mathematics teacher's guide grade 3

7/26/2019 Mathematics Teacher's Guide Grade 3

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A joint publication of National Institute of Education, Maldives

and Cambridge University Press, India

Exploring Maths3

eachers


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/ Ansari Road, Daryaganj, Delhi , India

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iii

Teachers are expected to play one of the most imperative role in implementing theNew National Curriculum.

This book intends to help teachers to bring the changes in the teaching andlearning process, based on the Mathematics Syllabus in the New NationalCurriculum. The book focuses on giving ideas for teachers to carry out practicalactivities by incorporating key competencies, skills and values for each strand in

the Mathematics Syllabus. The content of each unit includes outcomes, indicators,incorporated key competencies, shared values and process skills. In addition,prior knowledge, ideas to introduce the concept, pedagogy and planning followedby integration is written. Furthermore, guiding materials to be used in assessmentfor learning practices are included. We hope this book will serve as a supportfor teachers in order to achieve the goals of Mathematics in the New NationalCurriculum.

We extend our sincere thanks to Cambridge University Press for partnering withus in this endeavour.

We are beholden to the members of the NIE Curriculum Team for the support

rendered.

Ali Adam

Education Development Ofcer Coordinator

Aishath Shiuny

Education Development Ofcer Coordinator

Preface


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iv

Contents

Strand: Numbers (N)

1. NumberConcept 1

2. Addition and Subtraction 15


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Unit 1: Number Concept (N1)1

Unit 1: Number Concept (N1)

1. Prior knowledge:

Count numbers up to 3-digits (999) in Dhivehi and English

Skip-count forwards or backwards

Count reliably a set of objects

Recognise the value of numbers up to 3-digits (999)

Use the vocabulary of estimation

Make and justify estimates of numbers

Round off whole numbers

Read and write other numerals

2. Indicators

N1.1 Counting

a. Skip-counts forwards or backwards by ones, twos, ves, tens, threes,hundreds and thousands, from a given number.

Outcome N1.1:

Count numbers up to 4-digits (9999) in Dhivehi and English. Skip-countforwards or backwards.

Outcome N1.2:

Recognise the value of numbers up to 4-digits (9999).

Outcome N1.3:

Use the vocabulary of estimation; make and justify estimates of numbers.Round off whole numbers.

Outcome N1.4:

Read and write other numerals.


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Exploring Mathematics Teachers Book 3 2

N1.2 Place Value and Ordering

a. Represents numbers up to 4-digits using pictorial and symbolic materials.(Eg: Abacus, Number discs and place value charts).

b. Identify the number that comes after, before or between given numbers up

to 9999.

c. Compares numbers up to 9999 in different ways. (Eg: more than, less thanand equal to).

d. Orders and positions numbers up to 9999 on. (Eg: number line).

e. Forms different numbers, given any four number cards.(Eg: largest numberand smallest number).

f. Partitions 4-digit numbers in different ways, including into multiples of1000, 100, 10 and 1.

g. Reads, writes and says numbers up to 4-digits in gures and words.

h. Records numbers up to four digits using expanded notation. (Eg: 6052 =6000 + 50 + 2).

i. Recognises that the position of a digit gives its value, in relation to 4-digitnumbers and knows what each digit represents.

j. Says the name and writes the numeral for the number that is 1, 10, 100 or1000 more or less than a given 1 to 4 digit number.

N1.3 Estimating and Rounding

a. Estimates a number of objects up to about 100.

b. Uses the appropriate vocabulary in estimation. (Eg: about, not less than,not more than, almost).

c. Rounds any positive integer less than 1000 to nearest 10.

N1.4 Other Numerals

a. Reads and writes numbers in Arabic Indic(Hindu Arabic) numerals up to30. (Eg: . . . . . . . . . ).

Process skills:Representing, communicating, problem solving, selecting tools,

reecting, connecting, reasoning and provingKey competencies:Understanding and managing self, Relating to people,Thinking critically and creatively, living a healthy life, using sustainable practices

Shared values:Values related to self, others and the environment

3. Introduction to concept

Students learn number concepts through their day-to-day activities and usingmanipulatives. In Grade 2, children learn to extend numbers from 2-digit (99)to 3-digit (999) numbers. In Grade 3, the students revise these numbers and

learn to extend the number range to 4-digits (9999). The main focus here is torepresent numbers, visualise their quantity and associate with their number


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3 Unit 1: Number Concept (N1)

name. Counting large numbers is a challenge for some students but it can beeased out if it is associated to their daily life experiences or with their priorknowledge. Language is a tool which supports the development of numberskills. Use one-to-one correspondence of non-identical objects in play andpractical situations helps in building a better understanding of numbers.

The introduction of large numbers using their place values help the studentsdevelop the number sense to relate to a given range of numbers. It makes iteasier to compare, order numbers and perform computations with the givennumbers. An understanding of place value acts a tool for learners to performoperations without knowing the algorithm.

Using stories, songs and different activities help the students connect withtheir learning and hence develop their interest that in turn brings clarity ofthe concept.

Notice the digits on the number plates of vehicles while coming toschool.

Divide the class into groups and plan an activity to role play to act avehicle with a certain number.

