Assignment 1- Part 2 Digital Portfolio

Weeks 5-9Evie- 2016

WEEK 5Pre-Number Concepts

BIG ideas covered this weekMy prior knowledge of pre-number concepts included what children have learned or their ‘general knowledge’ before understanding numbers and numeration. I didn’t particularly know what pre-number involved however, my recent understanding tell me that the skills and Early concepts that define Pre-number concepts includes: Determining attributes, Matching by attributes, Sorting by attributes, Comparing attributes, Ordering attributes PatterningThese 6 components form the basis of all later study of number relationships and numeration used in everyday life; whether it be defining items by the common attribute such as colours, sizes, shapes, differences, similarities or patterns

Concepts, Skills & Strategies

Each pre-number concept has its own concepts, skills and strategies. The example I will use is SORTING BY ATTRIBUTE

Concept- A child being able to take a large group of items (counters, teddy bears, attribute blocks) and group them into smaller amounts by separating, describing the defining the specified attribute (i.e. colour, size, shape, length etc.)

 Skills- has a clear idea of how they will group by attributes. How the child will choose to sort the attribute blocks, how the child will organise the piles

Strategies- Putting the concepts and skills into action. How the child goes about sorting the attributes. The process of action- moving the attribute blocks into a pile/ container/ sorting chart.

 

  

 

 

Language Model

 Teaching strategy and  resources that assist children to understand a key

mathematical concept Patterning for Year 1:

Activity 1

Allocate student a one- or two-digit number (e.g., 6,8,10,12 etc.) and a set of objects (MAB blocks, counters, bears).

Ask the children to show and record their number in as many different ways as possible and using the objects provided - in words, in diagrams, in numbers and using the objects.

 Students use cubes or plastic squares to build a staircase pattern. They draw, count and record the number of squares used in the pattern. Ask questions about the pattern the students have made.How many squares make up the first shape in the pattern? the second shape? the fifth shape?How many squares were added to the first shape to make the second shape? the second shape to make the third shape?

 

 

 

 

Misconception How would you avoid or remediate this misconception?

Students in year one might not be able to identify a growing pattern in the form of  

but rather confuse the situation by adding extra on to ‘fill the gaps’. I would try to break the pattern down to the core starting with counting how many are in each section of the pattern instead of setting it in a pictorial way … example- 1, 2, 3…? What’s next? From there, gradually and slowly I would use concrete counting materials such as small plastic bears, do set out the patterns in linear formations or groups, adding one on each time making sure the child is understanding and following. I would then try to relate it back to the pattern above asking if they she any relationships and similarities between what’s happening with the concrete materials and the pattern. I would then explain that when you look at patterns like these you are best to count the number in each section first then try and find something that is the same about it- whether it be counting by 1’s, 2’s ,5’s etc.

ACARA Links & Scootle Resources Patterning: FOUNDATION YEAR

Strand: Number and AlgebraSub-strand: Patterns and algebra ACMNA005Content Description: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawingsElaborations: observing natural patterns in the world around us, creating and describing patterns using materials, sounds, movements or drawings Site2see: http://www.resources.det.nsw.edu.au/Resource/Access/37f3cd25-eeb2-4be3-87e0-e83f98c717b7/1 In the ‘Early stage 1 and Stage 1’ part of the website there are some basic and age appropriate activities for children in foundation year to have a go of which copying, extending and creating new patterns.  

Comparing and Ordering: FOUNDATION YEAR

Strand: Measurement and Geometry Sub strand: Using units of measurement / ACMMG007Content Description: Compare and order duration of events using everyday language of timeElaborations: knowing and identifying the days of the week and linking specific days to familiar events, sequencing familiar events in time order Skwirk: http://skwirk.com.au/esa/Ordering_Events.html This link requires children to recall basic events of a day from a short video clip. The children are then required to order them correctly (digitally). This is a good link to begin to give children the idea of ordering.

(Australia Curriculum, Assessment and Reporting Authority, 2016)

 Resources & Ideas  For Young children creating basic knowledge is

important. By providing mats such as these children will be able to sort coloured bears or other small counting items into colour or size etc.

Again by providing colored bears and a temple for children they are able to pattern. Using templates (as pictured) children are able to Build, Copy ,Create, Extend a pattern and Insert the missing element.

Comparing- Providing scales in a Foundation Year setting (and older years) is a great resource which allows children to experiment with objects- creating the appropriate language such as more than, less than, heavier, lighter etc.  

By unintentionally teaching ordering to children they will begin to pick-up sequence. Whether it be the school routine, home routine or activities that surround sequencing. Activities such as the one below are frequently seen in Foundation year settings (and younger).

Textbook Notes  Number sense includes:

Understanding number concepts and operations of numbers

Development of strategies for dealing with numbers and operations

Accurately and effectively mentally compute to detect errors and recognize expected results

Decide flexible ways to decipher the correct mathematical judgments

An expectation that numbers are useful and that work with numbers is meaningful and makes sense

• Appropriate modeling, posing process questions, encouraging thinking and creating a classroom environment which supports number sense assists in developing number sense

Number sense is developed in early childhood and primary settings for a lifelong process which is continually build upon due to 3 stages

1. Pre-number and informal number Classification Patterning

2. Early number development Conservation Comparisons One-to-one correspondence

3. Number development and counting Place value Skip counting Counting back and forth Oral and written cardinal and ordinal number

recognition

PATTERNS:

1. Mathematics is the study of patterns. Problem-solving skills are required when creating, constructing and describing patterns and this is a very important part of mathematics learning. Patterns combine several attributes: geometric, relational, physical and affective attributes which help to develop recognition skills i.e. shape, symmetry, sequence, function, color, size, texture, number, like, happiness.

