Ministry of. Education SAMPLE LESSON PLANS. STRANDS: Number, Measurement, Geometry, Statistics and Probability and Algebra. Ministry of Education 2011

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1 Ministry of Education SAMPLE LESSON PLANS STRANDS: Number, Measurement, Geometry, Statistics and Probabiity and Agebra Ministry of Education 2011 Sampe Lessons copyedits-juy.indd 1 8/27/12 7:37 PM

2 Acknowedgements The handbook, Sampe Lesson Pans for Primary Schoos, is a direct response by the ministry of education to promote numeracy within the schoo for each teacher. This book has taken a number of months to compete. The period of time has made it possibe to appraise and test the essons using various strategies to ensure their effectiveness. The team of persons who worked on this project have years of experience in the teaching and earning process in the cassroom. They have contributed to the inteectua stimuus which aids the successfu competion of this project. an inteectua debt of gratitude is owed to these professionas. Therefore, the ministry wishes to extend sincere thanks to a who initiated, panned and prepared this vauabe document. Specia thanks to the Regiona mathematics Coordinators for their invauabe contributions to the deveopment of these essons. They undertook a most time-consuming and painstaking chore of writing some of these essons. They are: yashieka Backwood-Grant, Warren Brown, Caudette Henry-Harris, Davion esie, Christopher Reynods and eecent Waace. acknowedgements are aso due to the team of mathematics Speciaists for being creative in identifying and deveoping mathematica activities that are appicabe for use in schoos. Their efforts are greaty appreciated. The ministry is gratefu to the team of officers from the Core Curricuum Unit of the ministry of education for their priceess assistance, and to ms. Jean Hastings Director of education Systems Transformation programme (ministry of education) and Chairperson of the nationa Comprehensive numeracy programme Committee. In a these endeavours, it becomes manifest that except the ord buid the house, they abour in vain that buid it. Therefore, the ministry s personne want to thank God for his sustenance through the process. finay, sincere thanks to a other persons whose names do not appear, but who made vauabe contributions to the deveopment of the handbook. Seymour Hamiton nationa mathematics Coordinator Apri Sampe esson pans Sampe Lessons copyedits-juy.indd 2 8/27/12 7:37 PM

3 Contents Introduction... 6 NUMBER 7 esson 01 ordina numbers... 8 esson 02 ordina numbers...11 esson 03 pace Vaue...15 esson 04 addition with Renaming...19 esson 05 Changing mixed numbers to Improper fractions...23 esson 06 addition with Renaming...26 esson 07 fractions...30 esson 08 fractions...33 esson 09 Subtraction of fractions with Unike Denominators...38 esson 10 mutipication of Decimas by a Whoe number...41 esson 11 mutipication of Decimas by powers of Ten...44 esson 12 mutipication of fractions by a fraction...47 esson 13 Division of fractions (with mixed numbers)...51 esson 14 addition of Decimas...54 esson 15 Introduction to Ratios...57 esson 16 Ratio and proportion...60 MEASUREMENT 65 esson 01 measuring and estimating iquid...66 esson 02 perimeter...68 esson 03 estimating mass...71 esson 04 metric Conversion...74 esson 05 area...77 esson 06 Teing Time: minutes to the Hour...79 esson 07 area and perimeter...84 esson 09 Investigating Circumference of a Circe...87 esson 10 Scae Drawing...90 ministry of education Sampe Lessons copyedits-juy.indd 3 8/27/12 7:37 PM

4 GEOMETRY 93 LESSON 01 Shapes: Trianges and Rectanges...94 LESSON 02 Paths...96 LESSON 03 Lines of Symmetry...99 LESSON 04 Poygons LESSON 05 Types of Anges LESSON 06 Combining Geometric Shapes LESSON 07 Line of Symmetry LESSON 08 Identifying Rectanges LESSON 09 Sum of Anges in Trianges LESSON 10 Reguar and Irreguar Poygons LESSON 11 Introduction to Soids STATISTICS AND PROBABILITY 135 LESSON 01 Seecting Outcomes: Certain, Impossibe, Maybe LESSON 02 Conducting Probabiity Experiments and Recording Outcomes LESSON 03 Pictographs LESSON 04 Samping and Popuation LESSON 05 Mean LESSON 06 Bar Graph LESSON 07 Median LESSON 08 Constructing Questionnaires LESSON 09 Types of Graph (Picture, Line, Bar, Pie) LESSON 10 Using Data to Make Predictions and Inferences ALGEBRA 175 LESSON 01 Identifying Addends in Addition Probems LESSON 02 Using Agebra to Describe Reationships LESSON 03 n-sentences LESSON 04 Using Agebraic Ideas to Sove Probems LESSON 05 Creating Agebraic Expressions LESSON 06 Generating Number Patterns Sampe Lesson Pans Sampe Lessons copyedits-juy.indd 4 8/27/12 7:37 PM