Discuss about why such a big number is given to that particularvehicle, what each numeral represents (it can represent a state,area code, etc.)

Example

4. Details of Concept

Visualising helps in understanding the quantity of a number to carry outmeaningful counting. Students can nd many opportunities in their daily lifeto experience one-to-one correspondence with big numbers. They see andread four-digit numbers on the number plated of bus, car and other vehicleson the road. Once the students understand that large numbers are usedto count larger quantities, they will be look for more such examples, whichfurther strengthen their understanding of 4-digit numbers.

5. Pedagogy and Planning

Cut out pictures from old newspapers and magazines that have 4-digitnumbers. Discuss with them what all the numbers represent. Ask them to ndout what that numbers in the cut outs represent. Direct the discussion to theinformation these values give us.

Since the students are already familiar with the concept of skip counting, usethis opportunity to help the students practice skip counts of 4-digit numbersby 2s, 3s, 5s, 10s, 100s and 1000s using questions such as,

What if the number given in the cut out is increased by 2?

Will this change affect the data in any way? If yes, how?


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Help children make a collage using the newspaper cutting they haveon an A4 sheet of paper. Ask them to group themselves in sucha way that each group can be given a common theme name. For

example, vehicles on a road, problems in the city, households in thecity, students in schools, etc.

Turn a 1000s idea into a writing project. Ask children, What wouldyou do if you had MVR 1000? Have them write their response andillustrate it as well.

Collect tickets used for local transport or from past travels andobserve their costs. The students can be taken for a ride in the localor public transport system and asked to calculate the total cost oftravel of all the students in the class.

Cost of use of different means of transports available can beexplored, counted and compared.

Students can be encouraged to prepare their own travel tickets andcompare with the tickets prepared by other students.

Extension

ACTIVITY 1

This is activity on Dhivehi numbers. You need a set of ten cards having digits 0 to9 written in Dhivehi for each student. Only one digit should be written on a card.

Let all the students sit in a circle. Ask them to keep their number cards, face down,in front of them.

When you say ready, every student should pick up 4 cards at random and placethem face up. Then ask everyone to make the following numbers using their cards.

a. The greatest number b. The greatest even number c. The greatest odd number

d. The smallest number e. The smallest even number f. The smallest odd number

Now ask them to write the corresponding numbers using Hindu-Arabic numerals.

In Grade 3, student will also have to learn reading and writing Arabic-Indic

numerals up to 30. Following activity will help students learning Arabic-Indicnumerals.

ACTIVITY 2

This activity will help students to learn Arabic-Indic numerals.

Make around 20 number cards such that Hindu-Arabic numerals are written onhalf of them and corresponding Arabic-Indic numerals are written on the otherhalf. Keep the number cards on your table with face down. Ask 20 students tocome forward and pick up one card each.

Now one student will show his/her number card to the group. The student whichhas the number written in the other numeral will come forward and will stand


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beside the rst student. If any student makes any mistake, ask other students inthe class to correct it.

At the end of this activity, students will learn 10 pairs of numbers thoroughlywritten in both the number systems.

Now repeat this activity with remaining numbers.

Communicating:

Use understanding of the difference between counting of numbers forwards andbackwards and help the students practice problems related to 4-digit numbers.

Use skip counting by 2s, 3s, 5s, 10s, 100s and 1000s in practical situations.

The blue car has number 4356 and I saw a fruit shop around the corner

with the same shop number. My house number is 50 while Ali lives 5 houses from ours, that is, 55.

Examples: Discussion would introduce new vocabulary:

a) Names of objects stairs, car, shop, etc.

b) Words associated with skip count together, by, from

c) Names of colours blue, orange

d) Names of various transport car, bus, truck, tankers, metro railor interstate rail system

Examples

6. Integration : Thematic Approach: Road Transport

Prepare a presentation with children using number of vehicles on the road.This activity can be carried out after completing the whole strand.

Learning outcomes

Provide meaningful contexts for teaching mathematics.

Students can learn to work together collaboratively, with each studentengaging in tasks suited to his/her own level of ability/comfort.

Planning the presentation

Students discuss and plan to count the number of different types of vehicles atdifferent time intervals. For example, coming to school, while going back home,going for an outing with family, going for shopping or to buy grocery with parents,going to play in the park, etc.

Learning experiences include:

Identifying different types of transports for different needs

Making a list indicating the quantity of each type of vehicle


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Allocating different tasks for presentation, to each student such as collectingpictures of vehicles, collecting and keeping data for different types of vehiclesobserved

Distance travelled by people

Cost of travel in terms of tickets, stay during the travel, etc.

Asking children to explore why a particular vehicle is used for a particulartype of activity such as the use of a bus to carry 40 children or people at atime, trucks are used to carry heavy loads, 4-seater vehicles to carry fourpassengers, use of railways and airways to cover long distances

Understanding the choice of a mode of transport based on the costs involved

Discussing the effect of increase in road trafc and pollution

Understanding the importance of use of public means of transport to reduce

problems related to road trafcTravelling:

Learning experiences may include:

Using public means of transport and spreading awareness about its benets

Finding out different means of road transport available in the city/island

Learning the trafc and driving rules followed in the country

Using appropriate social skills and behavior while sitting in the bus/dhoani/ferry. For example, fastening the seat belt, stopping at the red light, use of

the horn, efciently using the sitting space available in the public means oftransport, offering seat to the elderly and those in need

Learning measures to avoid accidents

Preparing for the travel

Students make rules to travel by a motorbike. Students plan to prepare cards thatcan be distributed in public.

