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Mathematics Unit Planner Equivalence / improper fractions Fractions as division Fractions as part whole || **Year Level: ** || **Term: Week: ** || **Start Date: ** || Compare and order common unit fractions and locate and represent them on a numberline. Compare, order and represent decimals. Solve problems involving addition and subtraction of fractions with the same or related denominators. Add and subtract decimals with and without digital technologies and use estimation and rounding to check the reasonableness of answers. Multiply decimals by whole numbers and perform divisions that result in terminating decimals, wih and without difital technologics. Make connections between equivalent fractions, decimals and percentages. || Rope String Number Cards Number lines <span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Woodlands maths Website <span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Pegs |||| **<span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Vocabulary to develop: ** <span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Equal parts, half, quarters, thirds, percentages, ratios, improper, proper, same as, equal to, ||
 * **<span style="font-family: 'Calibri','sans-serif'; font-size: 13px;">TOPIC: Fractions ** || **<span style="font-family: 'Calibri','sans-serif'; font-size: 13px;">Key ideas: **<span style="font-family: 'Calibri','sans-serif'; font-size: 13px;">Definition
 * **<span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">Key Mathematical Understandings being constructed: **
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; margin-top: 0cm;">We understand the denominator tells us the name or size of part. We understand the numerator tells us the number of parts.
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; margin-top: 0cm;">We understand that equivalent fraction can be represented in different ways. ½ = 2/4
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; margin-top: 0cm;">We understand that a fraction is part of a whole. ( shrink – fractions as operator – ¾ of 12 = 9)
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">We understand that fractions is division. Halving is dividing <span style="font-family: 'Calibri','sans-serif'; font-size: 13px;"> . |||||| **<span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">Related VELS focus/Outcomes: **<span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">[|Australian] Curriculum
 * ** Skills to develop and Practice: **
 * <span style="font-family: 'Calibri','sans-serif'; font-size: 15px; margin-top: 0cm;">Children will be able to recognise different equivalent fractions for common fractions ie 1/2 = 2/4 = 4/8.
 * || **<span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Equipment/Resources: **
 * ** Teaching Strategies: **
 * Add hyperlink here - teaching strategies **
 * Teaching Questions – add hyperlink ** |||||| ** Links to other contexts/subjects: ** ||

