Australian Curriculum Year 6 Solve problems involving addi1on and subtrac1on of frac1ons with the same or related denominators (ACMNA126)
Key Ideas • Adding and subtrac1ng frac1ons with like
denominators • Recognise that equivalent frac1ons occupy
the same place on the number line.
Resources • FISH • Blank number lines & strip s1ckies
Vocabulary denominators numerators add subtract equal parts difference common rule equivalent
Introductory Ac9vity Process What is a frac9on
Learning inten9on: Review the anatomy of a frac1on. Display
Watch www.khanacademy.org/math/arithme1c/frac1ons/understanding_frac1ons/v/numerator-‐and-‐denominator-‐of-‐a-‐frac1on The top one is called the numerator, the boSom one is called the denominator, and these two numbers are separated by a line. The line can be horizontal or slanted—they both mean the same thing and simply serve to separate the numerator from the denominator. The boSom number in a frac1on shows how many equal parts the item is divided into. Some frac1ons may look different, but are really the same. It is usually best to show an solu1on using the simplest frac1on. That is called Simplifying, or Reducing the frac1on Ask learners to describe the typical number of slices in a pizza (8) be aware some students will answer with however many people are sharing. If I want to know what frac1on of the whole 2 pieces are ⅛ + ⅛ is the same as 2/8. The common factor of 2 and 8 is 2. If I divide 2 into itself it is 1 and if I divide 2 into 8 the answer is 4. 2/8 is the same as 1/4 Ask learners to model two equivalent frac1ons for 2/8 and demonstrate how their answer is reasonable? This ac1vity can be differen1ated by allowing learners to use frac1on strips used in MAG 6.1.13. Adding and subtrac1ng frac1ons with like denominators is
similar to adding and subtrac1ng whole numbers.
Ac9vity Process: Adding Two friends shared a foot long subway roll. They divided the roll according to their appe1tes. The first friend ate 7/12 or the roll and the second friend ate only 3/12 of the roll. How much of the roll was eaten. 7 3 10 + = 12 12 12 The frac1ons have the same (like) denominators so the numerators only need to be added together. The answer can be simplified by looking for the greatest common factor of 10 and 12. if you divide 2 into the numerator and the denominator you can simplify the answer to 5/6. One sixth of the lunch role was uneaten. Ac9vity Process: Subtract If I wanted to know how much more the first friend ate than the second one I could subtract the frac1ons 7 3 4 -‐ = 12 12 12 The difference is 4/12 and the (GCF) is 4. which can be simplified down to 1/3. One friend ate 1/3 more than the other. Ask learners to think about and record a rule for adding frac1ons with like denominators in their learning journals. Can this rule also be applied to subtrac1on?
Ac9vity Process: Using a number line model Model using a blank number line model a simple addi1on of 4/10 and 3/10 Ask learners to work with a partner and demonstrate 5/8 minus 3/8 a 1/3 plus 2/3. remind learners to simplify their answers if possible. Inves9ga9on: Using 3 digit denominators write an addi1on that results in half as the simplest form
Small Group Ac9vi9es Ac9vity Process: Using number proper9es Learners have a good understanding of co-‐ordina1ng the numerator and denominator of frac1ons when they demonstrate that they do not need materials or images to make comparisons. Do%y Pairs Game Game: The students play in pairs. One student takes dots the other takes crosses. They take turns rolling two six sided dice.
Both dice are rolled and the numbers used to form a frac1on, e.g., 2 and 5 are rolled so 2/5 or 5/2 can be made. One frac1on is chosen, made with the frac1on pieces, if necessary, and marked on a drawn 0–6 number line with the player’s iden1fying mark (dot or cross). Players take turns. The aim of the game is to get three of their marks uninterrupted by their opponent’s marks on the number line. If a player chooses a frac1on that is equivalent to a mark that is already there, they miss that turn. Ac9vity Process: Frac9on simplifica9on Playing deck with face cards removed 1. Learners create a frac1on bar sheet
by drawing a line across a piece of paper.
2. Set up the game so that the players face one another.
Ac9vity Process: The bar model-‐frac9ons and propor9onal thinking Sally went shopping for a new pair of shoes. She purchased a pair for $48 and spent 4/7 of her money. How much money did she have to start with? The bar has been divided into sevenths. The informa1on (BLUE fish) tells us that 4/7 was $48 dollars. 48 divided by 4 is 12. So each par11on is worth $12. 3/7 which is the money unspent is the same as $36. Added $48 and $36 comes to a total of $84. Sally started shopping for shoes with $84 Inves9ga9on: Using this model ask learners to inves1gate the statement. There are 3/5 as many boys as girls. If there is 75 girls, how many boys are there?
48
Money spent Money unspent
Total Money
3. Shuffle the deck of cards and distribute the deck evenly faced down in front of the two players. 4. The game begin by simultaneously turning over a card from their decks and place it on the frac1on bar sheet. Each player should place one card above the frac1on bar. The cards above the frac1on bar represent the numerator. 5. Players then place one card below the frac1on bar. The card below the bar represents the denominator. 6. There should now be a card above the bar and a card below the bar, for each player. There are four cards in total. 7. The first player to correctly simplify the frac1on shown by the cards wins all four cards. If a 1e results, split the cards evenly. If the frac1on can't be simplified, each player should collect the card that the other player put down and posi1on it at the boSom of his deck. 8. Play con1nues un1l one player has accumulated all of the cards or a set 1me limit on the game runs out. Assessment-‐Inves9ga9on: 365 Penguins adapted from hSp://nzmaths.co.nz/resource/365-‐penguins • Prior to reading the book ask learners to think about the numbers involved in a calendar year and how they could be
represented in frac1ons-‐record ideas in learning journals • Ask learners to read the picture book and write a summary of the story eg On New Year’s Day a family receives a penguin
in the mail and over the next year, one penguin con1nues to arrive each day. The problems and penguins pile up, as the family have to come up with solu1ons for housing, feeding and keeping track of the ever-‐increasing number. The sender of the penguins is finally revealed on New Year’s Eve.
• Ask learners to simplify the frac1on on a number line using the denominator 365 so that it represents a year
• Ask learners to represent the story sequence in frac1ons ‘At the end of January they have received 31 of 365 penguins. How do we write that as a frac<on?’
• Invite learners to inves1gate more calendar frac1ons by dividing the year into terms, seasons, number of lunar cycles etc. Look at places in the world where the year is divided into halves: wet and dry seasons. Using this informa1on learners should provide label their number line appropriately.