by whole numbers to 10. Indicator: Multiply by single digit numbers.Calculators 3.17 Uses a calculator for operating on whole numbers, amounts of money and measurements


• Creating equal and unequal groups

• Recognition of multiplication symbol (x) and language (groups of, lots of, times)


• Counting rows and arrays

• Skip countingTeaching Tips:

• Times Table Poster.- You may choose to select the set of times tables students use so that aclass set can be created for display purposes.

Setting the Scene:


• Pattern Scramble – Select a number pattern and write it on the board in a jumbled manner.

Students need to un-scramble the pattern.Tunning In and Activity Introduction:

Revise: The relationship between counting patterns, repeated addition and multiplication. Discuss: Times tables and how they make solving multiplication and repeated addition problemsquick and easy.

Demonstrate: The structure of times tables and strategies to solve them.Sharetime: Students share some time tables facts that they know of have learnt during the lesson.



24


Multiplication Learning Centre Activities.Magic Tables Table:Complete the following table:

x 1 2 3 4 5 6 7 8 9 10

1

23

4

5

6

7

8

9

10

Write about any patterns you can see or any strategies that you could use to make it easier toremember your tables.

Times Tables Races.Play in a groups of 3 or 4.Pick a number from 1- 10 and each player needs to write that set of tables as fast as they can. The

person who shouts stop first is the winner.

Times Table Poster.Use a desk top publishing program to create a poster to display a set of times tables. Times tables

begin at 0x ? = and continue in number order (1, 2, 3,etc) until 12. Times tables consist of repeatedaddition number patterns and start at the 1s times tables and end at the 12 times tables. Select one of these number patterns or a number pattern in-between them to create your times tables poster.Include:The multiplication number problem.The repeated addition number problem.A picture to match the number problems.

Table Songs.Select a set of times tables and use musical instruments to create a song. Practice the song and

perform it to the class. Remember the song should help you learn your times tables so make surethat the accompanying music has a consistent beat.



25


Teacher Notes:

Topic Focus: Number -Division

Student Outcomes:


Indicator: Select an appropriate division to deal with sharing and grouping where the divisor is

a whole number and smaller than the dividend. Equations 3.13 – Uses understanding of whole numbers and fractional numbers, relationships and operations to construct and complete simple statements of equality.


Written Computation – 3.16 Uses understood written methods to add and subtract any wholenumbers and amounts of money and to multiply and divide whole numbers by whole numbers to 10.

Indicator: Divide a whole number by a one digit number, expressing the results withremainders or fractions.


• Sharing collections of objects to create equal and unequal groups.

• Identifying the relationship between counting patterns, multiplication and division. • Recognition and use of division symbol (÷)

• Making, drawing and writing division number stories

Setting the Scene:


• Reorganise the collection. –Ask students to each take a large handful of counting materials andto organise this large group into smaller equal groups.


Discuss: How groups of collections were reorganised, if they were all successful in creating equalgroups and if not what did they do with the left overs.

Explain: The strategies of division and what to do when numbers can’t be divided equally. Demonstrate: How to estimate and solve division problems and then record them.Sharetime: Students share something they found to be interesting about division.



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Division Learning CentresLucky Dip DivisionSelect a number ticket from the lucky dip box and then divide it by these numbers:5, 7, 3, 2, 8, 9, 12

Record your estimation and the strategies you used to solve these problems. Keep selecting ticketsto solve new division problems.

Multiplication Flips.Flip these multiplication sums to create division sums. You may need to complete some first.2x3=6 5x3=15 6x2=12 3x4=125x5=25 2x4= 7x2= 4x?=1610x3= 11x?=22 9x6=? ?x7=776x4=? ?x8=32 3x?=0 7x?=2112x?=36 4x?=20 7x2=? 8x8=64

Sweets for my Sweet.A group of friends were at a birthday party together and on the table was a bowl full of sweets. Thefriends decided to share them as fairly as they could so they decided to divide them between eachother. Create a computer generated poster displaying how they may have done this and how manyeach friend got. Was there any left over, if so how many and what did they do with them?

Division Bingo.Create a Bingo board game using division problems. Your boards may include the sums with theanswer cards used to be drawn out or the answers may be on the board with the question cards usedto be drawn or a combination of both.



27


Teacher Notes:

Topic Focus: Number – Using Brackets and the Four Processes

Student Outcomes:


Indicator: Complete numerical statements involving brackets where only one number is

‘missing’.Mathematical Concepts:

• Brackets in algorithms.