Sine Maths Test - pretest ||  ||   || Pre-test sheets || Go through Times tables. || Mathematics Continuum 2.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 1] :// What is the same and what is different? // emphasises that it is the relative size (with respect to the whole/one) that determines the fraction. Discussion about relative size and absolute size. Absolute size means the same amount, but relative size relates to the fraction. || Using a variety of diagrams students identify what is the same and different. Shapes should be different sizes. || What were the similarities? Why did you put these diagrams together? What are some common rules for fractions? || Responses to the diagrams- knowledge of relative size and absolute size. || How did you identify the different fractions? Why in the second diagram is the shape not one fifth? || Assessing those students who have bisected 1 third by doing half twice trying to make thirds || Maths continuum - Multiples and Fractions of Fractions: 3.25 || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px;">[|Activity 1]: // Making a fraction wall //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px;"> is a good introductory activity with diagnostic potential.[|Activity 2] and [|Activity 3] consolidate and extend these ideas. <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px;">Students need 3 strips of paper for folding <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px;">List of instructions to follow from Maths Continuum website <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px;">Scripted exercise || <span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Scripted Exercises – question part of the script <span style="font-family: 'Arial','sans-serif'; font-size: 12px;">Copy of script in planning files. || Assessment of the number strips || Strips of paper needed again || How can we rename these fractions. How could we order these fractions? How could we group these fractions? ||  || See sample from Maths Continuum Website (copies in Fraction/decimal planning folder) Students consolidate ||  ||   || Maths continuum <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 1]: // Comparing Fractions Diagnostic Test //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> provides a diagnostic test to determine how students are conceptualising fractions. ||  ||   || Completion of the diagnostic test || <span style="background: white; color: #333333; font-family: 'Times New Roman','serif'; font-size: 13px; margin: 0cm 0cm 0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">This activity focuses on the 'density' of the real number line: we can always place a real number in between two numbers. || // Number Between //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> is a game that highlights the position of fractions on a number line, emphasises relative size, develops number sense and shows the property of number density for fractions. ||  ||   || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">The students roll 2 dice – I normal dice and the dice marked with fractions as above. Example 4 x 1/10 the students shade in 4/10 of the sheet. // ==== ||  ||   ||   || ==== //__<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">NSW Website __////<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;"> p 128 Stage 3 // ====
 * **Mathematical Objective**  (What you want the children to come to understand or appreciate)  ||  **Tools Session**   (a short sharp task relating to fluency in mental computation or the focus of the lesson)  ||  **Whole Class Focus**   (Set the scene/context for what students do in the independent aspect – eg problem posed, open ended question, story etc)   Teacher questions to stimulate discussion  ||  **Independent Learning**   (Extended opportunity for students to work in pairs, small groups or individually. Teacher to work with small group and probe students thinking)  ||  **Share time and Teacher Summary**   (focused teacher questions and summary to draw out the mathematics and assist children to make links)  ||  **Assessment**   (should relate to objective including what the teacher will listen for, observe, note analyse)  ||
 * **Session 1:** || Quick revision of subtraction – using a dice game using six numbers to make the lowest possible answer) || Pre-testing Fractions
 * **Session 2:** || Hold up a picture of a half – students write down everything they know about a half.
 * **Session 3:**
 * definition**
 * quantity** ||  || <span style="background: white; border-bottom: #555555 1pt solid; border-left: #555555 1pt solid; border-right: #555555 1pt solid; border-top: medium none; display: block; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"><span style="background: white; margin-bottom: 0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"><span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 2]: //<span style="color: #333333; font-family: 'Arial Unicode MS','sans-serif'; font-size: 13px;">What fraction is this? //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> continues the focus on relative size by providing diagrams that can generate various fractions.   (diagrams form the Maths Continuum website exercise 2.5 activity2) || Students are given two diagrams which contain shapes that contain more than one fraction –Eg square shown with ½ and ¼ students are then to write down which fraction they can see and explain their answer || What did you learn?
 * **Session 4:**
 * definition size**
 * part whole**
 * as division** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 3]: // Folding paper strips into halves, quarters and eighths //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> and
 * **Session 5**
 * definition size**
 * part whole**
 * as division** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 4]: // Folding paper strips into thirds and sixths //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> encourage active folding/partitioning of a linear model to create equivalent fractions. || Follow using scripted -n from previous exercise
 * **Session 6:**
 * number triad** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 5]: // Consolidating links between representations with a think board //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> provides an opportunity for students to link words, symbols, materials and drawings. || Students use a thinkboard
 * **Session 7:** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 6]: // Making the whole or one //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> is a ‘reverse’ activity as students need to create the whole/one given a certain fraction. ||   ||   ||   ||
 * **Session 8:** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 7]: // Skip counting by fractions //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> provides practice renaming as well as appreciating how numbers that involve fractions fit between other numbers (ie 2 <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 8px;">1 <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">/ <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 8px;">4 <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> is between 2 and 3). ||   ||   || Some of the more advanced students are able to skip count using equivalent fractions, but the majority of the group will need to consolidate this later in the year. ||
 * **Session 9:** ||  || Fractions as a Number 3.5
 * **Session 10** ||  || <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">[|Activity 2]: // Using area models better //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;"> provides guidance on ensuring that fraction concepts are not lost when concrete models are used. A short diagnostic task to see if students understand that area models show the fraction as a part-whole relationship is included. ||   ||   ||   ||
 * //** Session 11 **// ||  || <span style="background: white; border-bottom: #555555 1pt solid; border-left: #555555 1pt solid; border-right: #555555 1pt solid; border-top: medium none; display: block; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">====<span style="background: white; color: #333333; font-family: 'Times New Roman','serif'; font-size: 13px; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">Activity 3: Play 'Number Between' ====
 * //** Session 11a. **// ||  || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Dice game – Rolling a fraction dice to fill in a sheet – the sheet is divided into 1/10, 1/100, 1/1000. // ====
 * //** Session 11b. **// ||  || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Adding and subtracting fractions // ====

==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">In small groups students are given a circle template that has been divided into sixths, eighths and twelfths. // ====

//<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">3/12 + 7/12 + 5/12 = 15/12 = 1 3/12 //
||  ||   ||   ||
 * //** Session 11c. **// ||  || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">The answer to the question is 1 ½ what is the question? // ====