Tasks can be organised at an appropriate level for each student. Tasks caninclude cutting the paper for the card, writing the slogans, writing on the

card, writing the rules to be followed while travelling. The importance of safety is emphasised while distributing the cards.The students work independently and co-operatively and list down theinstructions/rules to be followed while travelling in a sequential manner (inwritten form for advanced learners or in pictorial form for others).

Once the cards are made, students get involved in the distribution processof the cards. Once again, the importance of interacting appropriately will beemphasised.

A discussion can be conducted in the class on the kind of response receivedfrom the people to whom the cards were given, the awareness lacking amongthe masses.


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7. Lesson plan referring to work book: Number concepts:

Recall prior knowledge of numerals, two and three digit numbers and numbernames using a number card game after that workbook can be taken; refercounting in the workbook

To introduce students to 4-digit numbers, plan some activities withmanipulative such as number cards with 3 digits and more, make numbersusing 4 digits, introduce the term thousand as done in grade 2

Plan a visit to the local supermarket to buy grocery. With this the studentsunderstand to read price tags on items and the total amount of money to bepaid at the cash counter (2- and 3-digit gures).

Representing numbers on the abacus, give pages with numbers having blankssuch as 4_32, 45_2, 489_ . asking the students to identify the place valuesof digits in the numbers(refer activities to be completed in the workbook like

completing the grid with peer, etc.). Use tickets made in the class, ask them who will sit where according to thenumber on the ticket , discuss with smaller number rst, what comes after,before and in between, ascending and descending, more than 5 or 1, etc. canbe taken up. Do the task given in the workbook. Let them do it in groups orwith their peers.

Explain what is rounding off by 10, 100 and 1000 using number cards .Takethe numbers one by one. First make them understand about ones place, thenextend their learning towards 10, 100 and 1000.

Discuss how we write numbers in Arabic, introduce the numerals using oneto one correspondence, give them cards from 0 to 9 and let them match it,ask them their number names, ask them to extend the numbers and take thecounting till 30 and ask to write it on a piece of paper with their group, askthem to do it individually after some time on a piece of paper, ask them to dothe task in the workbook.

Give the students a few more numbers with blanks at thousands place and askthem to do a group activity. Use these numbers for a comparison: greater than,less than or equal to. Refer book for doing activities with number given in that.

Plan more activities according to the need from the integration in the theme

8. Assessment

1. Questioning

Sample questions

a. Can you count ve numbers backwards of the number ______?

b. Can you count ve numbers forwards of the number ______?

c. What number comes after skip count by ___?

d. What if I put ve more in _______ and then add another 5 to it?


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e. What if I take away ve from _________ and then take ve more awayfrom it?

f. Represent the number _________ on the abacus.

g. Can you represent number ______________?

h. Write the number name of the number _________.

i. What will come in between these given numbers?

j. Which is bigger number out of the two given numbers?

k. Which is a smaller number out of the two given numbers?

l. What number will it become after it rounded off to 10, 100 or 1000?

m. What is the place value of the number _________ in the given number?

n. Can you write the Arabic-Indic number for the number _______.

2. Sample Rubric for teachers:

IndicatorsScore

1 2 3 4

N1.1 Topic: Counting

Uses number

names tocount orallyup to 3-digit(999) inDhivehi andEnglish

Student

cannot usenumbernames tocount orallyfrom numbersgivenbetween100-999 inDhivehi andEnglish.

Student needs

constantassistance touse numbernames to countorally numbersgiven between100-99 inDhivehi andEnglish.

Student can use

number namesto count orallynumbers givenbetween 100-999 in Dhivehiand English withno more than 2errors.

Student

independentlyuses numbernames andconsistentlycounts to 100-999 in Dhivehiand English withno errors.

Counts

orally andrepresentsnumbersbackward andforward usingnumber cardsfor a givennumber in 3-4digits

Student

cannot usenumbernames tocount orallyand representnumbersbackward andforward usingnumber cardsfor a givennumber 3-4

digits.

Student needs

constantassistance touse numbernames to countorally andto representnumbersbackward andforward usingnumber cardsfor a given

number 3-4digits.

Student can use

number namesto consistentlycount orallyand representnumbersbackward andforward usingnumber cards fora given number3-4 digits withno more than 2

errors.

Student

independentlyuses numbernames toconsistentlycount orallyand representnumbersbackward andforward usingnumber cards fora given number

3-4 digits with noerrors.


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IndicatorsScore

1 2 3 4

Demonstratesability tosort and skipcount by ones,twos, threes,ves, tens,hundreds andthousandsfor a givennumber

Studentcannot sortand skipcount byones, twos,threes,ves, tens,hundreds andthousandsfor a givennumber.

Studentsneeds constantassistance tosort and skipcount by ones,twos, threes,ves, tens,hundreds andthousands for agiven number.