5 LESSON 07 Substituting Vaues into Expressions LESSON 08 Soving Simpe Equations LESSON 09 Creating Agebraic Expressions LESSON 10 Creating Equations LESSON 11 Agebraic Expressions Ministry of Education Sampe Lessons copyedits-juy.indd 5 8/27/12 7:37 PM

6 Introduction It is the start of the new schoo year and Mrs. Baxity is thinking about her new students and the mathematics esson she has to deiver. She wi be meeting her students for the first time, but aready has their performance data at hand. She has to teach Number, but is quite puzzed. She is aware that she wi need to deiver an effective mathematics esson one that wi heighten students interest, buid computationa fuency and deveop their skis to reason and sove probems. most cassroom teachers wi admit they have had an experience simiar to mrs. Baxity s; panning an effective mathematics esson can be chaenging. In ight of the varying earning styes of students, it is of paramount importance that essons are designed to meet such diverse needs and to maximize a students earning. mathematics shoud be taught through processes which focus on modeing, communication, connections, reasoning, proofs and probem soving. Such processes shoud be considered when panning to teach a esson in any of the mathematics strands: number, Geometry, measurement, agebra, Statistics and probabiity. effective teaching requires the deveopment of students cognitive abiities; students earning occurs most efficienty when they are afforded rich experiences through a student-centred, activity based approach. effectivey empoying such an approach requires carefu panning of essons. This handbook is designed to provide teachers with esson panning ideas for the teaching of mathematics at the primary eve. It features a set of sampe esson pans for each of the five content strands of the Revised primary Curricuum: number, Geometry, measurement, agebra, Statistics and probabiity. essons have been incuded, per strand, for each GRaDe eve so that teachers of a grades in the primary schoo may gean ideas for improving their essons. The essons are written using a three-part mode: STaRTeR activity, main activity and penary. appropriate assessment activities are aso incuded. The STaRTeR activity is intended to awaken students interest in the TopIC to be taught. Some of these activities may aso be usefu in assessing students mastery of the prerequisite concepts and preparing them for the TopIC to be deivered. The main activity is the key teaching point of the esson and usuay entais students discovering some new idea through their engagement in carefuy panned activities. The penary acts as the summary for the esson and cements the TopIC taught. The essons incuded in this handbook are meant to be a guide for the teacher in seecting earning objectives and corresponding teaching strategies for attaining these objectives. The order in which essons are presented in the handbook is not to be taken as a mode for sequencing the teaching of various concepts. each esson is to be considered on its own. Whie compete essons are presented, the writers are aware that there are various formats for esson pan writing. Teachers are therefore free to modify the essons according to the accepted esson pan format for their schoo and the abiities and interests of the students. Care shoud be taken however to ensure that a the critica eements of the esson pan are maintained. 6 Sampe esson pans Sampe Lessons copyedits-juy.indd 6 8/27/12 7:37 PM

7 NUMBER ministry of education Sampe Lessons copyedits-juy.indd 7 8/27/12 7:38 PM

8 LESSON 01 ORDINAL NUMBERS SUB-TOPIC: Identifying ordina numbers GRADE LEVEL: Grade 1 DURATION: 1 hour SPECIFIC OBJECTIVE By the end of the esson, students shoud be abe to: use the ordina numbers first, second, third, through to fifth PREREQUISITE KNOWLEDGE Students shoud aready: a) have knowedge of number names and their symbos up to 10 b) be abe to count in order up to 10 MATERIALS/MANIPULATIVES picture, number cards, word cards, objects from the environment CONTENT OUTLINE an ordina number is a number that states the position of an object in a sequence. The symboic representations of ordina numbers are formed by combining the corresponding cardina number and the ast two etters of the ordina number name. note the pattern: o first is written by combining 1 and st to produce 1 st o Second is written by combining 2 and nd to produce 2 nd o Third is written by combining 3 and rd to produce 3 rd o fifth is written by combining 5 and th to produce 5 th PROCEDURE Menta/Ora Starters The entire cass wi be taken outside in a controed area. Severa items (such as a eaf, a stone, a stick, a botte cover, or a botte) wi be strategicay paced for five students to find. a five students wi return to the starting point with the objects. 8 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 8 8/27/12 7:38 PM