==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Dad has a recipe for 20 buns that needed 5 cups of flour. If he only wanted to make 6 buns, how much flour will he need? // ====

//<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">What fractions have a difference of ¾? //
||  ||   ||   || // Analysing –n //
 * //** Decimals 1 **// ||  || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Pretest – University of Melbourne // ====

//<span style="color: #333333; font-family: 'Arial Unicode MS','sans-serif'; font-size: 13px; font-weight: normal;">Identifying how students think in the place value of decimals //
||  || // Line of symmetry in a number // // Place Value chairs // // Focus on partitioning – 1.2 = one and two tenths or 12 tenths // ||  || //** Place value **// || // Human number line with fractions and decimals // || ==== ====
 * //** Decimals 2 **//

// · // //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Discuss the features of the number //
||  ||   ||   || // Box Cars Maths // //**__ All Hands on Deck __**//// by Joanna Currah, Jane Felling and Cheryl MacDonald //
 * //** Session 12 **// || // Introduction maths games //

//Games//
// Adding Decimals p 21 // // What’s your Number p24 // // Decimal Dots p 26 // // Decimal dance p27 // // Do Your Decimals p 28 // // Dicey Decimals p29 // || ==== //<span style="font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Comparing decimal numbers 4.0 maths continuum // ====

//__<span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Activity 2 __//// : //// Decimal numbers between. Open-ended task. //
//<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal;">Ask students to write down 15 numbers between 3.1 and 3.4 // ==== //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px; font-style: normal; font-weight: normal;">Some students will claim that there are only two numbers 3.2 and 3.3, while others will appreciate that 3.18 is between 3.1 and 3.2. Encourage students to share their answers and to explain why their numbers are between 3.1 and 3.4, using models and diagrams to support their explanation // ==== ||  ||   ||   || ====<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px; font-weight: normal; margin: 0cm 0cm 0pt;">Ask students to fill the boxes with some of the digits 0, 1, 2, ...8, 9 to make the following true. The digits do not have to be the same and can be reused. ==== <span style="background: white; border-bottom: #555555 1pt solid; border-left: #555555 1pt solid; border-right: #555555 1pt solid; border-top: medium none; display: block; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;"><span style="background: white; margin: 0cm 0cm 0pt; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm;">**<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">Task 1 ** // What do you understand about the first number? // // What is the sign telling you? // // What number is smaller than 3 and how can you fit into these boxes? // // Is there any other numbers? // ||  ||
 * //** Session 13 **// || // Box Cars maths Activity – see session 12 // || ==== <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 12px;">Activity 3 <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 15px;">: //<span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 12px; font-weight: normal;">Less than - more than // ====
 * <span style="color: #333333; font-family: 'Arial','sans-serif'; font-size: 13px;">Task 2 ** ======== ||   || // Questions //
 * //** Session 14 **// || // Box Cars maths Activity – see session 12 // || ====<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Linear Arithmetic Blocks[|Linear Arithmetic Blocks] are a simple model for decimal numbers, which can be purchased commercially or made from simple materials. The size of a decimal number is modelled by length, which is conceptually simpler than other material such as multi-base arithmetic blocks (MAB) which represent size by volume.Linear Arithmetic Blocks can be used to compare numbers, as well as to demonstrate arithmetic operations in a similar way to MAB. ====

|| ** See notes in Maths Folder ** || ** See notes in Maths Folder ** ||  ||
 * == Session 15 ==