• Completing number sentences with missing symbols or digits. Teaching Tips:

Setting the Scene:

Five Minute Energiser Don’t Burst the Balloon!- Draw 20 balloons on the board and a blank number problem. E.g. _ _ _=_ Students need to guess what the number sentence is by asking yes or no questions. For example isthe first number a double digit number. A no answer leads to the popping (crossing out) of a

balloon. Students need to guess the answer before all the balloons have been burst.Tunning In and Activity Introduction:

Discuss: Strategies used to complete the number sentence in the fastest way. Introduce: Brackets and their function (i.e. complete first) in algorithms. Demonstrate: How to solve algorithms that include brackets and missing digits or symbols.Sharetime:



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Brackets and the Four ProcessesThe Jumbled TableThe following number sentences have been put into a table to show their place in a problemhowever due to a computer error the table has become jumbled and the only column that is correctis the answer column. Un-jumble the table to create the correct number sentences

Digits Symbol Brackets Answer 200 + (5x8) 40

10 x (77+99) 60

22 - (10÷2) 144

88 - (132-32) 55

55 + (62-14) 1000

11 ÷ (27+62) 24

12 x (54-17) 125

100 + (6x3) 4

Try creating your own jumbled table and give it to a friend to solve.

Multiple Choice Questions about AlgorithmsYou have a choice of answers A, B or C find the correct one. Show your working out to prove your answer correct.1. The answer which question is 35. 2. 76-(10x3) = 3. Brackets are completed when in sums:A.20 + (20-5) = A. 44 A. In the order they come.B. (25-5) + 20 = B. 43 B. FirstC. 25 – (20 + 26) = C.46 C. Last

4.When adding numbers the answer should be --- than first?A. Lower B. Higher C. The Same

5. Multiplication is the same as:A. Subtracting different numbers repeatedlyB. Adding different number repeatedlyC. Adding the same number repeatedly.

Create your own multiple choice questions about using brackets and the four processes.

Computer Generated Board Game

Create a computer generated board game using a variety of sums to direct the players around the board. For example: You could create cards that players need to pick up and solve a word or number problem to find out how many places they can move. Or this could be displayed on the

board itself.Include a variety of multiplication, division, subtraction, addition number or word problems andalso some that involve the use of brackets.

Tickets Please!Select three tickets out of the luck dip number box. Arrange them so you can successfully createaddition, subtraction, multiplication or division problems that involve using brackets.For example: If you selected the following combination 24, 35 and 6 your could create the

following sums (35-6) + 24= or (24 + 35) – 6= or (24 6) + 35 =



29


Teacher Notes:

Topic Focus: Number – Money

Student Outcomes:


Indicator: Regroup money to fewest possible number of notes or coins

Use decimal notation to two places to represent quantities and money Mathematical Concepts:

• Identifying features of coins and notes.

• Exchanging coins and notes.

• Skip counting


Teaching Tips:

• Learning & Earning -Classroom money can be created and used as a positive behaviour rewardsystem before conducting money lessons. Students can use the money they earned in the ClassAuction.

• How can I pay?- Collect a variety of catalogues that students can use to cut out for this activity.Setting the Scene:


• Counting the Cash- Tell students that you have some coins and notes in your purse and alladded up it equals to $10.50. As a class guess the possible combinations of notes and coins thatmay be in your purse.


Discuss: The strategies used to create the different combinations of coins and notes. Whichcombination used the least amount of coins and notes, is there another?

Introduce: The concept of swapping coins and notes to attain the fewest possible coins and notes. Demonstrate: Which combinations can be exchanged to achieve smallest amounts e.g. 5cent coins

x10 could be exchanged for 1 50cent coin.Sharetime

Select a student from each group to share their activity and show their combinations of money. Ask the whole class to point out each combination that showed the least amount of coins in eachactivity. Ask students if there are other combinations that use even fewer coins or notes.



30


Money Learning CentresMoney RubbingsCreate coins rubbing pictures to show the combination of coins that could make up these amounts.50 cents $2.20 $3.80 $5.60 $7.30 $9.50

Change Please!I bought some lollies at the corner shop this morning and they cost me $3.95 and I gave the shopkeeper a $20 note. Create a list of the possible combinations of change I got back.Circle the combination with the least amount of coins and notes.Underline the combination that used the most coins and notes.

I Don’t Have the Right Change!Use a draw program on a computer to draw a note or note. Try to include as many of its features as

possible. Then create a list of coins or notes that also equal that amount.

How can I pay?

Use a catalogue to find items and their prices. Create a poster by cutting out the item and its price.Write the least amount of coins and notes that you would need to pay for that item.



31


Teacher Notes:

Topic Focus: Number – Money and Decimals

Student Outcomes:


Indicator: Regroup money to fewest possible number of notes or coins

Use decimal notation to two places to represent quantities and money Calculators 3.17 Uses a calculator for operating on whole numbers, amounts of money and measurements.

Indicator: Enter and read amounts of money and measurements on a calculator, roundingcalculator to the nearest cent or unit, and recognising, for example, 1.5 as $1.50


• Decimals and money

• Identifying features of coins and notes.