2. Patterns help children develop number sense, ordering, counting, sequencing. They are also helpful in developing thinking strategies. Encourage children to “think out loud” as they search for patterns and ask them to explain what they did. Encourage them to share their thinking.

3. Children need opportunities to create their own patterns. These can give insight into their mathematical thinking. Copying a pattern requires children to choose the same pieces and arrange them in the same order, or finding the next one to continue and complete a pattern. Extending a visual pattern gives children the opportunity to explore different mathematical ideas.

GROUP RECOGNITION:

4. Subitising: The skill to “instantly see how many” in a group. It is an important skill to develop. Sight recognition of quantities up to 5 or 6 is important. It is much faster to recognize the number in a small group than counting each individual member of that group.

5.  Children who can name small groups demonstrate a knowledge of early order relations. They understand that 3 is more than 2, and that 3 is 1 less than 4. From here, they will develop more sophisticated counting skills. It also accelerates the development of addition and subtraction.

6.  Sight recognition. As children grow older, their ability to recognize quantities will improve. Sight recognition is evidenced by children’s skills in reading the number of dots on a domino. Certain arrangements are more easily recognized. Children usually find rectangular arrangements easiest to follow. The grouping of objects in common patterns is also effective in the counting process. Research supports the notion that subitising is a prerequisite for counting.

COMPARISONS AND ONE-TO-ONE CORRESPONDENCE:1. Comparison of quantities is another important part of learning to count and the development of number awareness.

When making comparisons, children must be able to discriminate between important and irrelevant attributes.2.   Children need to become familiar with descriptions of relationships such as “more than”, “less than”, “as many as”3.  Ordering is involved when comparisons are made among several different things. Children will realize that 4 is the

number between 5 and 3. Graphs can also be used and can be particularly helpful for children in the early development of numbers.

COUNTING:1.   Rational counting is a goal for all young children. A ‘rational counter’ says each number name and realizes that the

last number counted represents the number in the group.2.  Four important principles of counting include: Each object to be counted must be assigned one and only one number

name, the number-name list must be used in a fixed order every time, the order in which the objects are counted does not matter, the last number name gives the total of the objects in the group.

3.  Rote counting: A child using rote counting knows some number names but these names are not in correct counting sequence. Rational counting: Rational counters exhibit all four counting principles. A Child gives a correct number name as object are counted, uses one-to-one correspondence and is able to answer the question about the number of objects being counted.

4.  Counting on: A child gives correct number names as counting proceeds, and can start at any number and begin counting. Counting-on practice leads children to discover valuable patterns and is also essential for developing addition. Counting back: Many children find it difficult to count backwards. It helps children establish sequences and relate each number to another in a different way. A number line can be used for counting on or backwards from any starting point.

5.  Skip counting: The child gives correct names but instead of counting by 1’s, counts by 2’s, 5’s or other values. This method provides counting practice, early recognition of even and odd numbers, and readiness for multiplication and division.

6.  Counting change is a very important skill. Most of the difficulties associated with counting change can be traced to weaknesses in counting, particularly skip counting. Teachers should encourage accurate and rapid skip counting.

(Reys, et al., 2012)

WEEK 6Place Value and Mental Computation

BIG ideas covered this week.I didn’t have very much prior knowledge on

number sense or numerations at all before learning about its concept. I had never really thought about the underlying significance if the way numbers are order, why place value was important and the concept of operations. This is known as Number knowledge, which organised by formal ideas (numeration and place value) and informal ideas (number sense).

Concepts, Skills & Strategies  Number Sense Concepts: Number sense essentially refers to a student’s “fluidity and flexibility with numbers,”

(Gersten & Chard, 2001). He/She has sense of what numbers mean, understands their relationship to one another, is able to perform mental math, understands symbolic representations, and can use those numbers in real world situations

 Skills: solve problems, spot un/reasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates

 Strategies: Model different methods for computing: record a number of different approaches to solving a problem Ask students regularly to calculate mentally: Mental math encourages students to build on their

knowledge about numbers and numerical relationships. Have class discussions about strategies for computing: Having high quality classroom discussions

about strategies help students to develop their own thinking while providing them the opportunity to critically evaluate their classmates’ approaches.

Make estimation an integral part of computing: Most of the math that we do every day— reading the time, looking for house numbers, how much paint to buy, how much money you have in your wallet, which line to get in at the grocery store relies not only on mental math but estimations.

Question students about how they reason numerically: Asking students about their reasoning—both when they make mistakes AND when they arrive at the correct answer—communicates to them that you value their ideas, that math is about reasoning, and, most importantly, that math should make sense to them. Exploring reasoning is also extremely important for the teacher as a formative assessment tool. It helps her understand each student’s strengths and weaknesses, content knowledge, reasoning strategies and misconceptions.

