maths program proforma s1 yr 2t2-s tooney 2

Sharon Tooney

MATHS PROGRAM : STAGE 0NE

Year Two

WEEKLY ROUTINE

Monday Tuesday Wednesday Thursday Friday

Whole Number 1 Terms 1-4 Number & Algebra Terms 1 & 3: Addition and Subtraction 1 / Patterns and Algebra 1 Terms 2 & 4 : Multiplication & Division 1 / Fractions and Decimals 1

Statistics & Probability Terms 1 & 3: Data 1 Terms 2 & 4 : Chance 1

Measurement & Geometry Term 1: Length 1 / Time 1 / 2D 1 Term 2: Mass 1 / 3D 1 / Position 1 Term 3: Volume and Capacity 1 / Time 1 / 2D 1 Term 4: Area 1 / 3D1 / Position 1

Sharon Tooney

K-6 MATHEMATICS SCOPE AND SEQUENCE

NUMBER AND ALGEBRA MEASUREMENT AND GEOMETRY STATISTICS & PROBABILITY

TERM

Whole Number

Addition & Subtraction

Multiplication & Division

Fractions & Decimals

Patterns & Algebra

Length Area Volume & Capacity

Mass Time 3D 2D Angles Position Data Chance

K 1 2 3 4

Yr 1 1 2 3 4

Yr 2 1 2 3 4

Yr 3 1 2 3 4

Yr 4 1 2 3 4

Yr 5 1 2 3 4

Yr 6 1 2 3 4

NB: Where a content strand has a level 1 & 2, the 1 refers to the lower grade within the stage, eg. Whole Number 1 in S1 is for Yr 1, Whole Number 2 is for Yr 2.

Sharon Tooney

MATHEMATICS PROGRAM PROFORMA

STAGE: Yr 2 ES1 S1 S2 S3

STRAND: NUMBER AND ALGEBRA

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Whole Numbers 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › applies place value, informally, to count, order, read and represent two- and three-digit numbers MA1-4NA

Background Information The learning needs of students are to be considered when determining the appropriate range of two- and three-digit numbers. Students should be encouraged to develop different counting strategies, eg if they are counting a large number of items, they can count out groups of ten and then count the groups. They need to learn correct rounding of numbers based on the convention of rounding up if the last digit is 5 or more and rounding down if the last digit is 4 or less. Language Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, number line, number chart, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, round to. The word 'and' is used when reading a number or writing it in words, eg five hundred and sixty three.

Develop confidence with number sequences from 100 by ones from any starting point • count forwards or backwards by 1s, from a given 3-digit number • identify the numbers before & after a given 3-digit number - describe the number before as 1 less than & the number after as 1 more than a given number Recognise, model, represent and order numbers to at least 1000 • represent 3-digit numbers using objects, pictures, words & numerals • use the terms more than & less than to compare numbers • arrange numbers of up to 3 digits in ascending order - use number lines & number charts beyond 100 to assist with counting & ordering - give reasons for placing a set of numbers in a particular order Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences • count forwards & backwards by 2s, 3s & 5s from any starting point • count forwards & backwards by 10s, on & off the decade, with 2 & 3 digit numbers • identify number sequences on number charts Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting • apply an understanding of place value & the role of zero to read, write & order 3 digit numbers - form the largest & smallest number from 3 given digits • count & represent large sets of objects by systematically grouping in 10s & 100s - use models such as base 10 material, interlocking cubes & bundles of sticks to explain grouping • use & explain mental grouping to count & assist with estimating the number of items in large groups • use place value to partition 3 digit • state the place value of digits in numbers of up to 3 digits • partition three-digit numbers in non-standard forms • round numbers to the nearest 100 • estimate, to the nearest 100, the number of objects in a collection & check by counting Count and order small collections of Australian coins and notes according to their value • use the face value of coins and notes to sort, order and count money - compare Australian coins and notes with those from other countries - determine whether there is enough money to buy a particular item • recognise that there are 100 cents in $1, 200 cents in $2, … • identify equivalent values in collections of coins and in collections of notes

Learning Across The Curriculum

Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s engagement with Asia Sustainability General capabilities

Critical & creative thinking Ethical understanding Information & communication technology capability Intercultural understanding Literacy Numeracy Personal & social capability Other learning across the curriculum areas Civics & citizenship Difference & diversity Work & enterprise

Sharon Tooney

CONTENT WEEK TEACHING, LEARNING and ASSESSMENT

ADJUSTMENTS RESOURCES Reg

Develop confidence with number sequences from 100 by ones from any starting point Recognise, model, represent and order numbers to at least 1000 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting Count and order small collections of Australian coins and notes according to their

1 Put in, take out Prepare a set of “start with” cards displaying the numerals from eleven to twenty on coloured card, and a set of “put in” cards displaying the numerals from zero to nine on a different coloured card. Students will also require a large container and a supply of items, such as counters or beads, and writing material. Alternatively, if the students are able to read “start with” and “put in”, both sets of cards can be on the same coloured cardboard with the instructions written on them. Ask the first student to take a “start with” card from the pack, read the numeral and put a corresponding number of items into the container. The student then takes a “put in” card from the other pack, reads the numeral and collects the corresponding number of additional items to add to the container. Encourage the students to say what the total will be before they check by counting on from the first group as each additional item is dropped into the container. Have the students record their actions as number sentences.