• Exchanging coins and notes.

• Skip counting


Teaching Tips:

• Decimal Hunt – A number program such as or similar to Microsoft Excel is great to use for thisactivity.

Setting the Scene:


Money Groups: Give each student a coin (try to have a variety) and then call out a monetary amounte.g. $1.30 – Students need to find others in the class who have coins that will create thatcombination. When students have created that combination they sit down.Tunning In and Activity Introduction:

Discuss: The different combinations used to create the monetary amounts.

Introduce: The concept of decimal numbers. Demonstrate: How to recognise decimals in monetary amounts.Sharetime

Students each read out 5 decimal amounts.



32


Money & Decimals Learning Centre ActivitiesCalculator Money Adding.A cash register is another form of calculator. Select a receipt and choose some amounts or items toadd using a calculator. Create as many addition problems as you can and record the process youtook to solve them.

How Many Items can You Buy?You have $100 spending money to spend as you please. Use catalogues to find out how many itemsyou can buy with $100. Have a competition with others to see how can buy the most items. Create alist of the items you can purchase and their prices. You can use a calculator to add or subtractmonetary amounts.

Decimal HuntLook through catalogues or in the classroom to find as many decimal numbers shown as moneyamounts. Create a computer generated chart or table to order them from the smallest amount to thelargest amount. Don’t forget to include the name o the item also.

Decimal CombinationsList all the combinations of decimal monetary amounts that you can create with these coins andnotes:



33


Teacher Notes:

Topic Focus: Number -Fractional Numbers Student Outcomes:

Count and Order 3.11 -Counts, orders, estimates and describes with whole numbers, common fractions and decimal fractions for money or measurements (two places).

Indicators: Use materials and diagrams to represent fractional amounts where the whole may be

an object, quantity or collection.Express generalisations about fractional numbers symbolicallyCount in common fractional amounts.


Indicators: State fractional equivalents in words and symbolsMathematical Concepts:

• Recognising fractional numbers

• Fractional language.

• Recording fractional numbers.

• Making, drawing and writing fractional numbers.

• Fractional Equivalents

Teaching Tip:

• Shape Fraction Match – Draw common shapes onto A4 paper and cut them up into equal parts.Eg cut a square into quarters, a rectangle into sixths or a circle into 12ths.

Setting the Scene:


• Shape Fraction Match- Give each student a part of a pre- cut shape fraction (see teaching tip).Students need to move silently around the room to re-create the whole shape. Students need tothen express their part of the shape as a fraction.


Discuss: What is meant by the term fraction and how to we label them Demonstrate: How read and write fractions and how to identify their equivalents.Sharetime

Share strategies for creating equivalent fractions.



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Fractions Learning CentresBallsThere were a variety of balls in a sports bag. ½ were blue, ¼ were yellow and another ¼ were red.Draw what the contents of the bag may have looked like. Label the picture to show the fractions.In this problem can you find an equivalent fraction?

It’s in the Eyes.A third of our class has brown eyes, another third has blue eyes with the remaining third havinggreen eyes. Draw a picture of what our class looks like.

Fraction Poster.Use a desktop publishing program to create a poster that explains fractions.Include:A definition of a fraction.Definition and example of an equivalent fraction.A labelled fraction to show its numerator and denominator.

Diagrams to show fractional amounts.

Show Me the Fraction!Here is a list of number fractions. Create a cut and paste collage to show these amounts as pictures.½ 2/3 ¾ 5/8 4/6 7/11 9/10 5/12 8/16 3/20

Create equivalent fractional pictures or diagrams for some or all of the above fractions.



35


Teacher Notes:

Topic Focus: Measurement - Time

Student Outcomes:

Time 3.21 Measures time and duration of time, reading clocks, calendars and straightforward

timetables. Indicators: Estimate time of day, week or year using clues such as shadows, weather, clothing,

fullness of car park, shop signs, plant behaviour.Tell the time on digital and analog clocks.Read and make simple schedulesClassify events into those that take more than or less than or about one hour or onehalf hour or five minutes.Ask and answer questions about how long things took or will take and measure timeintervals using natural units of time, artificial non-standard units, or standard units.


• Investigating instruments that measure time e.g. digital and analog clocks.

• Recording time.

• Estimating time.

• Telling time.

• Creating time tables. Setting the Scene:


• What time could it be?- Explain a situation to students and using the clue they need to guess thetime of day. E.g. I went to the shopping centre and the car park was full, I bought some food andate it in the food court, Lots of others were buying food too. The tables around me were quitefull. I ate a salad sandwich – What time of the day was it?


Discuss: Events around us that can predict the time of day. Consider more formal ways of

measuring time. Demonstrate: How to tell the times using a digital clock and analog.Sharetime

Students tell a time on an analog or digital clock.



