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Fractions Choose three pieces of paper of the same colour. Choose a pen that will write on them. Take a seat. Have a chat. How can we fairly share the chocolate with those here? Does this help? How do you feel? What is it like to meet integration on a Wednesday afternoon? Did you feel uncomfortable? Did anyone suddenly understand how to calculate volumes of solids? Did anyone switch off? Did anyone want to walk out? Did anyone feel like misbehaving? How do they feel? Fractions and decimals – Australian Curriculum Year 1 Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016) Year 2 Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Year 3 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Fraction notation - delay Fractions and decimals – Australian Curriculum • Year 4 • Investigate equivalent fractions used in contexts (ACMNA077) • Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) • Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Fraction notation - delay Erin Gallagher's Fraction Calculators • Fold one of your pieces of paper in half. • Hold it above your head. • Open it. • Frame one side. • Name it. • • • • • • • Re-fold your piece of paper. Fold it in half again. Hold it above your head. Open it. Frame one of the smaller pieces. Name it. How did you make it? • Fold a new piece of paper in half. • Open it. Frame one side. Name it. • Refold it. Fold the half into thirds. To fold thirds, move one side towards the middle until the bit that will be folded is as wide as the single thickness bit. • Open it. Frame one piece. Name it. • Describe how you made it. • Refold it. Fold it into halves. • Open it. Frame one piece. Name it. • Describe how you made it. • Fold a new piece of paper in half. • Open it. Frame one side. Name it. • Refold it. Fold the half into fifths. • How do we fold into fifths? • Open it. Frame one piece. Name it. • Describe how you made it. • You now have three pieces of paper from the 'half' family. Thirds family. • Choose another colour of paper. Take 2. • Fold one of your new pieces of paper in thirds. • Open it. Frame one side. Name it. Extension Make ninths or fifteenths. • Refold it. Fold the shape in half. Choose another colour for a fifths family. • Open it. Frame one piece. Make tenths by fifthing Name it. then halving. • Describe how you made it. • Compare it with your sixth from your half family. Erin Gallagher's Fraction Calculators • Great for teaching area concept of fractions. • Great for multiples of unit fractions. • Great for equivalent fractions. • Have been successfully used to fill in gaps in fraction knowledge up to college age. • Don't go too far in one lesson. Fraction Wall Game Roll one die to see what fraction you can colour. You may colour the fraction (brick) you roll, or fractions (bricks) that total your roll. You may NEVER split a brick. You need an exact roll to win the game. Fractions and decimals – Australian Curriculum Year 5 Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Recognise that the place value system can be extended beyond hundredths (ACMNA104) Compare, order and represent decimals (ACMNA105) Fractions and decimals – Australian Curriculum Year 6 Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129) Multiply and divide decimals by powers of 10 (ACMNA130) Make connections between equivalent fractions, decimals and percentages (ACMNA131) Caroline's strips Similar folding, but in 1D, not 2D. More transferable to number lines. Fold a strip into twelfths. Improper fractions - multiple strips. Number lines 1 = 1m is helpful. Do after fraction game and folding strips. Attach whole numbers first, then halves, then quarters etc. Use pegs so fraction position can be tweaked – sticky tape in place later. Fractions of collections Start with conversations • ‘half the class‘. • ‘We will share the blocks evenly between the group, let’s have a quarter each.’ • etc. Fractions of collections Which is bigger, one quarter or 5? One quarter of my class is bigger than 5 students. This is why many students find fractions of collections confusing. Fractions of collections - with strips • Only attempt after class is familiar with folding strips. • Use smiley strip to find half of 24. • Two thirds of 24. • Three quarters of 24. Decimats -year 4 • Only attempt after class is familiar with tenths using strips and/or fraction calculators. Decimats -year 5 and 6 • Use to show decimals and add decimals. Decimats - game (after using decimats in class) Fraction Wall Good for relative size of fractions and equivalent fractions. Ties in well with strips. Fraction and Decimal Wall Good for connections between fractions and decimals. Pencil only, no texta. Take in turns to roll then colour. Colour what you roll, or an equivalent fraction e.g. 1/2 could do 3/6 No cutting fractions up e.g. 1/2 can't do 1/3 and 1/6 Check your partner Extension - after you roll your fraction, you may roll a 4 sided dice. You get that many pieces, unless it is 1 or more, then you get nothing. e.g. you roll 1/3. You choose to roll 4 sided dice. You roll a 4, you can't use 4/3, so you miss your turn. e.g. you roll 1/2. You choose not to use 4 sided dice. You colour 1/2. e.g. you roll 1/6. You choose to roll 4 sided dice. You roll 3. You colour 3/6 or 1/2 or 4/8 • Other ideas • Keep it real - cooking and science (e.g. 3/4 cup of water). • Share pizzas or birthday cake. • Cut play dough shapes. • Decimal place value - expanders and sliders. • String across room to peg fractions on number line. • Use blocks/teddies for fraction of collections. • etc.