9 Main Activity The five students who participated in the race wi be asked to ine up in the order in which they returned to the starting point. The cass wi be asked to expain why each chid was paced in his or her respective position. Through further discussion, the concept of first, second, third, fourth and fifth wi be estabished. The students who participated in the race wi be given cards with the names of their positions. Five other students wi be given cards with the numbers 1 to 5. They wi be asked to stand beside their partner aready in ine. Each pair of cards wi be paced on the chakboard. Chidren attach ordina number cards to the first 5 positions in race. The cass wi be engaged in discussions to ascertain if they can write symboic representations for ordina numbers. Students wi then be seected to write the symbos for ordina numbers first to fifth on the chakboard. PLENARY Students wi observe the picture beow which depicts a 100m fina. They wi isten whie the teacher reads the story, The Race, recorded beow. The students wi be ater engaged in a discussion about the outcome of the race. The Race Maron and John are the fastest runners at Hope Primary Schoo. They were very excited as it was Sports Day and they woud both compete with each other in the fina race of the day. The gun went off and the boys started running. Members of their houses were cheering as they knew either boy woud win. As the race progressed, the cheering sowy died down, as Pau, a ta unpopuar boy, ran past the other boys as they approached the finish ine. Everyone was surprised to see that Pau won the race, outpacing Maron who came second and John who came third. They both started crying. James, who aways finished ast, was very happy because he was fourth. Ministry of Education Sampe Lessons copyedits-juy.indd 9 8/27/12 7:38 PM

10 ASSESSMENT Divide the cass into groups of 5. To each group, randomy distribute pre-prepared 2-sided cards with the ordina number symbo on one side and its ordina number name on the other side (each group gets a set of cards with ordina numbers 1 st /first to 5 th /fifth). Instruct students to order themseves based on the position on the card they receive. 10 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 10 8/27/12 7:38 PM

11 LESSON 02 ORDINAL NUMBERS SUB-TOPIC: Sequencing GRADE LEVEL: Grade 1 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson students shoud be abe to: appy ordina number concepts to rea-ife situations use the terms "before" and "after" correcty in reation to ordina numbers PREREQUISITE KNOWLEDGE Students shoud aready: a) have knowedge of number names and symbos b) have basic knowedge of ordina numbers c) have knowedge of the names and order of the days of the week and the months of the year MATERIALS/MANIPULATIVES Cooured chak, caendar, name cards (days of the week and months of the year), picture story cards CONTENT OUTLINE an ordina number is a number that states the position of an object in a sequence. The symboic representations of ordina numbers are formed by combining the corresponding cardina number and the ast two etters of the ordina number name. for exampe: o first is written by combining 1 and st to produce 1 st. o Second is written by combining 2 and nd to produce 2 nd. o Third is written by combining 3 and rd to produce 3 rd. o Twefth is written by combining 12 and th to produce 12 th. ministry of education Sampe Lessons copyedits-juy.indd 11 8/27/12 7:38 PM

12 PROCEDURE Menta/Ora Starters The students wi observe a sequence of three actions demonstrated by the teacher. The cass wi then ist the actions performed in order. o Touch your head (first), stand at attention (second), and hop (third) o These wi be written on the chakboard and used to pay Simon says For exampe, the command Simon says third action woud be given and students woud be required to hop. Teacher wi indicate the time aotted for this activity. Main Activity Students wi be asked to read or say the months of the year as the teacher points to the words on her chart. Five students wi be asked the months in which they were born. They wi be given a card on which their birth month is written. Teacher wi pose the foowing questions to the cass: a) Whose birthday comes first? b) Whose birthday is ast? c) Whose birthday is third? d) Whose birthday comes after? e) Whose birthday comes before? The chakboard wi be divided into two coumns. In one coumn the ordina numbers 1 st, 2 nd, 3 rd th wi be written. The other coumn wi be abeed months of the year. The students wi be asked the foowing questions in the stated order. Once the correct answer for a question is received the student who provided the answer wi be given a name card to pace on the board beside the reevant position. a) What is the third month of the year? b) Which month comes before the third month? c) Which month comes after the third month? d) Which month comes before the second month? e) What is the ninth month of the year? f) Which month comes before the sixth month? g) Which month comes after the sixth month? 12 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 12 8/27/12 7:38 PM