Peer tutor grouping strategies

Set of cards

2

Bees Construct cardboard bees using the BLM attached. Write numerals, selected from the range 11 to 20, on the middle section of each bee. On the wings, display dot patterns which, when added together, equal the numeral displayed on the body. The stencil will need to be cut so that the wings and body are in separate pieces. Place the wings and body parts down on the floor in a random arrangement. Ask the students to select one of the bee bodies and to find the correct pair of wings which, when the dot patterns are added together, will equal the numeral written on the body.

Questioning techniques Encourage one to one count for students struggling and subitising techniques for others

Bee cards

3

Unit squares Provide the students with thirteen squares of paper. Each square should have one side coloured green and the other side red. Place the cards in a line in front of the students, with the red side face up. Indicate to the students that the squares represent the number sentence: 13 + 0 = 13. Turn one card over to reveal a green side and discuss the number sentence that is now represented by the green and red squares, that is, 12 + 1 = 13. Continue turning over additional cards to reveal the green side. Encourage the students to state the number combinations represented by the red and green squares. Vary the number of coloured squares used.

Questioning techniques Red and green squares

4

Dice toss Provide the students with two dice. Use dice which display a range of numerals other than those on a traditional die. Ask the students to take turns to roll the two dice and add them together to find the total. Provide material for students to record the number sentences.


Variety of dice, paper and pencil

5

Combination flip Construct a number strip displaying numerals in the range 4 to 18. Prepare numeral cards for the numbers 2 to 9 and an additional card with the numeral 9 written on it. Place the cards in order from 2 to 9, face down. Have the students take turns to turn over two cards

Questioning techniques Number strips, numeral cards, counters

Sharon Tooney

value

and add the total. The students then place a counter on the corresponding numeral on the number strip.

6

Number balances Prepare a stencil displaying a balance. The stencil should show one box resting on the left-hand side of the balance and two boxes stacked on the right-hand side of the balance. Prepare two sets of numeral cards, each set on a different coloured cardboard. The first set should contain the numerals 2 to 20 and the second set contain two cards for each numeral from 1 to 10. Have the students select a card from the first set and place it onto the left-hand side of the balance. Students then find two numeral cards from the second set which, when added together, total the numeral on the left side. The students then place the cards on the right side of the balance.


Balance stencil as illustrated, numeral cards

7

Domino addition Prepare domino cards which resemble commercially produced dominoes, or use traditional dominoes for this activity. Provide the students with a supply of the domino cards, or dominoes, and writing material. Deal five dominoes to each student in the group. Ask the students to record both dot patterns displayed on the dominoes as addition number sentences.


Domino cards or sets of dominoes

8

Coin Totals In pairs have students draw a coin collection card (see attached) from the pile and add up the total number of coins displayed and record their answer. Have students discuss the strategies they used to count the coins.

Provide play money for students that need to manipulate and group coins to count.

coins, coin collection cards

9

Finding Money totals With Notes and Coins Using a variety of objects in the room, label them with dollar and cents price tags. Using play money or attached money print outs, have students select and item and make the correct amount in the smallest number of coins and notes. When they are satisfied that they have the correct amount they check with the teacher before selecting another object.

Use a buddy system for students that are struggling with combining notes and coins.

coins and notes

10

Revision Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Multiplication and Division 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › uses a range of mental strategies and concrete materials for multiplication and division MA1-6NA

Background Information There are two forms of division: Sharing (partitive) – How many in each group? eg 'If 12 marbles are shared between three students, how many does each get?' Grouping (quotitive) – How many groups are there? eg 'If I have 12 marbles and each child is to get four, how many children will get marbles?' This form of division relates to repeated subtraction, 12 – 4 – 4 – 4 = 0, so three children will get four marbles each. After students have divided a quantity into equal groups (eg they have divided 12 into groups of four), the process can be reversed by combining the groups, thus linking multiplication and division. When sharing a collection of objects into two, four or eight groups, students may describe the number of objects in each group as being one-half, one-quarter or one-eighth, respectively, of the whole collection. An array is one of several different arrangements that can be used to model multiplicative situations involving whole numbers. It is made by arranging a set of objects, such as counters, into columns and rows. Each column must contain the same number of objects as the other columns, and each row must contain the same number of objects as the other rows. Formal writing of number sentences for multiplication and division, including the use of the symbols × and ÷, is not introduced until Stage 2. Language Students should be able to communicate using the following language: add, take away, group, row, column, array, number of rows, number of columns, number in each row, number in each column, total, equal, is the same as, shared between, shared equally, part left over, empty number line, number chart. The term 'row' refers to a horizontal grouping, and the term 'column' refers to a vertical grouping. Refer also to language in Stage 1 Multiplication and Division 1.

