OUTCOMES: · Web viewAddition and Subtraction 2 WORKING MATHEMATICALLY:MA2-1WM, MA2-2WM, MA2-3WM...

TERM: 1 WEEK: 10 STRAND:Number and Algebra

SUB-STRAND:Addition and Subtraction 2

WORKING MATHEMATICALLY:MA2-1WM, MA2-2WM, MA2-3WM

OUTCOMES: 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

CONTENT: Students: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to and including five digits, eg 159 + 23: 'I added 20 to 159 to get 179, then I added 3 more to get 182', or use an empty number line:

pose simple addition and subtraction problems and apply appropriate strategies to solve them (Communicating, Problem Solving) use a formal written algorithm to record addition and subtraction calculations involving two-, three-, four- and five-digit numbers, eg

solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)solve addition and subtraction problems involving money, with and without the use of digital technologies use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving) reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning) calculate change and round to the nearest five cents use estimation to check the reasonableness of solutions to addition and subtraction problems, including those involving money

ASSESSMENT FOR LEARNING(PRE-ASSESSMENT)

Children work out addition/subtraction equations using as many different strategies as they can eg. Jump, split, compensation, bridging, extending number facts, changing order of addends (13 + 15 + 7 = 13 + 7 + 15)

WARM UP / DRILL Two and three digit addition and subtraction Provide the students with a blank piece of paper and ask them to fold the paper into quarters. Write on the board two addition and two subtraction problems, eg 78 + 36, 348 + 189, 95 – 46 and 800 – 241. Ask the students to solve each problem, using a quarter of the paper, recording the strategy they used.

TENS ACTIVITYNEWMAN’S PROBLEMINVESTIGATION

I added two numbers together, each with two digits. I got the answer 86, what might the numbers be?

QUALITY TEACHING ELEMENTS INTELLECTUAL QUALITY QUALITY LEARNING ENVIRONMENT

SIGNIFICANCE

Deep knowledge Deep understanding Problematic knowledge Higher-order thinking Metalanguage Substantive communication

Explicit quality criteria Engagement High expectations Social support Students’ self-

regulation Student direction

Background knowledge Cultural knowledge Knowledge integration Inclusivity Connectedness Narrative

RESOURCES Empty number lines, number charts (1-1000)

WHOLE CLASS INSTRUCTION MODELLED ACTIVITIES GUIDED & INDEPENDENT ACTIVITIES

Modelled ActivitiesWhole class activities

Revisit strategies for addition and subtraction using two-, three- and four-digit numbers, including:– the jump strategy eg 23 + 35; 23 + 30 = 53, 53 + 5 = 58– the split strategy eg 23 + 35; 20 + 30 + 3 + 5 is 58– the compensation strategy eg 63 + 29; 63 + 30 is 93, subtract 1, to obtain 92– using patterns to extend number facts eg 5 – 2 = 3, so 500 – 200 is 300– bridging the decades eg 34 + 17; 34 + 10 is 44, 44 + 7 = 51– changing the order of addends to form multiples of 10 eg 16 + 8 + 4; add 16 and 4 firstRevisit recording strategiesrecording mental strategies eg 159 + 22;‘I added 20 to 159 to get 179, then I added 2 more toget 181.’or, on an empty number line

Explain 3 different ways to solve 257 + ? = 735. Show how you would use an empty number line to solve 63 – 27. 103 – 47 = 144. Explain where you think this student made errors.

LEARNING SEQUENCE

Remediation

Number Charts (1-1000)Children learn to add and subtract ones and tens by moving left, right, up and down on charts with numbers up to 1000 eg 45 + 20 etc

LEARNING SEQUENCE

Mental StrategiesStudents are asked to calculate 34 + 17 in their heads. They are then asked to record the strategy they used. This process is repeated for other problems, such as:73 – 25 162 – 6963 + 29 188 – 89Students discuss which methods are the most efficient.Extension: Students are given increasingly more difficult problems to solve mentally. Students explain and discuss the strategies they use eg for ‘188 – 89 = ?’ A student may say, ‘I took away 88 and that was easy because it left 100 but I had to take away one more, because 88 + 1 = 89, so the answer is ‘99.’ Students record the mental strategies they use.Possible questions include:❚ is there a better strategy?❚ what is the best method to find a solution to this problem?