Students canconsistently tosort and skip countby ones, twos,threes, ves, tens,hundreds andthousands for agiven number withno more than 2errors.

Studentindependentlysort andconsistently skipcount by ones,twos, threes,ves, tens,hundreds andthousands for agiven number withno errors.

N1.2 Topic: Place Value and Ordering

Able topresentnumbers upto 4-digits(9999) usingpictorial andsymbolicmaterial suchas abacus,number discsand placevalue charts

Studentcannotpresentnumbers upto 4-digits(9999) usingpictorial andsymbolicmaterial suchas abacus,number discsand placevalue charts.

Studentsneeds constantassistanceto presentnumbers up to4-digits (9999)using pictorialand symbolicmaterial suchas abacus,number discsand placevalue charts.

Student can usenumber namesconsistently topresent numbersup to 4-digits(9999) usingpictorial andsymbolic materialsuch as abacus,number discs andplace value chartswith no more than2 errors.

Studentindependentlyand consistentlypresents numbersup to 4-digits(9999) usingpictorial andsymbolic materialsuch as abacus,number discsand place valuecharts with noerrors.

Able toidentifynumber thatcomes after,before orbetween givennumbers up to

9999

Studentcannotidentifynumber thatcomes after,before orbetween given

numbers upto 9999.

Student needsconstantassistance toidentify numberthat comesafter, before orbetween given

numbers up to9999.

Student canidentify numberthat comes after,before or betweengiven numbersup to 9999consistently with

no more than 2errors.

Studentindependentlyand consistentlyidenties numberthat comes after,before or betweengiven numbers up

to 9999 with noerrors.

Able tocompare upto 9999 indifferentways such asmore than,less than andequal to

Studentcannotcompare upto 9999 indifferentways such asmore than,less than andequal to,

Student needsconstantassistance tocompare upto 9999 indifferent wayssuch as morethan, less thanand equal to.

Student canconsistentlycompare up to9999 in differentways such as morethan, less thanand equal to withno more than 2errors.

Studentindependentlyand consistentlycomparesnumbers up to9999 in differentways such asmore than, lessthan and equal towith no errors.


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IndicatorsScore

1 2 3 4

Able to orderand positionnumbers up to9999 using anumber line

Studentcannot orderand positionnumbers upto 9999 usinga numberline.

Student needsconstantassistanceto orderand positionnumbers upto 9999 usingnumber line.

Student can orderand positionnumbers upto 9999 usingnumber lineconsistently withno more than 2errors.

Studentsindependentlyorders andpositionsnumbers upto 9999 usingnumber line withno errors.

Able to formdifferentnumbers,

given any fournumber cards(E.g.: largestnumber andsmallestnumber)

Studentcannot formdifferent

numbers,given anyfour numbercards (E.g.:largestnumber andsmallestnumber).

Student needsconstantassistance to

form differentnumbers,given anyfour numbercards (E.g.:largest numberand smallestnumber).

Student canconsistently formdifferent numbers,

given any fournumber cards(E.g.: largestnumber andsmallest number)with no more than2 errors.

Studentsindependentlyand consistently

form differentnumbers, givenany four numbercards (E.g.:largest numberand smallestnumber) with noerrors.

Able topartition4-digitnumbers indifferent ways

Studentcannotpartition4-digitnumbers indifferentways.

Student needsconstantassistanceto partition4-digitnumbers indifferent ways.

Student canconsistentlypartition 4-digitnumbers indifferent wayswith no more than2 errors.

Studentindependentlyand consistentlypartition 4-digitnumbers indifferent wayswith no errors.

Demonstratesunderstandingby reading,writingand sayingnumbers up

to 4-digit ingures andwords

Studentcannot read,write and saynumbers upto 4-digit ingures and

words.

Student needsconstantassistance toread, write andsay numbersup to 4-digit

in gures andwords.

Studentconsistently read,write and saynumbers up to4-digit in guresand words with

no more than 2errors.

Studentsindependentlyand consistentlyread, write andsay numbersup to 4-digit in

gures and wordswith no errors.

Able to recordexpandednotation ofnumbers up to4-digit

Studentcannot recordexpandednotation ofnumbers upto 4-digit.

Student needsconstantassistance toread, write andsay numbersup to 4-digitin gures andwords.

Student canconsistently read,write and saynumbers up to4-digit in guresand words withno more than 2errors.

Studentsindependentlyand consistentlyread, write andsay numbersup to 4-digit ingures and wordswith no errors.


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IndicatorsScore

1 2 3 4

Able torecognize theplace value ofeach digit in agiven number4-digitsnumber

Studentcannotrecognize theplace value ofeach digit in agiven 4-digitnumber.

Student needsconstantassistance torecognize theplace value ofeach digit in agiven 4-digitnumber.

Student canconsistentlyrecognize theplace value ofeach digit in agiven numberof 4-digits withno more than 2errors.

Studentindependentlyand consistentlyrecognizes theplace value ofeach digit in agiven 4-digitnumber with noerrors.

Able to saythe number

name andwrite thenumeral thatis 1, 10, 100or 1000 moreor less thanthat of a given1 to 4 digitnumber

Studentcannot say

the numbername andwrite thenumeralthat is 1, 10,100 or 1000more or lessthan a given1 to 4-digitnumber.