36


Time Learning CentresClassroom Timetable.Create a timetable to show all the activities that you and your class participate in during the week.Include the time they start and finish.

Do you have the Time?Create a poster to display these times on both an analog and digital clock.9:30pm 7:35 am 6.47pm 9:56pm 5:15am 7:32pm 4:18pm 3:38am 14:44 17:52 23:41

Pictures and Words to Describe TimeUse a desktop publishing program to create a list of pictures and word poster that describe times of the day.E.g. Sunrise

night

How long is an hour?Classify activities that take an hour to complete, more than an hour and less than a hour. Include theapproximate times that it does take to complete them



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Teacher Notes:

Topic Focus: Measurement - Angles

Student Outcomes:

Measuring 3.19 Directly and indirectly compares things including by counting uniform units of

angle, area, capacity and mass and measuring length to the nearest marked graduation.

Indicators: Identify angles in turns or rotations.

Order angles by direct comparison of the amount of turn and by using such units as aquarter turn or an angle of their own making.


• Introducing angles and their relationship to everyday objects.Setting the Scene:

Five Minute EnergisersSelect one or both of the following activities:

• Human Clock. – Ask students to stand up and use their arms to create different times on ananalog 12 hour clock face.


Discuss. That as their hands were moving and creating different times it reminded you of angles.

Consider what an angle is and what students already know about angles. Introduce: The concept and use of angle. Demonstrate: How to label and identify angles that show a quarter turn, half turn, ¾ turn and fullturn.Sharetime

Students each share something they learnt about angles during the lesson.



38


Angles Learning CentresAngles in shapes.Select a variety of 2D shapes, draw them and find all their angles. Label the angles you havediscovered in these shapes. Eg A square has four angles and they are all equal. They are all quarter turns.

Angles in triangles.Here is a variety of triangles:Scalene Isosceles Right angle Equilateral

Investigate the angles in these triangles.Are they all the same why or why not?Why do you think a triangle is called a triangle?Identify and label the angles in the above triangles.

Angles in our LivesUse a word processing document to create a poster to display all the angles that you can find ineveryday objects.Insert clipart pictures, identify and label the angles.

Angle ClassificationClassify objects in your classroom according to their angles. Criteria for classification couldinclude: Objects with a quarter turn, Objects with more than one quarter turn, Objects with less thana quarter turn etc.List and draw as many classroom objects that you can find that fit these descriptions.



39


Teacher Notes:

Topic Focus: Measurement – Length

Student Outcomes:



Indicators: Measure length to the nearest marked graduation.

Use numerical measurements of objects to order the objects. Estimating 3:20 Makes sensible numerical estimates using units that can be seen or handled and

uses words such as ‘between’ to describe estimates.

Indicators: Make sensible numerical estimates based on provided units.Use body parts and movements as a unit to help estimate length


• Language of measurement

• Measuring lengths using informal and formal units

• Estimating lengths

• Comparing lengths

• CountingTeaching Tips:

• String Measuring: Cut up different lengths of string, make sure you have an equal amount thatare the same length and an equal amount that are uneven

• Measure and Order Paper Strips: Cut up a varying lengths of A4 and A3 paper to create acontainer full of paper strips.


• String Measuring: Give students each a length of string and ask students to find something inthe room than is ½ the size, twice the size or the same length. Select a variety of students toshare their discoveries.


Discuss: What strategy students used in order to find their objects. Ask students is they know of amore accurate way of measuring to find objects that are exactly the same, ½ or twice the size.

Demonstrate: How to accurately measure using a ruler.Sharetime

Students share the measurement of the longest or shortest objects they measured and provide a brief explanation or demonstration of how they measure these objects.



40


Length Learning CentresMeasure and Order Paper Strips.Take a handful of paper strips. Estimate their length using an informal unit and then use your informal unit to measure this length. Then estimate and measure your strip using a formal unit of measure. After you have measured all of them arrange them in order from longest to shortest.

Height Measuring Device.Design and create a device to accurately measure the height of all the students in your class. Useyour devise to measure the heights of the students in your class.

The Meter E-Book.Use a digital camera to take photos of 3 objects around the school or your classroom that are equalto, less than or more than a meter. Estimate and measure their length using a meter ruler. Use a slideshow program to create an e-book that displays your findings.On each slide include:Your photo

Your estimate and the objects measurement.A small explanation of how each object was measured.

The Difference in Lengths.Use a ruler to measure these lines. First record your estimate and then its actual measurement.When you have measured their length find the difference in length between the shortest and thelongest line.Extension idea: Rule your own set of lines. Estimate and measure their lengths and then order themfrom shortest to longest.