Recording on Empty Number LinesStudents are shown the number sentence 157 + 22 and an empty number line. The teacher marks the number 157 on the number line.Possible questions include:❚ what is the next multiple of ten after 157?❚ how many do you add on to get that number?Students record their answers on the number line.Possible questions include:❚ can you work it out with fewer steps?❚ can you visualise the number line in your head and do it?❚ can you write the numbers on paper to help you keep track?

Estimating Addition of Three-Digit NumbersThe teacher briefly displays the numbers 314, 311, 310, 316, 312 on cards, then turns the cards over so that the numbersbe 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 three-digit numbers and with four-digit or five-digit numbers.

Differences on Number LinesIn pairs, students draw an empty number line. Student A chooses two three-digit numbers and places them on the number line. Student B uses the number line to work out and record the difference between the two numbers. Students explain the mental strategies they used to find the answer. They reflect on their method, considering whether it can be improved.

Which Way is Best?Students are asked to solve problems in three different ways: using a mental strategy, a formal written algorithm, and a calculator eg ‘Our class has 356 points and another class has 567 points. How many points do we need to catch up?’ Students compare the strategies used and discuss the advantages and disadvantages of each method. If students come up with different answers, they are asked to show which answer is correct.Variation: Students write their own problems and swap with others. Students could use four-digit or 5-digit numbers.

Adding and subtraction with 2, 3, 4 and 5 digit numbersStudents fold a piece of paper into 4 sections and write two addition and two subtraction problems provided by the teacher. Students explain how they solved each problem.

LEARNING SEQUENCE

Extension

Mental StrategiesStudents are asked to calculate 216 + 124 in their heads. They are then asked to record the strategy they used. This process is repeated for other problems, such as:245 – 65 162 – 48163 + 229 588 – 89Students discuss which methods are the most efficient.Students explain and discuss the strategies they use. Students record the mental strategies they use. Possible questions include:❚ is there a better strategy?❚ what is the best method to find a solution to this problem?

Investigation:-How many different ways can you add 5798 + 3565 in your head? Write number sentences to explain your methods.

EVALUATION & REFLECTION

Student engagement: Achievement of outcomes:Resources: Follow up:




OUTCOMES: 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



solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)solve addition and subtraction problems involving money, with and without the use of digital technologies use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving) reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning) calculate change and round to the nearest five cents use estimation to check the reasonableness of solutions to addition and subtraction problems, including those

involving money


Students are given price tags with given prices on them eg $6.40, $3.20, $9.10 etc. They must select two items to purchase and add together the total to determine how much the two will cost altogether. Students may then use a calculator to check their answer.



Kim’s meal at a restaurant cost half as much as her dad’s meal. Kim and her dad paid $18 altogether for their friends. How much did Kim’s meal cost? $3, $12, $6, $9, $18


SIGNIFICANCE





RESOURCES Play money, price tags, objects for shopping, catalogues.



Whole DollarsDraw price tags showing $648 and $759. Ask: What do you know about the total? How will you work out the answer? Invite two or three volunteers to use play money to describe the thinking they could use to work out the answer. Record their thinking in vertical formats such as the examples shown below. Use the example of the left to help explain the algorithm shown in the example on the right.

Repeat for $789 and $838

Adding Dollars and CentsOn the board, draw the price tags $15.60, $28.80, $19.30. Draw the piggy banks $34.50, $45.40, $54.90. Ask students to choose two of the items. Which piggy bank will you need to pay for these two items? How do you know? Have the students work independently to make their choices and make notes to summarise the thinking they used.

LEARNING SEQUENCE

Remediation

Trading CoinsDraw a $1 coin on the board and ask: how can we represent this amount with 10c or 20c coins. How many different ways do you think we can do it? Encourage students to describe how they could trade two 10c coins for one 20c coin to create a new representation.