 Numeration Concepts: naming, writing, reading, interpreting and processing numbers Skills: using numbers in mathematics. Identifying a numeral with a written word, understand the value of a number and correctly using it in the appropriate form Strategies: teaching place value, actively using numbers in every-day conversations to bring familiarity to children from very young ages. Mental computation

Concepts: emphasises the mental processes used to achieve the answerSkills: using previously learnt strategies to work out and obtain exact or approximate answers mentally Strategies: dependant on the question the following strategies can be put into place to assist with problem solving (as many as needed can be used per question): Count on Count up Count back

Doubles/ halving Multiples of ten Remaining factorsPlace Value

Concepts: The value of a digit in the context of a number. (Ones, tens, hundreds, thousands, ten thousands,

hundred thousands, millions etc.)  Children begin with rote counting, 1,2,3,4... From

there they get to two digit numbers, 11, 12, 13 and to three digit numbers 100, 101, 102... To a child the 1 in 1, 10 and 100 often mean the same thing. However, in place value, a 1 is one, a 10 is 1 group of ten, 100, is ten, tens or 1 group of 100. Therefore, the difficulty is understanding the place of the specific number and knowing that the placement changes the value of the digit.

Skills: being able correctly identify the value of each numberStrategies: Base 10, 5,2,3 MAB blocks Expanders

Language Model YEAR 2&3

Student language- “Count the number of TENS and

ONES in the following pictures” “Circle the odd numbers and

square the even numbers” “Write the value of the

underlined digit”- “54=50” “Write the following sentences

in number form” “2 ONES, 6 TENS”

Concrete counters MAB Blocks

Work sheets which display pictures of houses, numbers etc. which can be used to assist with mathematical questions like Number Sense.

Materials language- “Write the following sentences

in number form” “4 ONES, 7 TENS 3 HUNRDEDS = 374”

“ Circle the greater number of the two” “652 or 1067” 

MAB blocks Pictures of MAB blocks

Mathematic Language- “ Colour in the provided squares required to

represent the following numbers” “Use a number expanded to investigate the

different values each number holds.” “Continue this pattern

“sixty-three, sixty-five, sixty-seven, _______”

Number expander Worksheets Numeric patterns Symbolic Language- “Write the following sum in correct place value

form” “Write down the value of the digits shown below”

222, 963, 1372, 22 “Write each number in expanded

notation”5,123, 380, 1,360

Teaching Strategy & Resources

Mental Computation- Year 3

To teach mental computation further, teachers would first assess the student’s basic addition and subtraction ability. Given that it was of standard, the teacher could start by asking simple addition and subtraction problems and have the children work them out mentally (5+7, 8+4 etc.), stopping and asking the children how they got to that specific answer (whether the answer be right or not). Moving onto double addition number children will be required to implement strategies to assist.Strategy: Nearest whole number. Ask questions such as 10-3, 20+13, 40+25 Ask the children how they worked that out… by adding the tens first, then the ones Given that all children are grasping that concept bring in other double-digit numbers to

see how they manage the sum, if they are finding the nearest whole number. This would require a lesson on counting on/back for number up to 3 then adding or

subtracting the count on/back off. These questions could be 32+58, 68+21,45+99 If children are having difficulties or aren’t developing as planned writing down the

workings of this strategy create a visual to work off when mentally computing.

MisconceptionsHow would you avoid or remediate this misconception?

A misconception is not being able to identify the meaning of place value in a number.

For example a teacher sets out 24 popsicle sticks and asks a student what purpose the 2 or 4 holds- meaning 2 collections of 10 sticks (20) plus an extra 4.

If a child isn’t able to answer this correctly it show that they are not recognising numbers as place value but rather ‘face value’- when seeing a ‘2’ and the ‘4’ children will assume it equals 2 sticks and 4 sticks respectively, when it really stands for 20 and 4. To avoid this misconception much emphasis needs to be placed on

helping children to gain a solid platform understanding of Tens and Ones. This can be done by completing and further explaining problems such as above by using manipulates to move into groups of Tens and Ones.

ACARA Links & Scootle Resources Year 1 Strand: Number and Algebra Sub-strand: Number and place value

ACMNA014 Content Description: Count collections to

100 by partitioning numbers using place value

Elaborations: understanding partitioning of numbers and the importance of grouping in tens, understanding two-digit numbers as comprised of tens and ones/units 

Scootle:   http

://www.scootle.edu.au/ec/viewing/S6182/index.html - I found this to be a wonderfully informative demonstration and explanation of place value

 https://content.echalk.co.uk/esa/Maths/units/units.html - ‘Digital whiteboard’ would be a great resource when showing a class the value that each column holds

Year 3 Strand: Number and Algebra Sub-strand: Number and place value ACMNA055 Content Description: Recall addition facts for single-digit

numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

Elaborations: Recognising that certain single-digit number combinations

always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers

Combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)

Scootle: http://www.scootle.edu.au/ec/viewing/S6194/index.html -

great strategies and methods of teaching mental computation, visual representations and information

https://www.scootle.edu.auh- Take away online activity which is able to be manipulated to assist with educational discussions about finding whole number or adding to the nearest 10 when learning to mentally compute.

(Australia Curriculum, Assessment and Reporting Authority, 2016)

Resources & Ideas Laminated place value mats are an

accessible and cheap classroom resource that students can write on, place concrete materials on and develop their skills.

Mathematical Place value dice rolling game- provides visuals and concrete resource opportunities for children’s assessment

http://www.topmarks.co.uk/place-value/place-value-charts

Digital resource child can be switched from teacher mode to student mode. It allows children to practice adding the values of numbers together. 