Decimals
__ Representing decimals in different ways __ Using common decimals children order themselves in the correct order – smallest to biggest. FQ. Does anyone have a decimal that will fit between. (no. will depend on what the children have chosen) || Everything about my decimal. Children are to complete the following tasks in relations to their decimal Lower Middle Higher Tell me how your worked it out? Can you rename this decimal? What can you rename it to? Can you think of another way to represent your decimal? __ Demonstrate the number triad. __ Where do you see this number in real life? || Anecdotal evidence Photos of activity || // Adding tenths and hundredths // // Recognising decimals in different formats/ // ||  || Computer Game Session on Decimals Myclasses pages – 5/6 ELFS //** Place value **// || Human Number Lines Students have cards with vulgar fractions, picture representations and decimal fractions. Each student have a card but only 6 students called up the front to discuss and to be positioned by the class. || Number Lines Students write a sequence of decimals – then they must put on a number line -
 * ** ‘as’ learning **
 * Numbers can be renamed ie 1.2 is one and 2 tenths and 12 tenths. || Human numberline
 * Write everything you know about your decimal
 * Represent your decimal on a numberline
 * Represent your decimal as part of a metre and cut a piece of string that is this long. || Given specific common decimals
 * Specific number 0.5
 * With tape measure that has increments of 0.1
 * Lengths of string cut to 1metre
 * Number
 * Using normal tape measure
 * Cut own string
 * Number between 6 tenths and 7 tenths
 * Cut own string || Use some children’s examples. Ask children to talk about what they did it.
 * Name (word)
 * Symbol (digit)
 * Picture (visual)
 * //** Session 16 **//
 * Decimaster
 * Wishball Challenge ||  || =====//What have you learnt today?//===== ||   ||
 * //** Session 17 **//

|| // Reporting back – students who have finished earlier – are assigned the digital camera to take the photos of the different number lines – // || // The students also have to come up with the questions to ask the students top get them to explain their answers. // // Picking from a list of probing questions // ||  || //** Decimal place value and angles **// ||  || ====<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Students make a paper plane – measure the angles - then the class goes outside to fly the plane – students then measure the length of the flight – record as a decimal and a fraction – convert to tenths or hundredths eh 3.15 = 31 tenths and 5 hundredths or 315 hundredths. ==== ||  || // Design of the paper plane must have certain angles – eg it must include 2 x 20 degrees and 4 times 45 degrees // ||   || Graphic Organiser 6 boxes Student work with the decimal 2.1 (Worksheet prepared) ||  || // Use of digital cameras – students reporting back on their answers – use of flip cameras as well // ||   || 5.13 = five plus 1/10 and 3/100 = 513/100 Using a think Board to demonstrate their knowledge on place value. Modelling of this exercise of begin the exercise – then students complete a think-board. ||  ||   ||   || Multiplication problem but some children will do repeated addition. Model 2.3 as 23 tenths (rename) X 6 = 138 tenths – then rename to 13.8 Measure rows of tables in room. ||  ||   ||   || Eg  2.4 million = 2 400 000 Election spending Football ladder – how do they work out the percentage – points for and against. 121/85 = 1.35 x 100 ||  ||   ||   || //** Anthony Added 3/8/11 **// ||  || Ordering fractions Equivalent Fractions Resource Students learn the game “Fraction Tricks.” Using pairs of cards to represent the smallest fraction. || // Working in groups of 2 – 4 // // Variations // // Simplified - dealing only 6 cards per student // // Extended // // Introduce the notion of “following suit” and “trumps” // || // Can a smaller fraction be made from the playing hand? // // How much smaller is your fraction than the smallest fraction in each target set? // // What is the smallest fraction you can make that is just bigger than any in the target set? // || // Observations and questioning throughout the game. // || Game “ Fraction Tracks.” Students using a card game to match frhactions with their decimal equivalence || // In groups 2-4 playing the game // || // Discussion on conversion techniques. // || // Observations and questioning throughout the game. // || Residual thinking Gap Thinking Fraction as a part Whole Resource __“Number Sense 4-6”__ ‘How Full is it?’ p 57 Students estimate what fractional part of the glass contains liquid || // Go through each glass one by one // // Encourage estimation // // Discuss // // “If it is less than ½ than 2/5 is agood answer and 3/5 isn’t” // || // Encourage to discuss their strategy // // eg “I could tell it was less than full, so I thought it would be 4/5 “ // //** Extend **// // Estimate the part that is empty (residual thinking) // // Find pictures in magazine etc of glasses aprt filled – estimate farction // // Students draw glasses given a specific farction // || // Discussion - // // Drawing activity // || Equivalence Resource __“Number Sense 4-6”__ “Finding Compatible Fractions” p 92-94 Students Find and use compatible fractions - to look at the relationship between fractions and looking at estimating fractions. || // Display the three circles // // “How are the fractions related?” _ // || // Study of equivalence // // Extend // // Ask students to name a fraction near but less than ½, near but less than 75/100, near but less than one. // // Name a fraction such as 90/365 – ask for a real world interperpretation // || // Worksheet naswers // || Equivalence Definition Farctions as Division Resource __“Number Sense 4-6”__
 * //** Session 18 **//
 * //** Session19 **// ||  || Extend Your Thinking
 * Divide it up
 * Make it bigger
 * Reverse it
 * Add to it
 * Substitute
 * Make it lighter
 * //** Session 20 **// ||  || Naming Decimals
 * //** Session 21 **// ||  || 6 tables are lined up end to end. Each table is 2.3m long, how long is the line of table?
 * //** Session 22 **// ||  || What numbers can be rounded of to 5.8? ||   ||   ||   ||
 * //** Session 23 **// ||  || Larger numbers
 * //** Session 24 **//
 * Work it out with Maths Games ** p 104
 * //** Session 25 **// ||  || Number Triad Relationships
 * Work it out with Maths Games ** p 106
 * //** Session 26 **// ||  || Benchmarking
 * //** Session 27 **// ||  || Triad Relationships
 * //** Session 28 **// ||  || Benchmarks