Money MattersPart AStudents are given a collection of coins. They demonstratedifferent ways to make 10c, 20c and 50c (and then $1 and$2) using the coins. Students record their findings.Possible questions include:❚ how many different ways can you represent 50c?❚ what counting strategy did you use to determine theamount of money you had?

Part B

The teacher creates shopping situations where one student is given an amount of money to spend. They purchase a list of items. The shopkeeper totals the items and calculates the change. Students discuss strategies used to determine the cost of the list of items and the change to be given.

LEARNING SEQUENCE

Totalling Up

Hand out containers containing different amounts of money in 5c,10c, 20c,50c,$1,$2 coins. Imagine it is money collected from drink sales at a school disco and needs counting. In small groups ask them to count each amount, deciding which way would be best. Deliberately give different assortments of coins to different groups. Ask each group to sort the coins out and total up each amount separately before finding the overall amount, keeping a record as they go. Ask them to think about quick ways of adding it up. Model their methods on the board.

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?

ShoppingChoose varying amounts of money, for example, 75c, $1.20. Ask children to choose an item from some items on display that they can afford to buy with the amount of money. Ask them to then choose an item that they cannot afford to buy with the amount of money.Money Problems (DENS)Provide the students with a collection of ten-cent coins (or play money). Nominate a starting amount, say 30 cents, and ask the students to use the coins to determine how much more is needed to equal $1.00

Open Ended QuestionsWhen I was in a music shop I saw that a CD cost about $22 and a tape about $15. What might have been the price tag on the CD and the tape?

In my pocket I have $36. What notes and coins might I have?

I bought something at a supermarket and got 5c change. How much did it cost and how much money did I give to pay for it?

The price tag on a toy car is $2.75. What coins would I use to pay for this?Show some different ways to give change for $2 for an item costing $1.35.

How could I spend exactly $20 at the supermarket? (Use a catalogue and a calculator to help).

Discuss each of the three possible combinations and explain how they decided which bank(s) they could use. As they describe their strategies, use column headings to help focus on the dollars and cents portions of each price.

Dollars Cents15 6028 80

Recording Steps for Mental AdditionDraw price tags for $385 and $59 on the board. Ask: What is the total you will pay for these two items? How can you work out the total? Allow time for the students to make notes or draw pictures. As the students are working, draw an empty number line on the board.

Invite volunteers to use the empty number line to draw arrows and jumps to help explain their thinking.

Adding Dollars and Cents – Rounding and AdjustingDraw price tags for $2.99, $2.98, $2.97 and $2.96 on the board. Point to the first price and ask: If you use coins to pay for this, what amount will you actually pay? Invite individuals to explain the rounding rules used for amounts that are not multiples of five cents. Write the amount to be paid, $3, just under the price tag for $2.99. Repeat the discussion for each of the other prices to establish when to adjust prices up or down. If necessary, repeat for prices from $2.91 to $2.94.

LEARNING SEQUENCE

Extension

Canteen Price ListThe answer to a calculation is 35c. What is the question?

Open Ended QuestionsI have more than $10 in coins, but I cannot change a $10 note into coins exactly. How much money might I have?

Scientific calculators cost $40 and basic calculators cost $12. How much might it cost for a class set of some basic and scientific calculators?

I have $14 000 and want to buy two cars. What could I buy?

I want to get $100 out of the bank. What are the different ways I can ask for this amount of notes?

Value for MoneyStudents collect supermarket brochures advertising weeklysales. Students investigate prices (eg 4 ice-blocks for $2.95 or 6 ice-blocks for $3.95), in order to recommend the best buys.Possible questions include:❚ can you explain the best buy? Why is it the best buy?❚ how did you work it out?❚ is there a better strategy you could use to work it out?


Student engagement: Achievement of outcomes:

Resources: Follow up:

Point to the first two prices ($2.99 and $2.98) and ask: What is the total of these prices? How do you know? Encourage individuals to describe how they would change one of both prices to nearby dollar amounts and then adjust the cents. Write number sentences to show their thinking (eg $3 + $3 – 3c = $5.97 or $3 + $2.98 – 1c = $5.97). Then ask: What will you pay?