13 PLENARY Students wi be asked to pick cards from a box with the months of the year written on them. They wi pace them on an interactive chart with sots that are abeed 1st month, 2nd, 3rd, etc. This wi be foowed by a discussion about the students pacement of the cards. ASSESSMENT Students and teacher wi read the nursery rhymes ( Jack and Ji and Litte Miss Muffet ) from a chart, mutimedia, etcetera, so that they are reminded of the sequence of events in the stories. The students wi be paced in groups and each group given a set of picture cards. The task is to arrange the cards in the correct order to te the story. In addition, questions reated to the stories wi be given. (These questions are isted beow at end of the two picture stories.) JACK AND JILL Ministry of Education 2011 Sampe Lessons copyedits-juy.indd /27/12 7:38 PM

14 Litte Miss Muffet a) What happened first? b) What happened after... (Miss Muffett saw the spider) (Jack fe down)? c) What happened before (she saw the spider) (Jack and Ji got the water)? d) Describe the third picture. 14 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 14 8/27/12 7:38 PM

15 LESSON 03 PLACE VALUE SUB-TOPIC: Understanding pace vaue GRADE LEVEL: Grade 2 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson, students shoud be abe to: use concrete materias to group objects to iustrate tens and ones use symbos (numeras to represent groups of tens and ones) identify the pace vaue of digits in a two-digit base ten numera PREREQUISITE KNOWLEDGE Students shoud aready know: a) how to count from 1 to 100 b) how to count in twos and threes MATERIALS/MANIPULATIVES Interocking cubes, die, organizationa mats, counters (botte caps, fudge sticks, etc.) CONTENT OUTLINE pace vaue is the position of each digit in a number. The pace vaue of each digit in a number increases in powers of tens, from right to eft. In a two digit number, there are two pace vaues, Tens and ones. PROCEDURE Menta/Ora Starters pace students in groups of four and provide each group with one of the foowing sets of counters: Instruct students to form as many groups of ten as possibe using the set given. each group shoud report resuts. ministry of education Sampe Lessons copyedits-juy.indd 15 8/27/12 7:38 PM

16 Main Activity The whoe cass wi observe as the teacher uses an organizationa mat to show the foowing numbers: 21, 18, 62 and 55. Chidren wi be provided with counters (cubes, botte caps, etc.) Working in pairs, students wi take turns to toss a die. For exampe, Mike tosses the die and gets a 6; he counts out 6 cubes and paces them in the ones coumn. Mike tosses again and gets a 5; he counts out 5 and paces them in the ones coumn. He notices that he can exchange a group of 10 cubes for 1 ten with one remaining. The trading game continues unti a the cubes that were provided are used up. Tens Ones 16 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 16 8/27/12 7:38 PM

17 PLENARY Hundred Chart Activity Using mini-hundred charts, students wi be asked to shade the numbers according to cues given to them. The numbers that are shaded on their mini-hundred chart shoud form a design. exampes of cues to be given to students incude: a) mark the numbers with 4 in the tens pace and 8 in the ones pace. b) mark the numbers with 6 in the tens, and 2 in the ones pace. c) mark the numbers with 5 in both paces. note Decide on a design and provide the additiona cues as required. Exampe, to teacher: circe the number which has 2 in the tens pace and 3 in ones pace. HUNDRED CHART ministry of education Sampe Lessons copyedits-juy.indd 17 8/27/12 7:38 PM

18 ASSESSMENT Students wi be given a Pace Vaue Worksheet to compete. PLACE VALUE WORKSHEET 1. Write the number that has a five in the ones pace and a three in the tens pace. The number is : 2. a) What is the pace vaue of each digit underined in the numeras beow? The pace vaue is: b) Students wi be shown diagram of artices in tens and ones and asked to write the numera to represent these. E.g. Ten fishes pus one fish gives. (Expected response is 11.) 18 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 18 8/27/12 7:38 PM