Recognise & represent multiplication as repeated addition, groups & arrays (ACMNA031) • model multiplication as repeated addition find the total number of objects by placing them into equal-sized groups& using repeated addition use empty number lines & number charts to record repeated

addition explore the use of repeated addition to count in practical

situations • recognise when items have been arranged into groups • use concrete materials to model multiplication as equal 'groups' & by forming an array of equal 'rows' or equal 'columns' describe collections as groups of, rows of & columns of determine & distinguish between the number of rows/columns

& the number in each row/column when describing collections recognise practical examples of arrays, such as seedling trays

or vegetable gardens • model the commutative property of multiplication Represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) • model division by sharing a collection of objects equally into a given number of groups, & by sharing equally into a given number of rows or columns in an array describe the part left over when a collection cannot be shared equally into a given number of groups/ rows/ columns • model division by sharing a collection of objects into groups of a given size, & by arranging it into rows or columns of a given size in an array describe the part left over when a collection cannot be

distributed equally using the given group/row/column size • model division as repeated subtraction use an empty number line to record repeated subtraction explore the use of repeated subtraction to share in practical

situations • solve multiplication & division problems using objects, diagrams, imagery & actions support answers by demonstrating how answer was obtained recognise which strategy worked/did not work & explain why • record answers to multiplication & division problems using drawings, words & numerals




Sharon Tooney



Recognise & represent multiplication as repeated addition, groups & arrays Represent division as grouping into equal sets and solve simple problems using these representations

1

Building Arrays 1. Roll the die twice. The first number you roll tells how many rows to make in your array. The second number you roll tells how many counters to put in each row of your array. Example: If you roll a 2 first and then a 5, you might make this: 2. Draw each array you make. 3. Record how many rows, how many counters in each row, and how many counters in all for each array you make.

Provide concrete materials for those students that need to manipulate objects. Extension: write algorithms without need for array

Dice, paper and pencils for recording, concrete materials

2

Number Story Arrays 1 1. Read the Number Story card. (see attached cards : red border) 2. Draw an array for the number story. 3. Write a number model to represent the story. 4. Repeat with other Number Story cards.


Array story cards, paper and pencil, concrete materials

3

Number Story Arrays 2 1. Read the Number Story card. (see attached cards : blue border) 2. Draw an array for the number story. 3. Write a number model to represent the story. 4. Repeat with other Number Story cards.


Array story cards, paper and pencil, concrete materials

4

Multiplication Bump x2 1. Work with a partner. Take turns to draw a number card from the pile, multiply the number rolled by two, and complete the math talk sentence. Concrete materials may be used 2. Find the product and put a cube on that number. If another player’s marker is on that number BUMP it off. If your marker is on that number, link the two cubes together to FREEZE the spot. See attached play board. 3. Keep taking turns until one player has used all of his/her cubes.


numeral cards, 10 different coloured unifix cubes for each player, play board, concrete materials

5

Multiplication Bump x2 1. Work with a partner. Take turns to draw a number card from the pile, multiply the number rolled by two, and complete the math talk sentence. Concrete materials may be used


numeral cards, 10 different coloured unifix cubes for each player, play board, concrete materials

I rolled ____. ___ multiplied by 2 equals____.

I rolled ____. ___ multiplied by 2 equals____.

Sharon Tooney

2. Find the product and put a cube on that number. If another player’s marker is on that number BUMP it off. If your marker is on that number, link the two cubes together to FREEZE the spot. See attached play board. 3. Keep taking turns until one player has used all of his/her cubes.

6

Groups (2,5,10) 1. Each player collects five counters. 2. Take turns to draw a card, multiply the number rolled by the number in the game’s title (groups of 2, groups of 5, groups of 10) complete the math talk sentence, and place a counter on the product (for example, if a 4 is rolled in the ‘Groups of 5’ game the player should put a counter on a ‘20’ for 4x5). If a number is already covered the player must remove the counter from that number and add it to his/her pile. 3. Play continues until one player has no counters left.


One Groups board (all players use the same board); 5 counters for each player; numeral cards showing 1-10, concrete materials Groups of 5

5 10 15 20 25 30 35 40 45 50

7

Array Picture Cards With problems Teacher provides students with a variety of array picture cards with sharing number sentences attached to each one. In small groups students solve sharing sentences individually and then check their results with each other at the end. Students may use concrete materials or draw grouping circles around pictures to solve problems.


Array picture cards, concrete materials, paper and pencils

8

Array Picture Cards Without Problems Teacher provides students with a variety of array picture cards without a sharing number sentence attached to each one. In pairs, students write a sharing sentence for an array picture for their partner to solve individually and then check their results with each other at the end. Students may use concrete materials or draw grouping circles around pictures to solve problems.


Array picture cards, concrete materials, paper and pencils

9 Revision

10 Assessment

ASSESSMENT OVERVIEW

I rolled a 4. 5 groups of 4 is 20.

Sharon Tooney

6 rows of chairs. 2 chairs per row. How many chairs?

Two rows of apples. Six apples in each row. How many apples?