41


Teacher Notes:

Topic Focus: Measurement – Length

Student Outcomes:



Indicators: Order regions by direct comparison of area and by using a unit.

Use numerical measurements of objects to order the objects. Estimating 3:20 Makes sensible numerical estimates using units that can be seen or handled and


Indicators: Make sensible numerical estimates based on provided units.With a physical model of unit available for comparison, estimate which regions theycan see have an area of about or less than or more than a square meter.

Choosing Units 3.18 Selects suitable and uniform things to use as units when measuring and a

common unit to compare two things.

Indicators: Choose same size objects to use as a repeated unit for measuring.Explain differences in the number of units different students took to cover an object

by referring to different sizes of the units.

Refer to gaps and overlaps in explaining differences in the number of units taken tocover an object.



• Measuring area using centimetre square

• Estimating area

• Comparing area

• CountingTeaching Tips:

• Area of a Table: Prepare enough 10x10 paper square for each group to cover a table top.

• Computer Generated Area- You may have to demonstrate this process to students and show

them how to change the table properties.

• Area of a Picture-Photocopy the grid paper (pg 53) for student use.Setting the Scene:


• Area of a Table –Students work in groups to figure out how to measure the area of a table topusing only square pieces of paper.


Discuss: What the area was, how they measured it and any problems they encountered. Introduce: Area and how it is formally measure e.g. centimetre or meter squared.

Demonstrate: How to measure the area of objects using square centimetres or informal units (such

as the paper units used above.Sharetime

Students share and compare the area of an object they measured.



42


Area Learning Centres

Court AreasMeasure the area of a basketball or tennis court. Construct a squared meter using paper, sticky tapeand a ruler. First estimate how many squared centimetres it will take to fill the area and then useyour squared centimetre make your measurement. Use chalk to outline the placements of your

square so that you can get an accurate measure of the area.

MAB Measurements.Base 10 blocks can be used to calculate the area of objects as they are generally constructed insquare centimetres. Use them to calculate the area of various classroom objects. Estimate and recordyour answers.

Area Poster Use a desktop publishing program to design a poster that displays how to measure the area of different objects.

Area of a Picture.Use grid paper to draw a picture, estimate and calculate its area.



43


Teacher Notes:

Topic Focus: Measurement – Volume, Mass, Capacity

Student Outcomes:



Indicators: Use numerical measurements of objects to order the objects.

Uses the number of uniform bricks or cubes as a measure of volume. Estimating 3:20 Makes sensible numerical estimates using units that can be seen or handled and


Indicators: Make sensible numerical estimates based on provided units.Choosing Units 3.18 Selects suitable and uniform things to use as units when measuring and a

common unit to compare two things.

Indicators: Choose same size objects to use as a repeated unit for measuring.Explain differences in the number of units different students took to cover an object

by referring to different sizes of the units. Mathematical Concepts:

• Understanding the difference between volume, mass and capacity.

• Weighing using a variety of scales. • Estimating and measuring volume, mass and capacity.


• Hefting

• Comparing volumes, masses and capacities. Teaching Tips:

• Mass is how much an object weighs.

• Capacity is how much an object can hold.

• Volume is how much space an objects takes up.Setting the Scene:

Five Minute Energiser • Weighing Without Scales- Line up a variety of different objects of the table, e.g a piece of

paper, pencil, empty can, full can, empty box, full box etc. Ask students to order them fromlightest to heaviest with out any tools.


Discuss: Discuss the strategies used to do this.Test: Conduct a test using the appropriate tool and determine who was closest.

Introduce and Consider: Introduce the terms volume, mass and capacity and set a challenge for students to find out what the difference between these measures are.Sharetime

Students share their definitions of volume, mass and capacity. As a class create a sentence to define

their differences.



44


Volume, Mass and Capacity Learning Centres

Box Volumes and MassSelect a box and an appropriate unit, for example MAB 1000 block to measure the total capacitycapabilities of the box. Estimate how many units it will take to fill the box then record your estimate. To work out it volume, measure its length, width and height and then multiply them. After

that place the filled box on a set of scales and weigh its mass. Record your result. Test a variety of different boxes.

How Much can it Hold?Using water find all the containers that can hold the capacity of a litre of water, half a litre of water,a cup, half a cup and a spoonful. Fill them with those amounts and then weigh them for weight.Did you find anything interesting about your results.

What’s the Difference Volume, Mass and CapacityCreate a computer generated poster than demonstrates and explains the difference between volume,mass and capacity.

Which one holds More?Hold up a piece of paper landscape way round and then roll it into a cylinder. Attach a circle to the

bottom to using tape to close off one end. Do the same to a piece of paper help portrait way up.Which one do you think holds more?Test your guess with sand.