19 LESSON 04 ADDITION WITH RENAMING SUB-TOPIC: Adding whoe numbers with a sum ess than one hundred GRADE LEVEL: Grade 2 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson, students shoud be abe to: add a two-digit number to a one- or two-digit number with or without renaming sove probems requiring the addition of two-digit numbers with or without renaming PREREQUISITE KNOWLEDGE Students shoud aready: a) have a cear understanding of the ten make one aspect of the base ten system b) have a basic understanding of addition facts c) know how to count and identify numbers up to 99 d) be famiiar with correct representation of two-digit numbers on pace vaue chart e) be famiiar with base ten materias MATERIALS/MANIPULATIVES Base ten materias, probem whee, card with menta starter, chart with story CONTENT OUTLINE addition is the combination of two or more sets Renaming is necessary when a sum of ten or more is obtained. PROCEDURE Menta/Ora Starters What is the message? Sove each addition probem and, using the code beow, write the corresponding etter on the ine and decode the secret message. ministry of education Sampe Lessons copyedits-juy.indd 19 8/27/12 7:38 PM

20 Main Activity manipuatives wi be paced on the desks ongs (one group of ten), and ones whie students work at the menta starter. each chid shoud be given ten ongs and thirty ones. Review tens and ones using the story beow. Note: The story wi either be written on the board before the cass begins or on a chart, so that teacher and students can read it together Jack and Ji were on their way to schoo. They stopped at a shop, Jack bought 24 marbes and Ji bought 8. Students wi use manipuatives to show Jack s marbes and Ji s marbes. Jack s marbes 24 = 2 tens 4 ones Ji s marbes 8 ones Students wi be asked the foowing questions: How many groups of ten and ones are in the group of marbes Jack bought? How many marbes did they buy atogether? Give the chidren time to investigate and use their own strategy to arrive at the answer. Coect the answers and ask individua students to expain how they arrived at their answer. Represent some of these strategies on the board. 20 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 20 8/27/12 7:38 PM

21 Seect the strategy where students trade ten ones for one ong for further discussion to bring out renaming as shown beow. Through questioning, students wi be guided to reaize that the probem can aso be written as The use of the coumns wi be faciitated to make a connection to what was practicay done. In this method, the ones coumn is first added. If there are ten or more ones, we trade ten of them for a ong as shown above. The 2 tens are now increased to 3 tens. The remaining ones, in this case 2 ones, are written under the ones coumn. Probem Whee A whee is to be created with eight sectors. Each sector of the whee wi contain a simpe addition story probem. Working in pairs, students wi take turns to spin the whee. With the use of fats and ongs they wi mode and sove the story probem indicated by the pointer. Ministry of Education Sampe Lessons copyedits-juy.indd 21 8/27/12 7:38 PM

22 PLENARY Engage students in a discussion about the need for renaming when adding two-digit numbers. Suggested questions incude: When does it become necessary to rename? Can you think of some addition probems where renaming woud be necessary (or not necessary)? ASSESSMENT Each chid picks a probem from a grab bag and provides a soution utiizing fats and ongs. Students coud use bocks to represent soutions in at east two different ways. 22 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 22 8/27/12 7:38 PM

23 LESSON 05 CHANGING MIXED NUMBERS TO IMPROPER FRACTIONS GRADE LEVEL: Grade 3 DURATION: 1 hour SPECIFIC OBJECTIVES At the end of this esson, students shoud be abe to: identify mixed numbers write mixed numbers as improper fractions PREREQUISITE KNOWLEDGE Students shoud possess knowedge of: a) the four basic operations on proper fractions b) the concept of fraction (how many haves, thirds, fourths, etc. make up the whoe) c) types of fractions (improper, mixed, proper) MATERIALS/MANIPULATIVES fractiona pieces (two sets of fractiona pieces), fraction bingo, worksheet CONTENT OUTLINE an improper fraction is a singe fraction that is more than a whoe, which is expressed with the number representing the numerator being arger than the number representing the denominator. exampe 5 / 3. a proper fraction is a singe fraction that represents an amount that is ess than the whoe, which is expressed with a numerator that is smaer than the denominator. exampe 2 / 3. a mixed number consists of a whoe number and a proper fraction exampe 1 2 / 3. PROCEDURE Ora/Menta Starters Students wi be given pairs of coour coded cards with cues such as bun, cheese, bread, butter, adam, eve, etc. one coour wi represent numerator and the other coour wi represent denominator. The cards wi be designed with numbers to give an improper fraction when matched. Students wi be asked to find their partner and read the improper fraction formed. ministry of education Sampe Lessons copyedits-juy.indd 23 8/27/12 7:38 PM