2 rows of cans. 7 cans per row. How many cans?

Seven rows of ants. Two ants in each row. How many ants?

8 rows of cars. 2 cars per row. How many cars?

Two rows of balls. Eight balls in each row. How many balls?

Sharon Tooney

2 rows of icecreams. 5 cans per row. How many icecreams?

Five rows of trees. Two trees in each row. How many trees?

2 rows of eggs. 10 eggs in each row. How many eggs?

Nine rows of turtles. Two turtles in each row. How many turtles?

10 rows of pigs. 2 pigs per row. How many pigs?

2 rows of elephants. 9 elephants per row. How many elephants?

Sharon Tooney

8 boxes of crayons. 5 crayons per box. How many crayons?

Five boxes of oranges. Six oranges in each box. How many oranges?

5 rows of cows. 4 cows per row. How many cows?

Seven rows of bugs. Five bugs in each row. How many bugs?

10 rows of bikes. 7 bikes per row. How many bikes?

Five packets of pens. Nine pens in each packet. How many pens?

Sharon Tooney

10 stacks of blocks. 3 blocks per stack . How many blocks?

Six buckets of shells. Ten shells in each bucket. How many shells?

10 nests. 5 eggs in each nest. How many eggs?

Ten rows of snails. Four snails in each row. How many snails?

8 coats. 10 buttons on each coat. How many buttons?

9 flocks of sheep. 10 sheep in each flock. How many sheep?

Sharon Tooney


X2

6

18

2 8 16 14

10 4 20 12

Sharon Tooney

X10

60

10

80

20

100

40

70

50

90

30

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Fractions and Decimals 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › represents and models halves, quarters and eighths MA1-7NA

Background Information In Stage 1, fractions are used in two different ways: to describe equal parts of a whole, and to describe equal parts of a collection of objects. Fractions refer to the relationship of the equal parts to the whole unit. When using collections to model fractions, it is important that students appreciate the collection as being a 'whole' and the resulting groups as being 'parts of a whole'. It should be noted that the size of the resulting fraction will depend on the size of the original whole or collection of objects. It is not necessary for students to distinguish between the roles of the numerator and the denominator in Stage 1. They

may use the symbol as an entity to mean 'one-half' or 'a

half', and similarly use to mean 'one-quarter' or 'a quarter'.

Language Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, one-half, one-quarter, one-eighth, halve (verb). In Stage 1, the term 'three-quarters' may be used to name the remaining parts after one-quarter has been identified.

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) • use concrete materials to model a half, a quarter or an eighth of a whole object, create quarters by halving one-half, eg 'I halved my

paper then halved it again and now I have quarters' describe the equal parts of a whole object, eg 'I folded

my paper into eight equal parts and now I have eighths'

discuss why is less than , eg if a cake is shared among

eight people, the slices are smaller than if the cake is shared among four people

• recognise that fractions refer to equal parts of a whole, eg all four quarters of an object are the same size visualise fractions that are equal parts of a whole, eg

'Imagine where you would cut the rectangle before cutting it' (Problem Solving)

• recognise when objects and shapes have been shared into halves, quarters or eighths • record equal parts of whole objects and shapes, and the relationship of the parts to the whole, using pictures and the

fraction notation for half ( ), quarter ( ) and eighth( )

• use concrete materials to model a half ( ), a quarter ( ) or

an eighth( ) of a collection

describe equal parts of a collection of objects, eg 'I have quarters because the four parts have the same number of counters' (Communicating)

• recognise when a collection has been shared into halves

( ), quarters ( ) or eighths ( )

• record equal parts of a collection, and the relationship of the parts to the whole, using pictures and the fraction notation for half , quarter and eighth • use fraction language in a variety of everyday contexts, eg the half-hour, one-quarter of the class




Sharon Tooney



Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

2

Are They Halves/Quarters? (Fractions Revision) Students are shown a collection of shapes eg circles. The collection should include some that show two/four equal parts and some that show two/four unequal parts. eg

Possible questions include: - do these circles show two equal parts? - how do you know? The activity should be repeated for quarters.

Equal/unequal visual supports Questioning techniques

Collection of shapes

3

Chocolate Bar Fractions Start by passing out a paper chocolate bar to everyone that has 12 parts. Tell the students that a friend has come over and they need to share the chocolate bar so that each of them gets an equal share. Talk about how the chocolate bar is a whole and when it is cut it in half, they see that 6 pieces=1 half. Now two more friends have arrived and the chocolate bar needs to be shared again. Discuss how this is possible and explain that when we divide a half evenly, we get a quarter. Have students glue the chocolate bar into their books labeling a whole, a half and a quarter. They should write number sentences to explain how many pieces of chocolate each person gets when it is shared in half and how many pieces each person gets when it is shared in quarters.

Equal share visual support Questioning techniques

Chocolate bar blackline master, scissors, glue, workbooks, pencils

4

Fairy Bread Fractions Provide each student with a picture of a piece of Fairy Bread. Discuss how it would need to be cut to share it equally between two people. -What are these two parts called? - How many halves make a whole? Provide each student with another picture of a piece of Fairy Bread. Discuss how it would need to be cut to share it equally between four people. -What are these four parts called? - How many quarters make a whole? Students glue pizza pictures into books correctly labelling fraction parts and writing a sentence on how many parts make a whole.