Student needsconstant

assistanceto say thenumber nameand write thenumeral thatis 1, 10,100or 1000more or lessthan a given1 to 4-digitnumber.

Student canconsistently

say the numbername and writethe numeral thatis 1, 10,100 or1000 more or lessthan a given 1 to4-digit numberwith no more than2 errors.

Studentindependently

say the numbername and writethe numeral thatis 1, 10,100 or1000 more or lessthan a given 1 to4-digit numberwith no errors.

N1.3 Topic: Estimating and Rounding(up to 100)

Able touse thevocabularyof estimationto makeand justifyestimates ofnumber ofobjects up to

about 100

Studentcannot usevocabularyof estimationto makeand justifyestimates ofnumber ofobjects up to

about 100.

Student needsconstantassistanceto use thevocabularyof estimationto makeand justifyestimates of

number ofobjects up toabout 100.

Studentconsistently usesthe vocabularyof estimation tomake and justifyestimates ofnumber of objectsup to about 100with no more than

2 errors.

Studentindependentlyand consistentlyuses thevocabulary ofestimation tomake and justifyestimates ofnumber of objects

up to about 100with no errors.

Able to roundany positiveinteger lessthan 1000 tonearest 10

Studentcannot roundany positiveinteger lessthan 1000 tonearest 10.

Student needsconstantassistanceto roundany positiveinteger lessthan 1000 tonearest 10.

Student canconsistentlyround any positiveinteger less than1000 to nearest10 with no morethan 2 errors.

Studentindependentlyand consistentlyrounds anypositive integerless than 1000 tonearest 10 withno errors.


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IndicatorsScore

1 2 3 4

N1.4 Other Numerals (Arabic Indic (Hindu Arabic) numerals up to 30)

Demonstratesreading andwriting othernumerals (Eg:.........)

Studentcannotread andwrite othernumerals.

Student needsconstantassistanceto read andwrite othernumerals.

Student canconsistently readand write othernumerals withno more than 2errors.

Studentindependentlyand consistentlyreads and writesother numeralswith no errors.

3. Self assessment for students:

Expert Practioner Apprentice Novice

Countnumbersup to 50

I understandit well andcan teachsomeone else

I can mostly doit myself butsometimes I getstuck and need help

I am starting tounderstand it butneed someone tohelp me

I am starting tolearn this butI do not reallyunderstand it yet

Compareand ordernumbersup to 50





I understandplace value ofnumbers upto 50.





I can skipcount by 2, 5,10 up to 50.





Vocabulary Learnt

Dhivehi numbers Estimation Rounding off numbers


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Unit 2: Addition and Subtraction15

Unit 2: Addition and Subtraction

1. Indicators

N2.1 Understanding Addition and Subtraction

a. Relates addition to counting on steps along a number line.

b. Relates subtraction as nding the difference between and complementaryaddition.

c. Recognises that subtraction is the inverse of addition and uses this to

check the results.d. Recognises that adding and subtracting zero leaves a number unchanged.

e. Responds rapidly to oral or written questions phrased in a variety of ways.(Eg: 94 add 10, add 60 to 14, 70 plus 50, what is the sum/total of 26 and 9?)

f. Responds rapidly to oral or written questions phrased in a variety of ways.(Eg: 15 take away 8, take 8 from 15, 63 subtract 40, subtract 8 from 15,subtract 40 from 95).

g. Finds the value of the missing term(s) in addition or subtraction sentences.

h. Records addition and subtraction sentences using +, and =.

i. Recognises that addition can be done in any order but not subtraction.

Outcome N2.1:

Demonstrate and use the operation of addition and subtraction and the relatedvocabulary.

Outcome N2.2:

Derive and recall: doubles of all numbers up to 20, and doubles of multiples of 5up to 100; all pairs of multiples of 5 or 100 that totals 100 or 1000 respectively.Know by heart and recalls all addition and subtraction facts up to 20.

Outcome N2.3:

Count on to nd the sum of two numbers. Partition into tens and ones to usein addition. Add several numbers. Find a small difference by counting up.Identify and uses near doubles in addition. Derive new facts using numberfacts already known.


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j. Uses the commutative principle (not the name) in addition and identiesthat this principle cannot be used in subtraction.

k. Uses associative principle Uses associative principle (not the name; pair upin any order that is easier to add) in addition.

l. Creates simple addition and subtraction stories.m. Solve 3 step word problems involving addition and subtraction.

N2.2 Rapid recall of addition and subtraction

a. Derives and recalls doubles of all numbers from 1+1 to 20+20.

b. Derives and recalls doubles of multiples of 5 from 5+5 to 100+100. (Eg: 85+85=170).

c. Derives and recalls all pairs of numbers with a total of 30.

d. Derives and recalls all pairs of multiples of 5 that total 100. (Eg: 15 ).

e. Derives and recalls all pairs of multiples of 100 that total 1000. ().

f. Recalls all addition and subtraction facts for all numbers up to 20.