Textbook NotesCHAPTER 8

EXTENDING NUMBER SENSE: PLACE VALUE

1. Children must have a clear understanding of our number system if they are going to be mathematically literate. Place value is critical to this understanding and is one of the cornerstones of our number system.

2. The number system that we use is called the Hindu-Arabic system. It originated in India by the Hindus and was transmitted to Europe by the Arabs, but many different countries and cultures have contributed to it’s development.

3. There are 4 important characteristics of the Hindu-Arabic system:

Place value….the position of a digit represents it’s value

Base of ten….The system has ten digits and ten is the value that determines a new collection

Use of zero…..this allows us to represent symbolically the absence of something.

Additive property….Numbers can be written in expanded notation and summed with respect to place value.

Once children understand these characteristics, the development of their number sense will improve.

4. Nature of place value: Place value develops from many various experience, such as counting and mental computation. 2 key ideas relating to place value:

Explicit grouping or trading rules are defined and consistently followed

The position of a digit determines the number being represented.

5, Children develop their skills with the aid of various models (i.e. base-ten blocks, abacus).

Place value mats serve as a visual reminder of quantities. Children are able to compose and decompose numbers and begin to recognize equivalent representations.

Understanding place value is essential to counting and facilitates operating with larger numbers. 

CHAPTER 10 Solving Mathematical problems  1. Children need to learn a variety of methods of problem solving and learn when to

use each. Students need to recognize that an appropriate method is needed to find a solution, decide on which strategy to use to solve the problem, be aware that estimation can be used, check the reasonableness of the result which is an important part of problem solving.

2. Mental computation can deepen children's’ understanding of how numbers work and increase fluency in mathematics. Mental computation is an important real-life skill that can be used in all aspects of life. More than 80% of all mathematical computations in daily life involve mental computation and estimation.

3. Research has shown that the use of calculators can improve a students skill with paper and pencil, both in basic operations and in problem solving. To use a calculation well, students need to enter and interpret the information correctly and know about it’s functions.

4. Estimation is a valuable process that produces answers that are close enough to allow for good decisions without performing exact computations. Before problem solving, students can use estimation to get a general sense of what to expect. During the problem, estimation is used to check if the computation is moving in the right direction. After solving the problem, students can use estimation to reflect on their answer and decide if it makes sense.

(Reys, et al., 2012)

WEEK 7Pre-Algebra

BIG ideas covered this weekSomething that I didn’t know or hadn’t thought

about was how the 6 early concepts and beginning processes have such big influence of pre-algebra, and that patterning was considered to be algebraic. A repeating pattern has a core element that applies geometric and number patterns to assist in translating pre-algebra. Pre-algebra explains the purpose of patterns and sequencing in math, problem solving to decide outcomes. This has all become clearer to me, as previously I had never thought that deeply about the working of algebra and the repetition and translation or an equation.

Concepts, Skills & Strategies

Concept: how numbers or objects are ordered to make a pattern. This requires students to use all 6 pre-number concepts to use number reasoning to evolve and discover the relationship between geometrical shapes and numbers.

Skills: being able to identify the elements, describe what is being repeated, repeat and copy, grow and extend, replace missing elements and translate number and geometrical patterns.

Strategies: by problem solving the function- the relationship between number and pattern, students will be able to work out answers. This can be set out in a table to display the information that you know and provides a space for the answer to which you have to discover using function.

Language ModelStudent Language: Pattern, repeating, growing, missing, replacing, changing

Can you repeat this pattern? Can you copy this pattern? Continue the following pattern by drawing the shapes

in the provided space Identify the pattern of following numbers-

2,4,6,8,10,12… what’s happening to the numbers? When looking at this scale, do you think it’s even?

(One with 6 stones the other with 2). What do we need to do to the side with 2, to make it even? 

Resources:

Laminated pictures of scales

Scales- concrete material

Concrete shapes, counters, MAB

Pictures of familiar objects

Symbols (#,*,4) 

Materials Language: Pattern, repeating, growing, missing, replacing, changing

Identify and fill in the missing pattern of the following numbers. 3,6,9,12,15,18, ___, 24,____,30.

 continue the following pattern

Resources:

Laminated pictures of scales

Scales- concrete material

Concrete counters- bears, stones etc.

Mathematics Language: Relationship, function, formula, expressions, equations, variables, equality, inequality

What is the relationship of the following numbers? 1,4,7,10,13,16,19,22?

Jessica is baking a cake. The recipe calls for 9 cups of flour. She already put in

3 cups. How many more cups does she need to add?

There were 9 roses in the vase. Jessica cut some more roses from her flower

Garden. There are now 15 roses in the vase. How many roses did she cut? Create a formula and equation to find the answer.

Joan bought a soft drink for 3 dollars and 5 candy bars. She spent

A total of 23 dollars. How much did each candy bar cost? Display a formula and answer to show the answer.

Resources:

Work sheets with working space, pictures and diagrams

Concrete counters to assist with workings

Symbolic language:

2 + __ = 5

__ x 4 = 20

2x + 5 =11

2x > 5

2x + 5 ≠ 2x + 3

 Teaching strategy and  resources that assist children to understand a key

mathematical concept  Variables to represent an unknown. x + 5 = 9  To get children to understand how to work out

unknown variables, concrete materials and their own individual laminated working which they can write on and use manipulative to assist them working out the answers.