45


Teacher Notes:

Topic Focus: Space- Location, Position and Orientation

Student Outcomes:

Visualising, analysing and representing arrangements and locations – 3.8 Visualises, follows and gives descriptions of locations and paths and attends to order and proximity in reading and making

maps.

Indicators: Recognise a map as a bird’s-eye view and attempt to provide this view of familiar locations such as their classroom.Attend to the order and proximity of things in drawing maps, giving directions or describing the main features of a familiar path.Use directional languageInterpret and order proximity from maps


• Language of position, movement and orientation

• Give and follow directions and paths

• Reading, interpreting and creating informal mapsTeaching Tips:

• Directions Tape- A recording device will be needed for this activity. If a tape player isunavailable a computer with a microphone also works effectively for this activity.

Setting the Scene:


• Help I’m Lost- Give students an oral explanation of a location somewhere in the school that youcould be found. E.g. I am standing next to a pole. It is near the big gumtree. I can see the oval tomy right and a classroom to my left. Where could I be?Activity Innovation-If you have access to walky-talkies perhaps you could get the students toactually do this activity using them.


Discuss: What strategies were used to solve the above problem. Introduce: A formal map and how they are used to read, give and follow directions. Demonstrate: How to create a map from a bird’s eye view.Sharetime

Students share some of the directional language used in their activities. Create a list of these anddisplay them.



46


Location Learning Centre Activities

Directions TapeUse a map of a familiar place and draw a path from one place to another on it. For example, draw a

path from your house to the nearest post office box. Use this map and the path you have created to

record a set of oral instructions. Record your instructions onto a tape and give it to a friend tofollow.

Back to Back InstructionsWork with a partner to complete this activity. Sit back to back with your partner both of you willneed blank paper and a pen or pencil. One partner needs to draw a simple picture on their page.They then need to give oral instructions to their partner, so that their partner can recreate the picturethat was drawn by the person giving the instructions. When you have finished swap roles, if you’ve

both had a turn do it again but make your pictures more complicated.

Classroom Map

Use a Paint or Draw program to produce a computer generated bird’s eye view of your classroom.Include all areas that are permanent fixtures and large objects such as tables and shelves etc.

Construction InstructionsUse a construction bricks and blocks to construct a model. Your model could be a house, buildingor vehicle. Take a photo of your finished constructions.Write a set of instructions for somebody else to follow and construct the model that you created.You will need to include a list of materials, step by step instructions, diagrams and your photo.



47


Teachers Notes:

Topic Focus: Space – Shape-2D

Student Outcomes:

Visualising, analysing and representing shapes 3.9 Interprets common spatial language and uses

it to describe and compare features of things.

Indicators: Integrate conventional names of shapes and parts of shapes into their descriptions of things.Identify prisms and pyramids in their environment.Describe and compare the spatial features of various mathematical objects they cansee and handle, including by the number of edges and vertices and the number, shapeand position of faces.Given a description of its spatial features, select an object from a collection.

Visualising, analysing and representing movements and transformations 3.10 Recognises and uses repetitions and movements of the same shape embedded within arrangements and patterns.


• Language of shape

• Identifying, drawing and constructing common 2D shapes and pictures

• Identifying attributes of 2D shapes such as sides, apex, vertices, corners

Teaching Tips:

• See page 57 for 2D shape outlines.

• The use of attribute blocks are highly recommended for these activities.Setting the Scene:

Five Minute Energiser:

• True or False 2D Shape Quiz- Each student needs to write a true or false answer on a piece of paper. Read out a set of questions about shapes that require a true or false answer. E.g. Anequilateral triangle has 3 sides. Give answer straight after quiz.

Tunning In and Activity Introduction:Survey: Find out how many right and wrong answers were given for each question.

Discuss: Any words used in the quiz that students did not understand. Eg equilateral triangle – dideveryone know the meaning of this?

Introduce: 2D shape categories such as polygons, triangles, quadrilaterals, circles, regular andirregular and their attributes.Sharetime: Students share their work and share an interesting fact about it or shapes.



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Shape (2D) Learning Centre Activities2D Shape ClassificationSelect a variety of categories to group 2D shapes, e.g. round, straight, sides, no sides, polygons,triangles etc. Begin with the shapes on the shape card and then add others, place the shapes into theappropriate groups.

Do any shapes fit into more than one group? If so which ones?

2D Shape Attribute Poster Create a poster showing a variety of 2D shapes. Next to each shape give a brief description about itfeatures and attributes.Eg. This is a hexagon.It has six equal sides.It can tessellate.It is a regular shape.It sides are straight.

Tessellating Digital Collage.Investigate and find out about shapes that tessellate. Select one to create a digital collage. Use aPaint or Draw program to create your digital collage. Add colour or patterns to your tessellations.