N2.3 Mental calculation strategies of addition and subtraction

a. Counts on from the larger number to nd the sum of two numbers. (Eg:12+25 add 10 to 25 and say 35, now count and say 36, 37).

b. Adds several small numbers by using various strategies. (Eg: look for pairsthat make 10 and do these rst, start with the largest number, look forpairs that make 9 or 11, and add these to the total by adding 10 and then

adjusting by 1).c. Partitions two digits numbers into tens and units, adds the tens rst.

(TU+TU).

d. Finds a small difference by counting up (recognises that when two numbersare close together, it is easier to nd a difference by counting up, notcounting back). Eg: 504498

e. Identies and uses near doubles using doubles already known to speed upaddition (up to 20).

f. Adds or subtracts 11 or 21, 9 or 19, to/from any three-digit number.

g. Develop and recognises a pattern. (Eg: 14 + 3 = 17, 14 + 13 = 27, 14 + 23= 37, OR 68 5 = 63 OR 68 15 = 53, 68 25 = 43).

h. Recognise and use patterns. (Eg: 4 + 8 = 12, 40 + 80 = 120, 400 + 800 =1200).

i. Given three numbers, say or write four different sentences relating tothese numbers.(Eg: using only the numbers 15, 17, 32, 34, 49, write asmany different addition or subtraction sentences as you can).

N2.4 Pencil and paper procedures of addition and subtraction

a. Uses the method counting on in multiples of 10 or 1 in adding TU&U, TU&TU.

(Eg: 86+57 = 86+50+7 = 136+4+3 = 143)


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17 Unit 2: Addition and Subtraction

b. Uses the method counting on in multiples of 100, 10 or 1 in adding HTU&TU,HTU&HTU (Eg: 356+427 = 356+400+20+7 = 756+20+7 =776+7 = 783).

c. Uses the method adding the most signicant digits rst in adding TU&U,TU&TU. (Eg: 67+24 = 80+11 = 91).

d. Uses the method adding the least signicant digits rst in adding TU&U,TU&TU (preparing for carrying)

e. Uses the method counting up from the smaller to the larger number(complementary addition) in subtracting TU&U, TU&TU.

f. Uses the compensation (take too much, add back) method in subtractingTU&U, TU&TU.

g. Uses the decomposition method in subtracting TU&U, TU&TU (preparingfor efcient standard method). (Eg: 81 57 = [(80+1) (50+7) = (70+11) (50+7) = (20+4) = 24)]

2. Prior knowledge:

Demonstrate and use the operation of addition and subtraction and therelated vocabulary.

Derive and recall: doubles of all numbers up to 15, and doubles of multiplesof 5 up to 50; all pairs of numbers that totals 20, and all pairs of multiplesof 10 that totals 100.

Recalls all addition and subtraction facts up to 10.

Count on to nd the sum of two numbers.

Partition into ones and uses in addition.Add several numbers.

Find a small difference by counting up.

Identify and uses near doubles in addition.

Derive new facts using number facts already known.

Process skills:Representing, communicating, problem solving, selecting tools,reecting, connecting, reasoning and proving, Making and using strategies

Key competencies:Understanding and managing self, Relating to people, Thinkingcritically and creatively, living a healthy life, using sustainable practices

Shared values:values related to self, others and the environment

4. Introduction of the Addition and Subtraction of 3-digit numbersbackground information

Addition and Subtraction of 3-digit numbers:

Students learn addition and subtractions of 3-digit numbers by recalling andconnecting with their prior knowledge of addition and subtraction of 2-digit

numbers. To explore addition and subtraction, various activities from day-to-day life can be incorporated to make the connection visible and meaningful.


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The topic further strengthens with the usage of manipulative. In Grade 2,students have learnt addition and subtraction of 2-digit numbers (99) usingvarious strategies. In Grade 3, they will explore and take their understandingfurther by adding and subtracting 3-digit (999) numbers.

Using place value helps build understanding about quantifying sets of objectsby grouping them into tens and treating the groups as units and use writtennotations to capture this information about groupings. Usage of physicalmaterials and written symbols in representing different numbers, highlightdifferent aspects of the grouping structure. Connections must be visiblebetween different representations for more clear understanding of place value.

Procedures for addition and subtraction of multi-digit numbers should betaught in such way that it looks like as if they have developed them on theirown. It helps develop their independent thinking about procedure, which willeventually transfer in usage.

Daily- weekly parking of vehicles in a shopping mall (how manyvehicles are parked in a day? Then next day, then next to next dayor you can use Sunday, Monday, etc. Find total for three days.)

Understand the use of bigger denominations of money that add tovalues up to 4-digit numbers and use them in everyday life.

Divide the class into groups and plan an activity to nd out distancebetween two places and calculate their total and difference. Howfar is one place from another (describing/representing the distancebetween two places)

Example

5. Addition and subtraction help the students in understanding the applicationof maths in their daily life. Students nd many opportunities in their day-to-day life where 4-digit numbers are used. For example, utility bills, fee receipts,shopping experiences with parents help build the procedures, which furtherhelps in metal calculations. Constantly using a mathematical procedures helpin making doing the calculations faster and more accurately.

6. Pedagogy and PlanningAsk the students to bring some bills related to shopping, buying tickets andreceipts from home.

Ask them to list some more items and nd out their prices. Make a bill usingthe information gathered and then ask them to delete some items and addany other items in that. Find the total and difference when some items areadded or deleted.