If allergies allow, complete activity by making Fairy Bread first. Equal share visual support Questioning techniques

Fairy bread blackline master, scissors, glue, workbooks, pencils

5

Pizza Fractions Provide each student with a picture of a pizza. Discuss how it would need to be cut to share it equally between two people. -What are these two parts called? - How many halves make a whole?

Equal share visual support Questioning techniques

Pizza blackline master, scissors, glue, workbooks, pencils

Sharon Tooney

Provide each student with another picture of a pizza. Discuss how it would need to be cut to share it equally between four people. -What are these four parts called? - How many quarters make a whole? Provide each student with another picture of a pizza. Discuss how it would need to be cut to share it equally between eight people. -What are these eight parts called? - How many eighths make a whole? Students glue pizza pictures into books correctly labelling fraction parts and writing a sentence on how many parts make a whole.

6

Sharing Halves In pairs provide students with at least 20 jelly beans that they must share equally between themselves, so that they get half the jelly beans each. Have students discuss how they will go about sharing the jelly beans and decide on a method together, before sharing them. Students should record how they shared the jelly beans (ie, 1 at a time, 2 at time etc) and report back to the class about how they went about sharing half each. Teacher draws the student’s attention to the two piles of jelly beans that each pair has and makes links between arrays in sharing (division) and equal parts in fractions (halves). Students write number sentences to illustrate this link.

Check class allergies prior to lesson planning. Equal share visual support Questioning techniques

Jellybeans, workbooks and pencils

7

Sharing Quarters In groups of 4 provide students with at least 20 grapes that they must share equally between themselves, so that they get a quarter of the grapes each. Have students discuss how they will go about sharing the grapes and decide on a method together, before sharing them. Students should record how they shared the grapes (ie, 1 at a time, 2 at time etc) and report back to the class about how they went about sharing a quarter each. Teacher draws the student’s attention to the four piles of jelly grapes that each group has and makes links between arrays in sharing (division) and equal parts in fractions (quarters). Look also at how many quarters make a half. Students write number sentences to illustrate this link.


Grapes, workbooks and pencils

8

Sharing Eighths In groups of 8 (if 8 is not possible use toys to represent extra people required) provide students with at least 24 smarties that they must share equally between themselves, so that they get an eighth of the jelly smarties each. Have students discuss how they will go about sharing the smarties and decide on a method together, before sharing them. Students should record how they shared the smarties (ie, 1 at a time, 2 at time etc) and report back to the class about how they went about sharing half each. Teacher draws the student’s attention to the eight piles of smarties that each pair has and makes links between arrays in sharing (division) and equal parts in fractions (eighths). Discuss also how many eighths make a quarter and how many quarters make a whole.


Smarties, workbooks and pencils

Sharon Tooney

Students write number sentences to illustrate this link.

9 Revision

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney



STRAND: MEASUREMENT AND GEOMETRY

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Mass 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › uses objects, diagrams and technology to explore mathematical problems MA1-2WM › supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM › measures, records, compares and estimates the masses of objects using uniform informal units MA1-12MG

Background Information In Stage 1, measuring mass using informal units enables students to develop some key understandings of measurement. These include: › repeatedly using a unit as a measuring device › selecting an appropriate unit for a specific task › appreciating that a common informal unit is necessary for comparing the masses of objects › understanding that some units are unsatisfactory because they are not uniform, eg pebbles. Students should appreciate that the pan balance has two functions: comparing the masses of two objects and measuring the mass of an object by using a unit repeatedly as a measuring device. When students realise that changing the shape of an object does not alter its mass, they are said to conserve the property of mass. Language Students should be able to communicate using the following language: mass, heavier, lighter, about the same as, pan balance, (level) balance, measure, estimate. 'Hefting' is testing the weight of an object by lifting and balancing it. Where possible, students can compare the weights of two objects by using their bodies to balance each object, eg holding one object in each hand.

Refer also to language in Mass 1.

Compare the masses of objects using balance scales (ACMMG038) • compare and order the masses of two or more objects by hefting and check using a pan balance • recognise that mass is conserved, eg the mass of a lump of plasticine remains constant regardless of the shape it is moulded into or whether it is divided up into smaller pieces • use uniform informal units to measure the mass of an object by counting the number of units needed to obtain a level balance on a pan balance select an appropriate uniform informal unit to measure

the mass of an object and justify the choice (Problem Solving)

explain the relationship between the mass of a unit and the number of units needed, eg more toothpicks than pop sticks will be needed to balance the object (Communicating, Reasoning)