I would pose the question to child… what plus 5 make 9? How many more counters do you need to make 9? I would show them the counting on strategy… 5, 6,7,8,9 =4And would show them how to subtract to find the answer. 9-5=4Therefore 4+5=9.Once all children are on similar understandings we would work on more difficult numbers.

Misconception How would you avoid or remediate this misconception?

Misconception: Students not being able to identify the relationship or function of the pattern. Children might struggle to grasp the concept that as the number of cows increase by 1 the amount of fences required increases by 2. But rather see it as a more confusing equation, which they need to solve. In order to remediate this misconception I would use concrete materials to model what is happening in each step, highlighting to them that it only increases by 2 each time.

ACARA Links & Scootle Resources Foundation Year

Strand: Number and Algebra Sub strand: Patterns and algebra ACMNA005Content Description: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawingsElaborations:Observing natural patterns in the world around usCreating and describing patterns using materials, sounds, movements or drawingsScootle

https://www.scootle.edu.au/ec/viewMetadata.action- Site2See link- has some great online activities (which could be evolved into concrete classroom materials) about patterning, copying, ordering etc. which sets a basis for Foundation children https://www.scootle.edu.au/ec/viewMetadata.action?id=L10h - a visual and audio digital activity with assits children in comprehending creation and repetition of patterns by creating a pattern with sound and listening it back to ensure it follows pattern.  

Year 1

Strand: Number and AlgebraSub-strand: Patterns and algebra ACMNA018Content Description: Investigate and describe number patterns formed by skip counting and patterns with objectsElaborations:

Using place-value patterns beyond the teens to generalise the number sequence and predict the next numberInvestigating patterns in the number system, such as the occurrence of a particular digit in the numbers to 100Scootle:https://www.scootle.edu.au/ec/view- great resource that teaches patterning, numbers before and after, jumps of 10 etc. https://www.scootle.edu.au/ec/viewMetadata.action?idh - Site2see- Digital activity in Stage 2 and Stage 3 is a great resource which requires children to think and work out the numerical pattens in order to unlock a safe.(Australia Curriculum, Assessment and Reporting Authority,

2016)

 Resources & Ideas 

Having lots of numbered dice as a classroom resource will assist children in creating visuals to balance out their equation.

Having scales, which are available for student interaction, is an effective way to reiterate how to balance numbers out. Having two different variables will assist in balancing the scales to achieve equality. Also the bears which are photographed in the picture are a fantastic resource to display patterning, repetition and attributes.

Textbook Notes CHAPTER 15 Algebraic thinking Children need a solid foundation in arithmetic before they begin to study algebra. By building on their understanding of the number

system, students learn to describe relationships and formulate generalizations. Students learn to apply their number and algebra skills to conduct investigations, problem solving and communicate their reasoning.

Algebra is a study of patterns and relationships. It is a way of thinking and provides strategies for analyzing representations, modeling situations, generalizing ideas and justifying statements. Algebra is an art. Children gain a better understanding of the underlying structure and properties of mathematics. Algebra is a language that uses carefully defined terms and symbols. Algebra is a tool and children need to learn to use it in a practical and meaningful way.

Problems, patterns and relations are each an essential part of primary school mathematics. All of these have connections to algebraic thinking. Routine and no routine problems provide good opportunities for developing algebraic concepts and thinking. Patterns are an important part of mathematics because they help children organize their world and understand mathematics. A repeating pattern has the core element that it is repeated over and over. This simple pattern raises many questions about how children work with patterns. As children become familiar with repeating patterns, they can extend other patterns or make their own.

Two types of relation that can help children build algebraic concepts and thinking: Properties of numbers and functions. Use number properties to promote algebraic thinking (commutative, associative, distributive and identity). A function is a way of expressing that relation.

When helping children to learn to think algebraically, use algebraic terms and symbols as you would if you were teaching a foreign language. You should weave the terms and symbols naturally into your discussion. Children often use a mixture of symbols and words when they begin to express mathematical situations..

 Young children understand sharing equally and balancing a scale, but they can be baffled by the equal sign. Many children think that the equal sign means “get an answer”. You can help children grasp the meaning of the equal sign by introducing it in an activity in the classroom. Help children use the inequality symbols (< and >) to describe larger or small quantities.

 There are 3 different used of Variable. The most common in primary schools is a Placeholder i.e. 3 + a = 7. The letter or use of a box is a placeholder for the number that makes the sentence true. Variables are also used in Generalizations – any number subtracted from itself is equal to zero. Variables are also used in formulas and in functions. Functions may be treated as patterns. By making tables and discussing the patterns, you can help students find the general rule (the function) that relates the 2 quantities.

(Reys, et al., 2012)

WEEK 8Measurements

BIG ideas covered this weekMeasurements take into account length, area, time,

liquid, mass, which is essential in everyday living. Something which I had never thought about is the fact that it links a persons knowledge of numbers to spatial situations like measuring volumes, areas, lengths and angles along with everyday problem solving situation which we unconsciously perform.

Every subject throughout a child’s schooling life will involve an aspect of measurement whether it be geographically measuring how many kilometres an island is, or measuring how much paint is required for an art lesson.

Concepts, Skills & Strategies

Concept: Children must understand the attribute they are measuring, an

understanding of the concept under investigation is essential before decision-making. This is essential before a child moves any further. Example: the concept of volume. A child must know that the volume of an object refers to the amount of space, which is take up by a three-dimensional object. This might refer to how much water can be held inside a jug. This is measured as mm3, cm3,m3 etc.