Discuss different mental strategies which can be used to add or subtractfaster which they already know from Grade 2.

Ask them to develop their own mental strategies using the numbers whichtotal up to 100 or 1000.


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Help children make a bill using any old bills for reference. Ask themto group themselves in such a way that can be given a common themename. For example, shopping of clothes, daily utility items, make-up

items, house decorative items, etc.Turn a 1000s idea into a writing project. Ask children, What wouldyou do if you had 4 MVR 1000 notes? How would you like to spendthem and nd out prices of those items? Ask them to do the task ingroups.

Collect tickets used for local transport or from their past journey.Ask to nd out recent price of those tickets and nd out the totalamount spent now.

Extension

Communicating:Understanding of regrouping while adding and subtracting numbers

To subtract 3 from 2, I take 10 from the tens place and add it to the digitin the units place (2) to make it 12.

While adding number such as 289 + 341, I immediately nd that twodigits in the units place add up to 10.

Examples: Discussion would introduce a lot of vocabulary:

a) Names of objects related to different types of clothes, itemson bills, etc.

b) Words associated with grouping and regrouping

c) Names of different modes of transport car, bus, truck, boat,dhoni, etc.

d) Words related to addition and subtraction: add, total, sum,increase/decrease, more/less than, in all, take away, all, left,added to, etc.

Examples

7. Integration : Thematic Approach: Road Transport

Prepare a presentation with children using cost and distance travelled bydifferent types of vehicles on road such as motorcycle, car, local transport, etc.

Learning outcomes

Provides meaningful context for teaching mathematics.

Students can learn to work together collaboratively, with each student

engaging in tasks suited to his/her own level of ability.


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Planning the presentation

Students discuss and plan to count the number of different types of vehicles atdifferent time interval, for example motorbike and bicycle to reach a particulardestination.

Learning experiences include:

Identifying different destinations and distance between them

Making a list indicating each type of vehicle

Allocating different tasks for presentation, to each student such as collectingpictures of vehicles, collecting and keeping data daily for different types ofvehicles

Distance travelled to different destinations

Cost of travel in terms of 3- and 4-digit numbers

Exploring why some modes of transportation are more used than the othersand the reason for this preference

Learning different means of road transport that are available for travel tothe same destination

Learning with sensitivity that some people cannot afford due to budget, lackof money and various other factor

Discussing to choose transport to reduce time of travel

Exploring how to choose different type of vehicles

Travelling:

Learning experiences may include:

Finding out different modes of road transport and discussing about it

Using appropriate social skills and behavior while gathering the informationabout cost of different types of tickets for one destination

Planning for the travel

Students can make a plan to travel to different states. They can make different

travel plans and write on the brochure to give to their parents for differentdestinations.Tasks can be organized at an appropriate level for each student. Tasks can

include cutting the paper for the card, writing the information related toplace of travel, its climate and clothes needed, different destinations covered,distance from each other, daily distance covered, can be organized groupwise.

The cost of travel and local sightseeing can be included. The work can bedivided equally so as children get equal opportunity to perform.

The nal activity can be a sharing about what happened and what was the

response of the people.


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8. Lesson plan referring to work book:

Addition and subtraction:

Recall prior knowledge of zero adding to 2 and 3 1-digit numbers orally orusing Dienes bloc or sticks or buttons

Use sticks or tens block to perform addition and then conrm by doing thesum orally for vertical addition in class for 2- and 3-digit numbers or vice-versa. It can be a peer activity. Refer to 3-digit vertical addition questions inthe workbook.

To introduce them to different strategies in such a way that they think it isdeveloped by them. Ask them to do it in such a way that it makes 10 or 100rst and do more questions using strategies. Ask them to do activities relatedin the book.

Use tickets made in the class, ask them to write

cost on it. Ask them to do a peer activity to add2 tickets, what will be the total cost, differencebetween cost of 2 tickets.

Plan more activities according to need from theintegration in the theme.

Give them some 2- and 3-digit numbers and askthem to nd the total orally and then give tasksrelated in the workbook.

Give them Dienes block ready to use to give them

more clarity.

Ideas to make Dienes blocks or base ten block

You can make your own and laminate them.

http://www.havefunteaching.com/worksheets/math-worksheets/place-value-worksheets/printable-base-10-blocks

lrt.ednet.ns.ca/PD/BLM/pdf_les/base-10_blocks/base10_all.pdf

http://www.mathworksheets4kids.com/blocks/thousand-block-large.png

You can download the material required for your class and make many moreusing the same blocks.


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Art activity for children to make their own Dienes blocks and use them inaddition and subtraction activities (give them for home to keep practicingaddition and subtraction)

After making many blocks in class use, ask them to make questions in groups

and share in class group wise.Give them some more practice by using all the Dienes block in class which cancater to thousands position for addition and subtraction problems.

Use daily items with tags to create stories in class. For example, A dresscosts MVR 345 and another costs MVR 456. What is the total cost of the twodresses?