Repeat steps for $2.95 and $2.99.




OUTCOMES: 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

MA2-5NACONTENT: Students:

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)select, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to and including five digits, eg 159 + 23: 'I added 20 to 159 to get 179, then I added 3 more to get 182', or use an empty number line:


solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)

solve addition and subtraction problems involving money, with and without the use of digital technologies use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving) reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning) calculate change and round to the nearest five cents use estimation to check the reasonableness of solutions to addition and subtraction problems, including those involving money


Students are given price tags with given prices on them eg $6.40, $3.20, $9.10 etc. They must select two items to purchase and add together the total to determine how much the two will cost altogether. Students may then use a calculator to check their answer.



Kim’s meal at a restaurant cost half as much as her dad’s meal. Kim and her dad paid $18 altogether for their friends. How much did Kim’s meal cost? $3, $12, $6, $9, $18

QUALITY TEACHING ELEMENTS

INTELLECTUAL QUALITY QUALITY LEARNING ENVIRONMENT

SIGNIFICANCE





RESOURCES Play money, price tags, objects for shopping, catalogues.



Money ProblemsOn the board, draw the coins $1 and 20c, and the price tag $1.85.

Say: the total cost is $1.85. The $1 and 20c coins are all the coins I have. What extra coins will help me pay the total? Invite individuals to work with a partner to show the coins that could be used. Encourage them to draw a picture of the situation and then draw more coins to work out the coins that would total $1.85. Repeat with other money values.

Calculating ChangeOn the board, draw a price tag showing 75c. Ask: Can we use one coin to pay for this? What one coin can we use? ($1 or $2). On the board draw the arrangement below (without the labels) to suggest counting on from the amount of the price tag to the

LEARNING SEQUENCE

Remediation

Trading CoinsDraw a $1 coin on the board and ask: how can we represent this amount with 10c or 20c coins. How many different ways do you think we can do it? Encourage students to describe how they could trade two 10c coins for one 20c coin to create a new representation.

Money MattersThe teacher creates shopping situations where one student is given an amount of money to spend. They purchase a list of items. The shopkeeper totals the items and calculates the change. Students discuss strategies used to determine the cost of the list of items and the change to be given.

LEARNING SEQUENCE

How Much?Students are told that a tv and a table cost $2300. If the tv costs $900 more than the table, how much does the table cost? Students discuss. Students could pose other similar problems to solve such as ‘What does each item cost if together they cost $2300?’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?

$1 coin.

Ask: How can we work out the amount of change we should get back? Encourage students to use play money to show how they could count on. Draw the coins (20c and 5c) on the board, loop them and ask: What is the 75c (the $1)? (The price and the amount paid.) What do we call the money I have looped? (The change). Label the amounts as shown above.

Students work with partners to determine the amount of change if $2 was used to pay for the 75c item.

Repeat this activity with other values.

ShoppingChoose varying amounts of money, for example, 75c, $1.20. Ask children to choose an item from some items on display that they can afford to buy with the amount of money. Ask them to then choose an item that they cannot afford to buy with the amount of money.

Open Ended QuestionsWhen I was in a music shop I saw that a CD cost about $22 and a tape about $15. What might have been the price tag on the CD and the tape?

In my pocket I have $36. What notes and coins might I have?

I bought something at a supermarket and got 5c change. How much did it cost and how much money did I give to pay for it?

The price tag on a toy car is $2.75. What coins would I use to pay for this?Show some different ways to give change for $2 for an item costing $1.35.

LEARNING SEQUENCE

Extension

Canteen Price ListThe answer to a calculation is 35c. What is the question?

CANTEEN PRICE LISTVegemite Sandwich $1.10 Salad Sandwich $1.55Ham & Salad Roll $1.40 Bag of Chips 65cFruit Salad $1.15 Piece of Fruit 20cCookie 15c

Can children write more than one question? Do they limit their questions to addition or do they make others?

In the GardenI have $1 000 and wish to purchase plants for my garden. Azaleas cost $7.50, roses cost $25.00 and shrubs cost $30.00. How many of each can I buy? Is there only one alternative?