Skill: Using their knowledge about concepts to determine or discover ways to

find the volume of a shape.Strategy: This could be by sight- looking for a bigger or smaller volume, weight-

heavier or lighter or mathematically problem solving.

Language ModelChildren’s language:

Length

The table was very long but not very wide.Mary has two brothers. One is very tall and the other one is short.Perimeter

The farmer built a fence to keep his sheep in the paddock. Area

What shape is an orange? Round or square?The farmhouse was very large but the barn was small.Mass

Tip some water into an empty glass and it will soon become full.The elephant is a very big animal, and a mouse is so little.Capacity/ Volume

Which of the two cups is full/ empty?Time:If today is Monday, what day is it tomorrow?Mum will be here soon and Dad will arrive later. Angle:Circle the corners on the following shapesDraw a star on all of the right angled cornersMoney: How much does each of the following items cost?Order the following objects from most to least expensive Temperature: Warm, hot, cold, freezingWhat kind of weather is it today?Do you think the North Pole is hot or cold?  

Materials Language:

Length-can you build a fence that is 6 blocks long Perimeter- can you build square fences to keep the cows in? How many blocks did it take you to make the fence?Area- how many blocks have you used to cover the floor for your cubby house?Mass- which is heavier? Rocks or nails?Capacity/ Volume-

how many spoonful’s of rice will it take to full up that cup?

Time:

how many handclaps can you do before the ball land on the ground? Angle: If this angle were on a clock, what time would it be?Describe the angle. Is it a full turn, half turn or a quarter turn? Money

If 2 ice-blocks cost $2 each, how much money would I have to pay?If I have $1, how many lollies could I buy if they were 10c each?Temperature: What kind of clothes do you need when it’s hot or cold?What would you wear to the snow?Do you think this girl is going to a hot or cold place? Why?

Mathematics Language:

Length- Can you measure a piece of ribbon that is 6cm longIf I want 5 pieces of 12cm ribbon, how much will I have altogether? Perimeter- Find the perimeter

Area- Find the area of this shape

Mass- how many kg of bananas did you buy?Capacity/ Volume- which has more L? a bottle of milk or a can of lemonade?Time: Draw the hands on these clocks Angle: - How many degrees are a right angle, acute angle, obtuse angle, straight and reflect angle? Order them from biggest to smallest.

Money: I have lots of 10c and 20c coins. Can you make $2 using only those coins?Show me 3 different ways to make $3, using only 10c, 20c and 50c coinsTemperature: Do you think that 2° is hot or cold?What is the temperature today? Look at a thermometerIf it is 30° today, what type of clothes would you be wearing?    

 

 

Symbolic Language:

Length- - Measure the following shape to find the total length of the highlighted wall.Perimeter

Find the missing side  Area- find the area of the following circles

Mass- convert the following amounts

Capacity/ Volume- Compare the capacity. Which has more? And by how much more?

Time: what is the difference between 5:36pm to 10:55am the next day? Angle:work out the missing angle. Money: If I have $16 and needed to buy 4 apples worth $2 each, how much change would I have left over? I have $10, but I need $45 to by a dress. How much more money do I need? $45= $10+ $XI want to buy a hat, which costs $70. I earn $ 17.50 an hour. How many hours would I need to work before I could buy the hat? $17.50 × X=$70Temperature: if it was -2° how much hotter would it need to get to reach 4°? -2° + x= 4 

 Teaching strategy and  resources that assist children to understand a key

mathematical concept  Step 1: Identify the attribute (concept)Mass Draw on children’s personal experiences about common objects, using known language such as heavier and lighter.

This could be rocks, canned food, and toys. Show them example of 2 of the same cups with different amounts of sand in them- discuss which one is heavier/lighter, and why?

Step 2: Choose an appropriate unit of measurement for the attribute being measured Using a scale, children can use arbitrary units to determine weight of multiple blocks being placed on either end. By counting the blocks, we could say that 6 wooden blocks is lighter than 10 wooden blocks. Or 4 wooden blocks is

lighter than a 1 cup of sand. Moving onto standardized units, children could use electronic scales to determine whether 90grams of sand is more

or less heavy than 40grams of sand. This is an introduction to the language of MassStep 3: Measure the object using the chosen unit As in step 2, applying number concepts by counting the mass or items being weighed, comparing the weights,

ordering cups of sand from lightest to heaviest etc.  Step 4: Report the number of units Doing a classroom experiment, children would investigate some provided objects to weigh to determine their mass.

Children would be encouraged to draw pictures of what they see and write mathematical sentences such as 20grams of play dough is 30grams less than 50grams of play dough.

Misconception How would you avoid or remediate this misconception?

A misconception would be that children confuse the appropriate units of measurement for each attribute. An example might be that a child confuses the units for volume/capacity (ml, L etc.) with Mass (g, kg etc.). a way to avoid this confusion would be to make sure it clear is to children that there is a big difference between to two. Poster and indications should be placed on classroom walls and the two subjects should be taught a different times to ensure that children have a solid grasp on one concept before they move onto another.