9. Assessment Questioning:

Sample questions

a. Can you add these numbers?

b. Can you nd any other method to solve the question?

c. What will happen if I reverse the question? Will I get the same answer?

d. What number comes after subtracting or adding the two numbers?

e. Are you sure? How can you make sure that your answer is correct?

f. Observe childrens responses, probe further, and adapt with a smallerquantity when they make a mistake.

g. Can you show me how these numbers can be added using abacus?

h. Can you subtract or add and represent number ______________ onnumber line?

i. Can you show me your working? Can you explain your working of additionor subtraction to the class?

j. Why is the understanding of mathematical operations on large numbersbenecial in our daily life?


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Sample Rubric for teachers:

Strand:Numbers

Sub Strand:Addition and Subtraction

IndicatorsScore

1 2 3 4

Understandoperations ofaddition andsubtractionand the relatedvocabulary for

3-digit numbers

Student cannotunderstandoperations ofaddition andsubtractionand use

the relatedvocabularyfor 3-digitnumbers.

Student needsconstantassistance tounderstandoperations ofaddition and

subtraction anduse the relatedvocabulary for3-digit numbers.

Student canunderstandoperations ofaddition andsubtraction anduse the related

vocabulary for3-digit numberswith someassistance.

Studentunderstandsoperations ofaddition andsubtraction anduse the related

vocabulary for3-digit numbers

Derive andrecall doublesof all numbersfrom 1+1 to20+20 anddoubles ofmultiples of 5from 5+5 to100+10

Student cannotderive andrecall doublesof all numbersand doubles ofmultiples of 5.

Student needsconstantassistance toderive andrecall doublesof all numbersand doubles ofmultiples of 5.

Student canconsistentlyderive andrecall doublesof all numbers,and doubles ofmultiples of 5with no morethan 2 errors.

Studentindependentlyandconsistentlyderives andrecall doublesof all numbersand doubles ofmultiples of 5with no errors.

Derive andrecall pairs ofmultiples of 100that total 1000and recall alladdition andsubtraction

facts for allnumbers up to20

Student cannotderive andrecall pairsof multiplesof 100 thattotal 1000and recalls all

addition andsubtractionfacts for allnumbers up to20.

Student needsconstantassistance toderive andrecall pairs ofmultiples of 100that total 1000

and recalls alladdition andsubtractionfacts for allnumbers up to20.

Student canconsistentlyderive andrecall pairs ofmultiples of 100that total 1000and recalls all

addition andsubtractionfacts for allnumbers upto 20 with nomore than 2errors.

Studentindependentlyandconsistentlyderives andrecalls pairs ofmultiples of 100

that total 1000and recalls alladdition andsubtractionfacts for allnumbers upto 20 with noerrors.


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IndicatorsScore

1 2 3 4

Add severalsmall numbersby using variousstrategies

Studentcannot addseveral smallnumbers byusing variousstrategies.

Student needsconstantassistance toadd severalsmall numbersby using variousstrategies.

Student canconsistentlyadd severalsmall numbersby using variousstrategies withno more than 2errors.

Studentindependentlyand consistentlyadds severalsmall numbersby using variousstrategies withno errors.

Identify and usenear doublesusing doubles

already knownto speed upaddition

Student cannotidentify anduse near

doublesalready knownto speed upaddition.

Student needsconstantassistance to

identify and usenear doublesalready knownto speed upaddition.

Student canconsistentlyidentify and use

near doublesalready knownto speed upaddition withno more than 2errors.

Student canindependentlyand consistently

identify and usenear doublesalready knownto speed upaddition with noerrors.

Recognise anduse numberpatterns

Student cannotrecognise anduse numberpatterns.

Student needsconstantassistance torecognise anduse numberpatterns.

Student canconsistentlyrecognise anduse numberpatterns withno more than 2errors.

Student canindependentlyand consistentlyrecognise anduse numberpatterns withno errors.

Use knownnumber factsof addition andsubtraction toderive new facts

Student cannotuse knownnumber factsof addition andsubtractionto derive newfacts.

Student needsconstantassistanceto use knownnumber factsof addition andsubtractionto derive new

facts.

Student canconsistentlyuse knownnumber factsof addition andsubtractionto derive newfacts with no

more than 2errors.

Student canindependentlyand consistentlyuse knownnumber factsof addition andsubtractionto derive new

facts with noerrors.

Develop writtenmethods foraddition andsubtraction

Studentcannot developwrittenmethods foraddition andsubtraction

Student needsconstantassistance todevelop writtenmethods foraddition andsubtraction

Student canconsistentlydevelop writtenmethods foraddition andsubtraction

Student canindependentlyandconsistentlydevelop writtenmethods foraddition andsubtraction


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1. Self Assessment for students:

I am

condent

I need some

help

I am

confused

Understand operations ofaddition and subtraction andthe related vocabulary for3-digit numbers

Derive and recall: doublesof all numbers up to 20, and

doubles of multiples of 5 upto 100; all pairs of multiplesof 5 or 100 that totals 100or 1000 respectively. Knowby heart and recalls alladdition and subtractionfacts up to 20.

Derive new addition factsusing number facts alreadyknown

Subtract numbers bycounting up

Develoing written methodsfor addition and subtraction,and building on mentalmethods


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mathematics teacher's guide grade 3

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