• record masses by referring to the number and type of uniform informal unit used • compare two or more objects according to their masses using appropriate uniform informal units • record comparisons of mass informally using drawings, numerals and words, and by referring to the uniform informal units used • find differences in mass by measuring and comparing, eg 'The pencil has a mass equal to three blocks and a pair of plastic scissors has a mass of six blocks, so the scissors are three blocks heavier than the pencil' predict whether the number of units will be more or less

when a different unit is used, eg 'I will need more pop sticks than blocks as the pop sticks are lighter than the blocks' (Reasoning)

solve problems involving mass (Problem Solving) • estimate mass by referring to the number and type of uniform informal unit used and check by measuring




Sharon Tooney



Compare the masses of objects using balance scales

1

Which Is Heavier? Estimate then find which two objects is heavier(but the students are not allowed to heft them or put them on the balance together)

Questioning techniques Lighter/heavier visual supports

equal arm balance, objects to compare, blocks/suitable units for measuring mass

2

Heaviest Pencil Case Work in groups of three or four to estimate, then measure whose pencil case is the heaviest by measuring the mass of each pencil case with blocks (teddies, marbles, etc). Ensure that the same unit is selected for measuring. Record in order of mass.

Peer tutor grouping strategies Lighter/heavier visual supports

equal arm balance, pencil cases, blocks/ suitable units for measuring mass

3

Has To Be The Same Mass My mystery object can be balanced by five blocks. Find or make three objects that would have the same mass. How can you prove you are correct? Students record their trials and answers.

Same as visual supports equal arm balance, objects around the room, blocks, pencils and paper

4

Mystery Boxes Students are given three or four identical containers, such as margarine containers, which each hold one item. Students place the containers in order by mass and record their prediction of what the contents might be.

Lighter/heavier visual supports

equal arm balance, objects in containers, blocks, pencils and paper

5

No More Gaps Discuss and predict the mass of the same quantity of a specific object in two different structures. For example: - Does a flat have the same mass as 100 shorts? - Do ten loose popsticks have the same mass as a bundle of ten sticks? (ten loose interlocking blocks and a rectangular prism of ten blocks) Measure each quantity to find the mass.

Individual support as required

equal arm balance, popsticks, shorts, flats, interlocking blocks, etc

6

Work It Out Teacher or student measure the mass of an object in blocks (eg base ten blocks). Using this measure, students predict how many of another unit, eg how many ones, would be needed to balance the object. Record the estimate before using a balance to check the calculation.

Individual support as required

equal arm balance, blocks to measure with, smaller units to work with

7

Heavier Or Lighter? I have a bag with some blocks in it. Use given unit, such as marbles, to balance my bag. Do you think a marble is heavier or lighter than a block (a lot heavier or just a little)? Explain or write your answer.


equal arm balance, small bag of blocks, marbles or similar units, pencils, paper

8

Let’s be Accurate! Teacher models and whole-class discussion of technique, followed by student investigation in pairs or small groups. Class finds the mass of a given object using MAB materials. Commence by comparing with blocks. Students suggest how to measure more accurately by using smaller units (flats, then longs, then shorts). Discussion should occur at each decision point.


equal arm balance, blocks, MAB materials, objects to measure

Sharon Tooney

9 Solve The Mystery My mystery object can be balanced by (for example) three blocks and five pencils. How many pencils would it take to balance it? Predict and check. Record how you worked it out. Work Out How Many My mystery object has the same mass as two eggs. How many blocks would I need to balance it, (only give them one egg). Students should check that they are correct and explain or record their working.

Same as visual supports equal arm balance, new pencils/other unit, pencils, paper, eggs, small units

10

Revision and Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Position 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › represents and describes the positions of objects in everyday situations and on maps MA1-16MG

Background Information Making models and drawing simple sketches of their models is the focus for students in Stage 1. Students usually concentrate on the relative positions of objects in their sketches. Representing the relative size of objects is difficult and will be refined over time, leading to the development of scale drawings in later stages. Accepting students' representations in models and sketches is important. Language Students should be able to communicate using the following

language: position, location, map, path.

Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) • interpret simple maps by identifying objects in different locations, eg find a classroom on a school plan map • describe the positions of objects in models, photographs and drawings give reasons when answering questions about the

positions of objects (Communicating, Reasoning) • make simple models from memory, photographs, drawings or descriptions, eg students make a model of their classroom use knowledge of positions in real-world contexts to re-

create models (Communicating) • draw a sketch of a simple model • use drawings to represent the positions of objects along a path




Sharon Tooney



6

Shapes In A Grid Provide students with a five by five grid with a variety of different coloured shapes in each square on the grid. Pose questions, such as: - Which shape is two squares to the left of.....................? - Which shape is above the .....................? Have students use directional language to describe where given shapes are within the grid.

Questioning techniques Extension: students create their own grid and pose questions for it

Grid of shapes

7

Playground Treasure In small groups provide students with a map of the school and a large object (treasure) to hide somewhere in the playground. As a group they must write directions on how to get from the classroom to the hidden treasure, for another group to follow. When complete, discuss the accuracy of the directions and reasons why provided ‘paces’ with directions may be ‘tricky’.


School map, treasure object, paper and pencil

8

School Mystery Tour Provide the students with written directions to a location within the school. Just from the directions have the students predict where they may be going. Follow directions and check prediction. When the students have arrived at the correct location, have another set of directions waiting there for them to follow.