My New HomesI have won $5 000 000 in the Lotto. I wish to purchase a number of homes as an investment portfolio. Using copies of real estate advertisements find homes to purchase that total as close to $4 000 000 as possible. Calculate the change from $4 000 000.Students are then to create a simple spreadsheet to spend their lotto win being able to give reasons for selecting, prioritising and deleting items when creating a budget.




TERM: WEEK: 13 STRAND:Number and Algebra



OUTCOMES: 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



solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080)solve addition and subtraction problems involving money, with and without the use of digital technologies

use a variety of strategies to solve unfamiliar problems involving money (Communicating, Problem Solving) reflect on their chosen method of solution for a money problem, considering whether it can be improved (Communicating, Reasoning) calculate change and round to the nearest five cents use estimation to check the reasonableness of solutions to addition and subtraction problems, including those involving money


Children work out addition/subtraction equations using as many different strategies as they can eg. Jump, split, compensation, bridging, extending number facts, changing order of addends (13 + 15 + 7 = 13 + 7 + 15)



I added two numbers together, each with three digits. I got the answer 428, what might the numbers be?


SIGNIFICANCE





RESOURCES Place value chart, 0-9 numeral cards, base 10 material, cue (numbered 9, 8, 7, 6, 5, 4)


Ask an individual to roll a cube (with numbers 9, 8, 7, 6, 5, 4) six times. Write each of the digits rolled on the board. Then say: Use these digits to make two three-digit numbers you can easily add in your head. Have the students work independently to write several pairs of numbers using the six digits. Invite volunteers to write number sentences on the board and describe the steps they used to add mentally. For example, for the digits 7, 8, 5, 5, 4 and 9, the students might suggest 594 + 587 = ___ and work out the answer by adding the hundreds (500 + 500) and then using a compensation strategy (+ 6, - 6) to add 94 and 87 (100 plus 81). Encourage them to describe more than one method for each sentence that is suggested and discuss other addition sentences for the numbers rolled.

Written AlgorithmsEnsure students clearly understand the link between concrete materials and the formal algorithm.On interactive whiteboard model how to use to formal algorithm when solving problems. Demonstrate a variety of problems with/without trading. Use a formal written algorithm to record addition and subtraction calculations involving two-, three-, four- and five-digit numbers, eg

Draw price tags for $245 and $160 on the board. Ask: What is the total you will pay for these two

LEARNING SEQUENCE

Remediation

Provide students with a copy of a hundreds chart and tens blocks.Hundreds Tens Ones

Ask them to model 462 + 125 with the blocks. Model writing the algorithm in vertical format on the place value chart. Ask students to complete the addition with the materials. Write the answer on the chart. Repeat, using 348 + 237, 483 + 265 and 257 + 178. Model recording the exchanging of ten minis for one long as a small digit in the tens column and ten longs for one flat as a small digit in the hundreds column.

Repeat activity using subtraction.

volunteers to describe and write on the board the thinking they would use to work out the answer eg

245+100 345+ 60 405

SubtractionProvide students with a thousand place value chart and base10 materials.

Thousands Hundreds Tens Ones

Ask them to model 89 with materials. Model writing the number in vertical format on the place value chart. Ask students to take away 37. Model – 37 on the chart and write the answer underneath. Repeat using 387 – 147, asking students to record.

Ask students to model 94 – 36 with materials. Model recording exchanging using the decomposition method; for example

LEARNING SEQUENCE

Place Value Chart

Hundreds Tens Ones

Using the place value chart and 0-9 numeral cards, draw cards to make two 3-digit numbers and place the cards in the correct columns on the chart. Model adding the numbers, focusing on recording (using a small digit) the exchanging of ones to tens and tens to hundreds as appropriate. Repeat with other cards, asking students to complete the addition.

Using the place value chart ask them to throw two dice to make two 4-digit numbers and add them eg

Repeat, asking them to add a 2-, 3- and 4- digit number. Have students share their additions and discuss strategies they used for recording exchanging.

