# Stage 2 - Addition and Subtraction 2

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1 Tighes Hill Public School NSW Syllabus for the Australian Curriculum Number and Algebra Stage 2 - Addition and Subtraction 2 Outcome Teaching and Learning Activities Notes/ Future Directions/Evaluation Date Stage 2 A student: uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-1WM selects and uses appropriate mental or written strategies, or technology, to solve problems MA2-2WM checks the accuracy of a statement and explains the reasoning used MA2-3WM uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers MA2-5NA Ignition Activities Language Students should be able to communicate using the following language: plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, empty number line, strategy, digit, estimate, round to, change (noun, in transactions of money). Word problems requiring subtraction usually fall into two types either 'take away' or 'comparison'. Take away How many remain after some are removed? eg 'I have 30 apples in a box and give away 12. How many apples do I have left in the box?' Comparison How many more need to be added to a group? What is the difference between two groups? eg 'I have 18 apples. How many more apples do I need to have 30 apples in total?', 'Mary has 30 apples and I have 12 apples. How many more apples than me does Mary have?' Students need to be able to translate from these different language contexts into a subtraction calculation. The word 'difference' has a specific meaning in a subtraction context. Difficulties could arise for some students with phrasing in relation to subtraction problems, eg '10 take away 9' should give a response different from that for '10 was taken away from 9'. Greedy Pig 1. To play this game you need an ordinary 6-sided die. 2. Each turn of the game consists of one or more rolls of the die. You keep rolling until you decide to stop, or until you roll a 1. You may choose to stop at any time. 3. If you roll a 1, your score for that turn is If you choose to stop rolling before you roll a 1, your score is the sum of all the numbers you rolled on that turn. 5. Each player has 10 turns. 6. The player with the highest score wins. There are many variations of this game, the most common being a full class version in which the teacher rolls the die, and calls out the numbers. All students play using the same numbers and their score depends on when they elect to save their score. If they save their score any further rolls that turn do not count towards their score. If a 1 is rolled all players who have not saved their score get 0 for that turn and the next turn starts. The ones dice can be changed to adding tens, hundreds, thousands or ten thousands ~ 1 ~

2 by writing on blank dice. 1 could be changed to any other number as the key number to avoid rolling. First to 100 One child rolls the dice for the whole class. Other children all have ones/tens chart ruled up. Each child decides whether to put the number in the tens or ones column and find progressive total. First child to make it to 100 wins. Race To and From 100 In pairs, students roll a die and collect that number of popsticks. These are placed on a place value board in the Ones column. Eg The student continues to roll the die, collect popsticks and place them in the Ones column. The total number of popsticks in the Ones column is checked and bundled into groups of ten, when ten or more popsticks have been counted. The bundles of ten are then placed in the Tens column. When there are ten tens, they are bundled to make one hundred and the game is finished. After the idea of trading is established, students could record the total number of popsticks on the place value board after each roll. Variation: Students start with 100 popsticks in the Hundreds column. As the die is rolled, the number of popsticks is removed from the place value board by decomposing groups of ten. The game is finished when the student reaches zero. Variation: students to have a number board up to Four Turns To 100 Organise the students into groups of four. Provide each group of students with a pack of cards in the range 1 to 9. Each player draws a card from the deck and decides if the number they have drawn will represent ones or tens. For example, if a five is drawn it can represent five or fifty. The players take a second draw from the pack, again nominating if the number represents tens or ones and adds the number to their first card. Have the students record their total on an empty number line. Continue the activity until each student has drawn four cards. The player with the highest total not exceeding 100 wins. Variations Players start at 100 and subtract the numbers, after nominating if the number drawn represents tens or ones. The player closest to zero is the winner. Players draw two numbers from the pile and make the highest two digit number possible. This becomes their starting number and they continue to play as in the above variation. Developing Efficient Numeracy Strategies 2 (DENS 2) pg Cards ~ 2 ~

6 Students plan how to teach a person who made this mistake a correct method for obtaining solutions. Appropriate Calculations Students are given a calculation such as =136 and are asked to create a number of problems where this calculation would be needed. Students share and discuss response Estimating Addition of Three-Digit Numbers The teacher briefly displays the numbers 314, 311, 310, 316, 312 on cards, then turns the cards over so that the numbers be seen. Students are asked to estimate the total and give their reasons. The teacher reveals the numbers one at a time so that the students can find the total. The task could be repeated with other threedigit numbers and with four-digit or five-digit numbers. Take-away Reversals In pairs, students choose a three-digit number without repeating any digit and without using zero eg 381. The student reverses the order of the digits to create a second number ie 183. The student subtracts the smaller number from the larger and records this as a number sentence. The answer is used to start another reversal subtraction. Play continues until zero is reached. The process could be repeated for other three-digit numbers. Students discuss their work and any patterns they have observed. Extension: Students repeat using four-digit and 5-digit numbers. Estimating Differences The teacher shows a card with the subtraction of a pair of two-digit numbers eg Students estimate whether the difference between the numbers is closer to 10, 20, 30, 40 or 50 and give reasons why. The teacher shows other cards eg 51 18, 60 29, 43 25, Students estimate the differences and discuss their strategies. They are asked to think about rounding numbers on purpose. For example for 51 18, students may round 51 down to 50 and 18 up to 20. How Much? Students are told that a sofa and a desk cost \$1116. If the sofa costs \$700 more than the desk, how much does the desk cost? Students discuss. Students could pose other similar problems to solve such as What does each item cost if together they cost \$1054 and one was \$643 more than the other? Possible questions include: what strategy did you choose to use and why? what was the key word/s in understanding the problem? how could you check that you have the correct solution? could there be more than one solution? solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080) ~ 6 ~

10 cards with the tens and the picture cards removed. The Aces are is retained and represent 1 and the Jokers are retained and represents 0. Students flip two cards and assign place values to the numbers turned over. Students play Win 5000/ and Lose 5000/ to add and subtract three-digit and four-digit numbers. Students estimate their answer and then use formal written algorithms. Students could use a calculator to check their answer. Students are encouraged to pose problems, including money problems, using their numbers. Computer Learning Objects 4 Turns to 100-Stages 1-2 Addition Wheel Stages 1-2 Wishball Stages 2-3 Reference Number L867 Using Learning Objects To Teach Mathematics CD ROM Or Count Me In Too website (Click on link below) ~ 10 ~

12 Sheep and ducks I can count 20 legs in the paddock. How many ducks and how many sheep are in the paddock? How many solutions can you find? The farmer is taking ducks and sheep to market. Altogether there are 15 heads and 52 legs in the truck. How many ducks and how many sheep are going to market? Download the assessment proforma. ~ 12 ~

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