<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">P 97- 101 Sorting Fractions
|| // Complete worksheets in pairs // // Extension have students pair fraction cards so that the sum of the two fractions is close to one. // // Ask students to choose a fraction card and decide what fraction would need to be added to it to make 1 // // After cards sorted – students use a calculator to work out the equivalence // || // How can you recognise when a fraction is less than ½? // // What can you say about the numerator and denominator of these fractions? // // What fractions are the most difficult to sort/ Why? // // How can you think about the fraction 2/19? What common fraction is it near? // || // Worksheet answers // // Observation and discussion. // || Resource __“Number Sense 4-6”__
 * //** Session 29 **// ||  || ====<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Number Triad Relationships ====

<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Students comparing fractions/decimals/percentage
|| // Students compare two farctions // // Eg I chose 1/6 and 5/6. I know 5/6 is graeter, because it takes five 1/6 to equal 5/6 // // I chose 3/8 and 2/3. I know 2/3 must be graeter because it is more than ½ and 3/8 is less than ½. // || // Extending // // Students choose the two cards that are the closest. // // Order form laest to greatest // // Represent numbers with drawings // // Complete the triad relationship for all cards // || // Statements of comparison. // || Number Triad Relationships Resource __“Number Sense 4-6”__ __ ‘Where is it?’ p 116 __ Students placing numbers on unmarked number lines.
 * //** Session 30 **// ||  || Improper fractions

|| // Complete worksheet // // Vary the end of the number lines to get students to identify the points. // // Students draw their own number line and label their own points // || // Extend // // Students draw number lines and lable mid point and several poins on the number line // // Students draw arc or circles and label the ends points // || // Completed Worksheets // || Equivalence Partititioning Resource __“Number Sense 4-6”__
 * //** Session 31 **// ||  || Number Triad Relationships

<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Students demonstrating multipliable representation of fractions.
|| // Representations completed 149 // || // Recognsing the connection between addition and multiplication - // || // Student samples. // || Resource __“Number Sense 4-6”__
 * //** Session 32 **// ||  || ====<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Equivalence ====

|| // Worksheets completed // || // Extend // // Challenge students to make up their own letter fraction challenges. // // Students complete a word search were they find as many words as possible where one letter is 1/3 or more than ½ // // Choose a letter and find a word that represents ½, 1/3, ¼, 1/5 of a word. // || // Their responses and extended activities. // ||
 * //** Session 33 **// ||  || ====<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Number Triad Relationships ====

<span style="font-family: 'Times New Roman','serif'; font-size: 13px; font-weight: normal;">Partitioning.
Resource __“Number Sense 4-6”__ __ P152 – 156 __ __ Tile Patterns __ __ Lokin at tile patterns and giving fraction descriptions __

|| // Decsriptions // // e.g. // // half the tiles are white, about ¼ of the tiles are gray and ¼ are black. // // Each row is made of half of white tiles, and the rst are ½ black and ½ gray. So, ½ of the tiles are white, and since ½ of a ½ is a ¼, ¼ are gray and ¼ are black. // || // Extend Students create their own tile patterns for other students to analyse 0- must have a clear repeating pattern of no more than 3 or 4 types of tiles. // || // Tile samples the students have created and their responses from the original tile problems. // ||

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