ACARA Links & Scootle Resources Foundation Year Strand: Measurement and GeometrySub-strand: Using units of measurement ACMMG006Content Description: Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday languageElaborations: Comparing objects directly, by placing one object against

another to determine which is longer or by pouring from one container into the other to see which one holds more

Using suitable language associated with measurement attributes, such as ‘tall’ and ‘taller’, ‘heavy’ and ‘heavier’, ‘holds more’ and ‘holds less’

 Scootle:https://www.scootle.edu.au/ec/ceh- Teachers Resource which provides a page dedicated to comparing familiar objects related to weight and time. It has information, videos for teachers and children and lesson ideas.  https://www.scootle.edu.au/ec/viewMetadata.ah- Site2See- great resouce which has worksheets and digital activities about measurement, length. 

Foundation Year

Strand: Measurement and Geometry

Sub-strand: Using units of measurement ACMMG007

Content Description: Compare and order duration of events using everyday language of time

Elaborations:

Knowing and identifying the days of the week and linking specific days to familiar events

Sequencing familiar events in time order 

Foundation Year

Strand: Measurement and Geometry

Sub-strand: Using units of measurement ACMMG008

Content Description: Connect days of the week to familiar events and actions

Elaborations:

Choosing events and actions that make connections with students’ everyday family routines

 scootle

https://www.scootle.edu.au/ec/viewMetadata.actionh- digital game resource, which teaches children the different types of clocks, AM and PM, as well as teaching them how to tell the time.

 https://www.scootle.edu.au/ec/viewMetadata.actionh - an interactive video and game, which gives children an idea about routine and timing. The events, which most children would do during a school day with children’s language, used throughout. The children are required to watch the video and recall what happens

(Australia Curriculum, Assessment and Reporting Authority, 2016)

 Resources & Ideas 

Time: interactive resource which teachers could display on an interactive white board to show how time is read and counted through changing minutes. http://www.visnos.com/demos/clock

 The following link has heaps of great resources

which can be purchased for the classroom to display weight, volume and length

http://www.hand2mind.com/category/science/measurement/357

Textbook Notes Measurement is the main topic of

curriculum mathematics which is used most frequently in students everyday life

Measurement is one of the 3 content strands in the Australian Curriculum

Directly linked to other areas of mathematics such as multiplication, division, addition and subtraction as well as art, geography and SOSE.

Children develop estimation skills, problem solving

Measurement process involves:1. Identify the attribute being measured2. Measure with informal units3. Measure with formal units4. Apply the measurement to a real life

context Very young children grasp the concept of

length well as it is said to be the most easily perceived

Capacity is considered the attribute that describes 3D shapes

Mass is the amount of a substance- Weight is the pull of gravity on that substance

Area is the amount of surface within a plane shape or region within a boundary

To help children understand an attribute it is suggested the teacher compare 2 objects on that attribute: perceptually, directly and indirectly

ACARA stated that the attributes of measurements is studied in the primary years are length, area, volume, capacity, mass, temperature, time and angle

Language is crucial to develop at all stages as a process of estimation

(Reys, et al., 2012)

WEEK 9Geometry

BIG ideas covered this weekGeometry is an organized, logical and coherent

system for the study of shape, space and measurement. Geometry involves the study of lines 1D, planes 2D and solid 3D shapes. It is one of the earliest forms of mathematics and was used for navigation pyramids, Roman aqueducts. It is essential to everyday life and is central to mathematical processing. It is used for abstraction, generalization, consistency, patterning, reasoning, and also helps many mathematics ideas to be “pictured” such as multiplication, area of circles and other shapes.

Concepts, Skills & Strategies

Concepts: understanding that the different shapes all have different names and attributes to go with it. Skills: Skill 1: Visualising- understanding the shape, recognizing the shape from a picture or concrete display, being able to describe the attributes etc. Skill 2: Communication- children should be able to talk and write about the attributes of a shape or pattern, describing similarities and differences, using geometric language and describing spatial relationships Skill 3: Drawing and modeling- drawing the shape to scale and modelSkill 4: Thinking and reasoning- classifying, analysing and seeking similarities and differences, reasoning and synthesisingSkill 5: Applying geometric concepts & knowledge- to real life experiences. Link shapes to objects and functionStrategies: Effective exposure to the correct language And materials Response to visuals and touch- being able to get a sensory exposure to shapes helps

with defining the attributes

Language ModelChildren’s language: How many corners does a door have? How many sides does a box have? How many faces on a tin can? Does a ball have any corners?Resources: Familiar concrete materials- ball, can, boxMaterials language: How many sides does a square have? Do squares and rectangles have the same

amount of sides and corners? What’s different about them?

Describe a circle Resources: Attribute blocks, pictures of shapes

Mathematics language: Vertices, faces, perimeter, circumference, area, volume, scalene, equilateral, isosceles, quadrilateral, Name some quadrilaterals Work out the perimeter of a rectangle? Work out the circumference of a sphere Draw and describe the difference between

scalene, equilateral, isosceles trianglesResources- pictures, attribute blocks, worksheets Symbolic Language: Find the area of a rectangle that is 7cm long

and 5 cm wide Find A

 Teaching strategy and  resources that assist children to understand a key

mathematical concept  Using Skill 3 of the 5 basic skills of geometry, I

would provide my students with plasticine or play dough for them to mould and construct shapes in order for them to gain their own understanding about the attributes of each shape. They would them be required to write down exactly what they think and how they would describe the shape they have made.

Misconception How would you avoid or remediate this misconception?