Make it Add (Maths Tracks Stage 2)

Word ProblemsUsing the 2008 NAPLAN Year 3 question 15(Jim is 91 years old. Sam is 8 years old.What is the difference in their ages?), ask “What do I know?” Answer: Jim is 91 years old. Sam is 8 years old. What do I want to know? Answer; What is the difference in their ages?Think aloud: “I know how old Jim is and I know Sam is 8. I know that difference is another word for take away. I will solve this problem using subtraction”Model the solution of the problem using concrete materials and/or a drawing and writing the appropriate number sentence on the board.egStep 1: ‘How many to start with? Jim is 91.’ Put out 91 using tens and ones or draw this.Step 2: ‘How old is Sam? Answer:8. Move 8 ones away or cross out 8 drawn ones. Write 91-8= ‘How many left?’ Answer: 83. Write 91-8=83Step 3: ‘What is the difference in their ages?’Answer: 83. Discuss and model other possible solution strategies with the group using counters or drawings.Guide students to translate the information into a number sentence.91 take away 8 means I subtract so I use the – sign. I want to know many are left so I use the equal sign =. My number sentence is 91-8 =83

PartitioningExamine the partitioning method for addition and subtraction. Provide students with the following addition example:879 + 456 =We need to partition the numbers by using expanded notation.800 + 70 + 9

Students are given two sets of 0-9 numeral cards for each player. In pairs, students shuffle the cards and place them face down in a pile. Player one takes 4 cards and arranges them as shown.

Face up cards form the tens column and face down cards form the ones column. Each player may look at one of the face down cards. Each player estimates the total of the addition equation. Face down cards are then turned over and the addition carried out. The player with the closest estimate scores 1 point. Continue until one player has 10 points.

Which Way is Best?Students are asked to solve problems in three different ways: using a mental strategy, a formal written algorithm, and a calculator eg ‘Our class has 356 points and another class has 567 points. How many points do we need to catch up?’ Students compare the strategies used and discuss the advantages and disadvantages of each method. If students come up with different answers, they are asked to show which answer is correct.Variation: Students write their own problems and swap with others. Students could use four-digit or 5-digit numbers.

Base 10 MaterialStudents use 2, 3 or 4 dice to generate a two-, three- or four digit number and then represent this number using Base 10 material. Students then generate a second, smaller number by rolling one less die. Students represent this number using Base 10 material, then add the two numbers and show the result using Base 10 material. Students then write this as a formal written algorithm.

400 + 50 + 6Now we can add these numbers easily.800 + 400 = 120070 + 50 = 1209 + 6 = 15That gives us the final sum:1200 + 120 + 15 = 1335Provide students with the following addition example:8987 – 2341 =We need to partition the numbers first by using expanded notation.8000 + 900 + 80 + 72000 + 300 + 40 + 1Now we can subtract these numbers easily.8000 – 2000 = 6000900 – 300 = 60080 – 40 = 407 – 1 = 6That gives us the final sum:6000 + 600 + 40 + 6 = 6646

Students repeat this process, subtracting the second number from the first. Students record their solutions.

Missing DigitsStudents are shown a calculation to find the sum of two three-digit numbers, with some of the digits missing.

Eg

Students investigate possible solutions for this problem.Students are encouraged to design their own ‘missing digits’ problems. This activity should be repeated using subtraction.

AssessmentProvide students with a place value grid and ask them to solve 284 + 173, 1739 + 396, 2782 + 1093, and 4856 + 2478.

Provide students with a place value grid and ask them to solve 634 – 378, 5674 – 2432, 3084 – 1857, and 4702 – 2947.

LEARNING SEQUENCE

Extension

Make it Add (Maths Tracks Stage 2)Students can adapt the game by using 3- and 4-digit numbers. Students may also subtract.

What went wrong?Students are shown a number of completed subtraction problems with a consistent error eg subtracting the smaller number in a column from the larger number. Students correct the calculations and describe the error that was made eg


Students plan how to teach a person who made this mistake a correct method for obtaining solutions.




OUTCOMES: · Web viewAddition and Subtraction 2 WORKING MATHEMATICALLY:MA2-1WM, MA2-2WM, MA2-3WM...

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