Support: provide visual supports with written directions

Written directions

9

Mapping Your Surroundings Provide students with a map of the streets surrounding the school with a set block radius (depending on ability). In pairs have the students select a location on the map and write directions for their partner to follow, to get there from the school if they were travelling by car. Swap directions and see if you can accurately find your partners set location on the map.


Map, paper and pencils

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ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: 3D 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms MA1-14MG

Background Information In Stage 1, students begin to explore three-dimensional objects in greater detail. They continue to describe the objects using their own language and are introduced to some formal language. Developing and retaining mental images of objects is an important skill for these students. Manipulation of a variety of real three-dimensional objects and two-dimensional shapes in the classroom, the playground and outside the school is crucial to the development of appropriate levels of language and representation. A cube is a special prism in which all faces are squares. In Stage 1, students do not need to be made aware of this classification. Language Students should be able to communicate using the following language: object, shape, two dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, sphere, prism, surface, flat surface, curved surface, face, edge, vertex (vertices). The term 'vertex' (plural: vertices) refers to the point where three or more faces of a three dimensional object meet (or where two straight sides of a two-dimensional shape meet). In geometry, the term 'edge' refers to the interval (straight line) formed where two faces of a three-dimensional object meet. Refer also to language in Three-Dimensional Space 1.

Describe the features of three-dimensional objects (ACMMG043) • use the terms 'flat surface', 'curved surface', 'face', 'edge' and 'vertex' appropriately when describing three-dimensional objects describe the number of flat surfaces, curved surfaces,

faces, edges and vertices of three-dimensional objects using materials, pictures and actions, eg 'A cylinder has two flat surfaces, one curved surface, no faces, no edges and no vertices', 'This prism has 5 faces, 9 edges and 6 vertices' (Communicating)

• distinguish between objects, which are 'three-dimensional' (3D), and shapes, which are 'two-dimensional' (2D), and describe the differences informally, eg 'This is a two dimensional shape because it is flat' relate the terms 'two-dimensional' and 'three-

dimensional' to their use in everyday situations, eg a photograph is two-dimensional and a sculpture is three-dimensional (Communicating, Reasoning)

• recognise that flat surfaces of three-dimensional objects are two-dimensional shapes and name the shapes of these surfaces • sort three-dimensional objects according to particular attributes, eg the shape of the surfaces explain the attribute or multiple attributes used when

sorting three-dimensional objects (Communicating, Reasoning)

• represent three-dimensional objects, including landmarks, by making simple models or by drawing or painting choose a variety of materials to represent three-

dimensional objects, including digital technologies (Communicating)

explain or demonstrate how a simple model was made (Communicating, Reasoning)




Sharon Tooney



Describe the features of three-dimensional objects

2

2D, 3D Shape Revision Provide students with a selection of 2D and 3D shapes (in a pile as one group) and tell them that you want the shapes sorted into two groups. When the sorting is complete, discuss the way in which they were sorted. If they have not been sorted as 2D and 3D shapes, suggest this sorting method and ask the students to identify the name given to each of the groups. Go through the 2D and 3D shapes one at a time, having students name them. Create a classroom chart for each type of shape, listing the properties of each type.

Questioning techniques Extension: students create their own charts

2D and 3D shapes, chart paper, textas

3

2D Shapes In 3D Solids In small groups provide students with a set of 3D solids, and chart paper. Have students trace around the different shape faces of the solid and state how many of each makes up each 3D shape. Have students make generalisations about how the names of the faces help to identify some 3D shapes.


3D shapes, chart paper, pencils

4

Investigating 3D Shapes In small groups have students make a variety of 3D shapes out of playdough (provide concrete materials as a reference point). Investigate whether shapes roll, stack and/or slide. Record results. Using a plastic knife, cut each 3D shape in half and record the 2D face that this creates.


3D shapes, playdough, plastic knives, paper and pencils

5

Labelling 3D Shapes Introduce the students to the terms ‘face’, ‘edge’ and ‘vertex’. Label 3D shapes correctly with these terms. As a class, count how many of each, each 3D shape has. Discuss ‘flat’ and ‘curved’ surfaces when identifying and counting faces. Create a class chart of findings.

Questioning techniques

3D shapes, chart paper, textas

6

Let’s Build In small groups provide students with a variety of containers, boxes, etc to construct a building with. Students should select a building within their community to construct and select the most appropriate containers to do this with. Students should report on what 3D shapes went into the construction of their building and any difficulties they encountered in joining different 3D shapes together and how they overcame these issues.

Peer tutor grouping strategies Extension: write a report on construction process, citing issues and possible strategies to overcome these.