Shape AcrosticsCreate a Side by Side Acrostic poem about a 2D shape. A Side by Side Acrostic poem can be madeup of words and sentences that explain something about the topic you have chosen. In this case ashape. Write the name of the shape down the page and use each letter as a starting point to createyour poem.These poems look great displayed on a paper that is cut out the same shape as the poem.E.g.

Compasses are used to draw circlesIt has no sidesR oundContinuous line

ReguLar shape No End



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Teacher Notes:

Topic Focus: Space – Shape – 3D

Student Outcomes:

Visualising, analysing and representing shapes 3.9 Interprets common spatial language and usesit to describe and compare features of things.

Indicators: Integrate conventional names of shapes and parts of shapes into their descriptions of

things.Identify prisms and pyramids in their environment.Describe and compare the spatial features of various mathematical objects they cansee and handle, including by the number of edges and vertices and the number, shapeand position of faces.Given a description of its spatial features, select an object from a collection.

Using Spatial ideas, tools and techniques to interpret, draw and make 3.7a Pays attention to the

shape and placement of parts when matching, making and copying things, including matching netswith 3D shapes

Indicators: Make polyhedra in solid, hollow and skeleton forms.Discuss the features of 3D shapes emphasised by and best represented in solid,

hollow and skeleton forms.Mathematical Concepts:

• Language of shape

• Identifying, drawing and constructing common 3D shapes and objects

• Identifying attributes of shapes and objects such as edges, sides, apex, faces, vertices

Teaching Tips:

• The use of attribute blocks and 3D shape models are highly recommended to complete theseactivities.

• See page 58 for net outline that can be used in these activities.Setting the Scene:

Five Minute Energiser • Guess the Object- Place an object into a box and describe the object using spatial language such

as edges, sides, round, apex, 3D object etc. Students use the clues to guess the contents of the box.


Discuss: What words were most useful when guessing the object and why? Which words were notuseful and why?

Introduce: The features of 3D shapes and their terms. Demonstrate: How to identify and explain the attributes of 3D shapes.Sharetime

Students share something they learnt about 3D shapes.



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Shape 3D Learning Centre Activities3D MobilesCreate a mobile displaying 3D shapes. Use the nets provided and attempt to create your own nets tocreate other shapes. Attach a label to your shape and list real life objects that are created from thatshape. E.g. Cylinder=can or toilet roll

Construct a Polyhedron SkeletonsUse straws and sticky tape to construct a variety of polyhedrons. Stick on labels to identify thefollowing features:Apex, Vertex, Face, Edge, Side.Can you create a sphere or cylinder using straws? Why or why not?

What 3D Shape Am I? E-Book Use a slideshow program to create a ‘What Shape am I?’ e-book. Include a list of descriptors and a

picture with the answer.For example:

I am a polyhedronI have 6 faces that are all equal in their size.I have 8 verticesI have 12 edgesI can be used when playing a game.What am I?A: CubeHelpful Hint: You may like to include the word answer on your page and create a hyperlink toanother page that contains the answer and a picture.

3D Shapes Attribute Table

Select a 3D shape to investigate and then complete the table. The first one is an example.3D Shape No of faces No of Vertices Apex (yes or no) No of Edges

Dodecahedron 12 20 no 30



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Teacher Notes:

Topic Focus: Chance and Data - Chance

Student Outcomes:

Understanding, estimating and measuring chance variation 3.23 –Distinguishes certain fromuncertain things, describes familiar easily understood events as having equal chance or happening

or being more or less likely.

Indicators: Use data to compare events within their experience, describing them as more andless likely.Describe outcomes as having an equal chance or being equally likely.Order a few easily understood situations from least to most likely.


• Language of chance

• Comparison of events

• Probability of outcomes of eventsSetting the Scene:


• Snap- Play a game of snap using all the cards in a standard deck and then again purposely takingsome out.

Snap- Divide all cards equally between each other, cards need to be picture side down. Playerscreate two piles of cards by each taking a turn to add a card. When two of the same cards appear onthe top of each deck the first player to slap the pile with their hand is the winner and keeps thecards.Tunning In and Activity Introduction:

Discuss: In the first game did each card have an equal chance of being drawn? Explain answers.What about the second game, were the chances of each card being drawn equal? Explain answers

Introduce: The likelihood of events occurring in terms of equal, certain, uncertain, likely or lesslikely.

SharetimeStudents share something that they are certain will occur tomorrow.



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Chance Learning Centre ActivitiesChance ListsCreate a list of 5 events that are certain to occur tomorrow.Create a list of 5 events that likely to occur today.Create a list of 5 events that are less likely to occur on Saturday.

Give reasons why you have rated these events as certain, likely or less likely.

Dice RollRoll a dice 20 times and take a tally of your rolls. Which number was rolled the least? Whichnumber was rolled the most? Which number didn’t appear?