 A child not having being exposed to extended terms for shapes early enough and struggles with the terminology and ability to classify shapes into categories such as parallelogram, oblong, congruent and symmetry and struggle to keep up with the terminology that the teacher is using. If I had a child in my class who struggled with this, I would make a conscious effort to use those words when describing the attributes to them individually.

ACARA Links & Scootle Resources

Foundation Year Strand: Measurement and GeometrySub-strand: Shape ACMMG009Content Description: Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environmentElaborations: Sorting and describing squares, circles, triangles, rectangles, spheres and cubes 

Scootle: Video to help children become

aware of the shapes around them.

https://www.scootle.edu.au/ec/viewMetadata.action?id=M020186&q=&topic=&start=0&sort=alignment&contentsource=&contentprovider=&resourcetype=&v=text&showLomCommercialResources=false&field=title&field=text.all&field=topic&learningarea=%22Mathematics%22&contenttype=all&contenttype=%22Interactive%20resource%22&contenttype=%22Collection%22&contenttype=%22Image%22&contenttype=%22Moving%20image%22&contenttype=%22Sound%22&contenttype=%22Assessment%20resource%22&contenttype=%22Teacher%20guide%22&contenttype=%22Dataset%22&contenttype=%22Text%22&contenttype=%22StillImage%22&contenttype=%22MovingImage%22&contenttype=%22StillImage%22&contenttype=%22MovingImage%22&commResContentType=all&commResContentType=%22App%20(mobile)%22&commResContentType=%22Audio%22&commResContentType=%22Book%20(electronic)%22&commResContentType=%22Book%20(printed)%22&commResContentType=%22Digital%20item%22&commResContentType=%22Learning%20object%22&commResContentType=%22Other%22&commResContentType=%22Printed%20item%22&commResContentType=%22Software%22&commResContentType=%22Teacher%20resource%22&commResContentType=%22Video%22&userlevel=(0)&kc=any&lom=true&scot=true&follow=true&topiccounts=true&rows=20&suggestedResources=M019797,R10709,M019176,M019177,M009190,M013921,M019368,M019801,M019798,S4970,M009195&accContentId=ACMMG009&fromSearch=true

Site2see- Teachers resource to assist with teaching the basics of geometry. There are activities provided to help with 2D and 3D shapes.

https://www.scootle.edu.au/ec/viewMetadata.action?id=M016317&q=&topic=&start=0&sort=alignment&contentsource=&contentprovider=&resourcetype=&v=text&showLomCommercialResources=false&field=title&field=text.all&field=topic&learningarea=%22Mathematics%22&contenttype=all&contenttype=%22Interactive%20resource%22&contenttype=%22Collection%22&contenttype=%22Image%22&contenttype=%22Moving%20image%22&contenttype=%22Sound%22&contenttype=%22Assessment%20resource%22&contenttype=%22Teacher%20guide%22&contenttype=%22Dataset%22&contenttype=%22Text%22&contenttype=%22StillImage%22&contenttype=%22MovingImage%22&contenttype=%22StillImage%22&contenttype=%22MovingImage%22&commResContentType=all&commResContentType=%22App%20(mobile)%22&commResContentType=%22Audio%22&commResContentType=%22Book%20(electronic)%22&commResContentType=%22Book%20(printed)%22&commResContentType=%22Digital%20item%22&commResContentType=%22Learning%20object%22&commResContentType=%22Other%22&commResContentType=%22Printed%20item%22&commResContentType=%22Software%22&commResContentType=%22Teacher%20resource%22&commResContentType=%22Video%22&userlevel=(0)&kc=any&lom=true&scot=true&follow=true&topiccounts=true&rows=20&suggestedResources=M009190,M019368,M019177,R10709,S4970,M013921,M019798,M019797,M009195,M019176,M019801&accContentId=ACMMG009&fromSearch=true

(Australia Curriculum, Assessment and Reporting Authority, 2016)

 Resources & Ideas 

3D geometric shapes that unfold to the net of the shape. Helps children to understand that within 3D shapes there are a seris of 2D shapes that create them. http://www.teaching.com.au/product?KEY_ITEM=LER0921&KEY_ALIAS=LER0921#

  Geometric flip chart-

http://www.teaching.com.au/product?KEY_ITEM=NX8600&KEY_ALIAS=NX8600

Textbook Notes Geometry has been neglected in schools Geometry, along with measurement is one of the 3 essential content strands of the

Australian Curriculum More than preferred students only focus on the ability to recognize the shape and name,

rather than their ability to learn the defining attributes that make the shape what it is. Need to help children differentiate between a ball- which is hollow and a sphere which

sometimes is not Children need to be able to describe properties of 3D objects to explain how 2 or more

objects are alike to different geometrically Making 3D shape nets with an effective teaching strategy Geometry helps to represent the space in which live, describe out location ,movement and

relationships between objects and space Transformation and symmetry can be used to describe our world and to problem solve Although geometry is learnt though visual, pictorial and concrete materials, children also

need to be able to mentally view shapes and net. (Reys, et al., 2012)

BibliographyBibliographyAustralia Curriculum, Assessment and Reporting

Authority. (2016). Mathematics. Retrieved 5 29, 2016, from Australian Curriculum: www.australiancurriculum.edu.au

Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., et al. (2012). Helping children learn mathematics. Brisbane, QLD, Australia: John Wiley & Sons Australia Ltd.

(Reys, et al., 2012) (Australia Curriculum, Assessment and Reporting Authority, 2016)