Containers, boxes, scissors, glue, tape

7

Nets Alive Provide students with a variety of different nets which make 3D solids. Have the students predict which 3D solid each net will create. They should justify their prediction based on the 2D shapes, faces, edges and vertices that each net has. Construct nets and report on accuracy of prediction

Questioning techniques

Blackline masters of nets

10


Sharon Tooney

ASSESSMENT OVERVIEW

Sharon Tooney



STRAND: STATISTICS AND PROBABILITY

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Chance 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM › recognises and describes the element of chance in everyday events MA1-18SP

Background Information Students should be encouraged to recognise that, because of the element of chance, their predictions will not always be proven true. When discussing certainty, there are two extremes: events that are certain to happen and those that are certain not to happen. Words such as 'might', 'may' and 'possible' are used to describe events between these two extremes. Language Students should be able to communicate using the following language: will happen, might happen, won't happen,

probably.

Identify practical activities and everyday events that involve chance (ACMSP047) • recognise and describe the element of chance in familiar activities and events, eg 'I might play with my friend after school' predict what might occur during the next lesson or in the

near future, eg 'How many people might come to your party?', 'How likely is it to rain if there are no clouds in the sky?' (Communicating, Reasoning)

Describe outcomes as 'likely' or 'unlikely' and identify some events as 'certain' or 'impossible' (ACMSP047) • describe possible outcomes in everyday activities and events as being 'likely' or 'unlikely' to happen • compare familiar activities and events and describe them as being 'likely' or 'unlikely' to happen • identify and distinguish between 'possible' and 'impossible' events describe familiar events as being 'possible' or

'impossible', eg 'It is possible that it will rain today', 'It is impossible to roll a standard six-sided die and get a 7' (Communicating)

• identify and distinguish between 'certain' and 'uncertain' events describe familiar situations as being certain or uncertain,

eg 'It is uncertain what the weather will be like tomorrow', 'It is certain that tomorrow is Saturday' (Communicating)




Sharon Tooney



Identify practical activities and everyday events that involve chance Describe outcomes as 'likely' or 'unlikely' and identify some events as 'certain' or 'impossible'

1

School Sports Day Students distinguish between things that are impossible and those that might happen using a familiar school setting. Introduce the problem by discussing the school sports day and what the students know about this day Ensure the students have been introduced to the terms ‘might happen’ and ‘impossible’. Provide students with a set of different scenarios for the sports day. Students use the events that might happen to make a further distinction between those events that are ‘likely’ and those that are ‘unlikely’ and sort the scenarios into groups under these two headings. Possible questions to illicit response may include: - Is this something that is possible or is there no way that this would ever happen? - Look at the situations that you have decided are possible. Which ones are unlikely to happen? This means that there is almost no chance of it ever happening.

Support: Students may need assistance to distinguish between what is impossible & what might happen. Provide what if scenarios to help them decide. Extension: Ask students to make up events that are likely, unlikely or impossible for other familiar situations & explain why they have put them in these categories.

Scenario cards

2

Hands-on Activities and Games 1 − Give students some pictures of everyday events that could happen. Ask them to change the picture to turn it into something impossible. − Use spinners and dice to play chance games where students compare trials. − Ask students to search through magazines to find pictures of possible and impossible events. Students could then order the possible events to show how likely they are.

Support: Students may need help to realise that events in life are rarely black and white (certain or impossible), that there are many different possibilities, some of which are more likely than others.

Pictures, magazines, scissors, glue, paper and pencils, spinners, chance games

3

Hands-on Activities and Games 2 − Give students a selection of pictures of possible and impossible events and have them sort them into ‘possible’ and ‘impossible’ events. − Talk about events that people once thought were ‘impossible’ and how these are now possible through growth in scientific knowledge (e.g. landing on the moon, computers that are smaller than a whole room), and events that were thought of as ‘certain’ that have been avoided so far (e.g. running out of fuel, etc). − Give students some ideas for events that they think of as certain and ask them to come up with something that could happen to change the outcome (e.g. if they think that it is certain that they will have cake at their party – “but what if at the last minute someone dropped the cake?”).

Support: Students may need help to realise that events in life are rarely black and white (certain or impossible), that there are many different possibilities, some of which are more likely than others.

Pictures, paper and pencils

4

Is It Fair? Asks students to compare two possible spinners and work out which one is more “fair”. Students should realise that in order to be “fair” each colour should have an even share of the spinner. Discuss the use of ordered lists or other strategies to ensure they have listed all of the possible outcomes.

Support: Students may need help to understand the impact of the size of each piece on the outcome of the game. Extension: Ask students to

Spinners, paper and pencils

Sharon Tooney

Eg. Asks students to design a spinner for which the outcomes are not fair. They need to be able to decide which colour will need the biggest and smallest pieces, and to draw lines on the spinner to make the spinner represent this size. Ask students to justify their solution.

order the likelihoods from their spinners and decide which colours they would choose to have.

5

Holiday Fun Students are to select a location for a holiday (eg the beach, the snow fields, etc). Have the students write and draw something that will happen, might happen, won't happen on their holiday. Have students think about what they would need to take on holidays. Have them draw and label five thinks that they are likely to need and five things that they are unlikely to need.

Support: clear differentiation may be needed between will, might and won’t happen.

Paper and pencils

10


ASSESSMENT OVERVIEW

maths program proforma s1 yr 2t2-s tooney 2

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