Now roll your dice 50 times and take a tally of your rolls. Which number was rolled the least?Which number was rolled the most? Which number didn’t appear?Share your data with a friend and add both sets of data together.Can you see any patterns emerging? If so write about them.Which number had the most chance of coming up and why?

Chance Words Poster Use a desktop publishing program to create poster displaying all the words you know that describethe likelihood of events occurring. Make your poster interesting and chance the font and style of your words.

Card GamesPlay these card games.SnapAim: To get the most cards from the deck.How to Play: Divide all cards equally between each player, cards need to be picture side down.Players create two piles of cards by each taking a turn to add a card. When two of the same cards

appear on the top of each deck the first player to slap the pile with their hand is the winner andkeeps the cards.

Fishy Seven

Aim: To get the most pairs of cards.How to Play: Shuffle the cards and deal out 7 to cards to each player place the rest of the deck in themiddle of all the players. Players need to make as many pairs as possible. They do this by askingthe player to the left of them if they have the card they need to make a pair. If the player they askedhas this card they give it up. If not the player who asked the question needs to pick a card from thedeck. The winner is the person who has the most pairs when the deck is finished.

Were these games fair for all players, did the have an equal opportunity to win?Explain you answer.

Devise a card game that is unfair to one player.



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Teacher Notes:

Topic Focus: Chance and Data – Collecting, Displaying & Interpreting Data

Student Outcomes:

Collecting Data - 3.24 Contributes to discussions to clarify what data would help answer particular questions or test predictions, and takes care in collecting data.

Organising Data- 3.25 Classifies, sequences and tabulates data to help answer particular questions

and varies the classification to answer different questions. Displaying and summarising data 3.26 Displays and summarises data using frequencies,measurements and many-to-one correspondence between data and representation.

Interpreting Data – 3.27 Reads and describes information in simple tables, diagrams, pictographsand bar graphs. Mathematical Concepts:

• Creating tallies, Venn diagrams, Pictographs, Frequency Bar graphs

• Creating axis where one contains whole numbers

• Collecting and interpreting data.

• Counting

• Ordering

Setting the Scene:


• What’s Your Favourite Team- Select a type of a relevant type of sport to survey the class about.Create labels with the names of the teams on the. For example if Aussie Rules create a labeldifferent label for West Coast Eagle, Adelaide Crows, Richmond Tigers, No team etc. Ask students to stand behind the sign that shows their team. Ask students to tell you the team that isthe most and least popular. Record the results.


Explain: The together the class just created a human graph. Discuss: What information was discovered from creating a graph of this sort.

Consider: Other types of graphs such as frequency bar graphs, pictographs and Venn Diagrams. Demonstrate: How to conduct a survey, create tallies and create the above graphs.Sharetime

Share a strategy used to create a tally or conduct a survey. Students interpret someone else’s graphand share a fact about it.



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Data Learning Centre ActivitiesPopular Colours in the ClassSurvey the class to gather data about popular colours in the class. Organise your data and display itin a frequency bar graph. Then answer the following questions.What is the most popular colour in the class?

What is the least popular?How many class members like yellow?Were there any interesting results in the data?

Likes and DislikesWork with a partner to create a Venn Diagram displaying the similarities between your likes anddislikes.

Ask each other about your likes and dislikes of food, sport, clothes, music, books, subjects, hobbiesetc.

Eye Colour Digital Pictograph.Survey the class to find out about the eye colours in your class. Use a desk top publishing programto create a pictograph to display the results.Write a few sentences about the data your have collated.

Top 5sSurvey the class to find out about their top 5 favourite foods, least favourite foods, favourite books,favourite toys, favourite computer games and favourite seasons.Display your results in a tally.Write about the class’ top 5s.

DifferentDifferent

Name:

Name:

Sam

Soccer

Basketball

Chocolate



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1-100 Number Chart

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100 Please enlarge number chart to fit whole page and change font to an Australian school writing

font e.g Victorian Cursive.



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Grid Paper



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Multiplication Flash Cards.

2x4= 83x5= 15

4x3= 126x4= 42

3x11 335x5= 25

8x2= 169x6= 54



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Australian Money Insert pictures of all Australian Notes and Coins

MAB – Base 10 Materials

Insert picture of Base 10 thousands block Insert picture of Base 10 hundreds block Insert picture of Base 10 tensInsert picture of Base 10 ones cube



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Common Shapes

Insert pictures of these shapes:SquareEquilateral TriangleRight Angle TriangleIsosceles Triangle

ScaleneCircleOval/EllipseRectangleKiteDiamondHexagonPentagonOctagonDecagonRhombus

ParallelogramTrapezium



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3D Nets

CubeCylinder Regular PrismSquare PyramidTriangular Pyramid

Square PrismPentagonal Prism

Documents

Activities Middle Mathematics