24 Main Activity Students wi be paced into groups. each group wi be given a different number of fractiona pieces representing different fractions, e.g. thirds, fourths, fifths, etc. as revision. each group wi then be asked to use their fractiona pieces to make as many whoes as possibe. for exampe, students with thirds coud make 1 whoe with three thirds. The students wi be asked to expain their modes. Exampe: How many pieces did you begin with? How many whoes were made? How many were eft over? How woud you ca this fraction? How woud you write it? What represents the numerator, denominator, and the whoe? (emphasis must be paced on identifying the three parts: whoe number, denominator and numerator.) I had 4 thirds which is the same as 1 1 / 3. Students wi be given other fractiona pieces. They wi be ed into counting the number of each fractiona piece that they have and then writing these in words on the board. exampe: one group has eight thirds, another five haves, and another nine fifths. They wi then assembe them into whoes and fractiona parts and be required to write the mixed number form of the fractiona pieces given. For exampe: 7 parts modeed and the size of each part is one-fourth, therefore this is written as improper fraction seven-fourths written as 7 / 4 which is the same as 1 3 / 4 as a mixed number. Using the diagram beow, students wi be guided through questioning to seeing and understanding that the tota number of parts used is the numerator, and the size of each part gives us the denominator. Questions 1. How many parts are shaded in the three shapes beow? (Expected response 11) 2. What is the size of each part? (Expected response fourths) 3. Which represent the numerator and which represent the denominator? 4. How woud you write this as a fraction? (Expected response 11 / 4 ) 5. How many whoes are there? (Expected response 2) 6. How many fourths are remaining? (Expected response ¾) 7. How woud you write this as a mixed number? (Expected response 2¾) 24 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 24 8/27/12 7:38 PM

25 PLENARY Students in groups wi expain in their own words how to write a mixed fraction from a mode. This wi be organized as notes for students. ASSESSMENT The teacher wi guide students in a bingo game (Matching Three) Rues The teacher wi dispay a card showing a mode of a mixed number If the mixed number is on a student s game card, he or she may cover it The first payer with three in a row cas out BINGO That payer reads out his or her covered numbers for the teacher to check. If correct, the game is over and a new game wi begin. Sampe Bingo Card Ministry of Education Sampe Lessons copyedits-juy.indd 25 8/27/12 7:38 PM

26 LESSON 06 ADDITION WITH RENAMING GRADE LEVEL: Grade 3 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson, students shoud be abe to: add whoe numbers up to six digits sove probems which require the use of addition PREREQUISITE KNOWLEDGE Students shoud aready be abe to: a) add numbers without renaming b) rename up to thousands c) identify the vaue of each digit in a number up to four digits d) understand addition MATERIALS/MANIPULATIVES Dienes bocks (fats, ongs and units), abacus, worksheets, cards with probems CONTENT OUTLINE The decima system is based on a ten make one reationship. each pace vaue is ten times greater (or ess) than the pace to its right (or eft). addition is an operation on two or more numbers that gives a sum greater than each of the addends. PROCEDURE Menta/Ora Starters Students wi create paindromes from numbers that are not paindromes without renaming. These numbers wi be given to the students. exampes: 123, 12 and 53. This is to review addition without renaming. Note: Paindromes are numbers that are read the same way forward or backward. Exampe: 444 or Sampe esson pans - number Sampe Lessons copyedits-juy.indd 26 8/27/12 7:38 PM

27 The Activity Step 1: Write a given number Step 2: Write the reverse of the number Step 3: Add the numbers together. If the resut reads the same in either direction it is caed a paindrome For exampe, Main Activity Students in groups wi be given base ten pieces (fats, ongs and units) and cards with the same probems. (A groups wi be given the same probem.) The first probem wi be done as foows: Sandy bought 478 toys and Kim bought 637 toys. How many toys did they buy atogether? a) Students wi read the probem. b) Students wi write number sentence representing the probem ( ). Students wi represent the probem on a pace vaue chart or abacus and sove using their base ten pieces (Dienes bocks). Thousands Hundreds Tens Ones ones = 1 ten and 5 ones 11 tens = 1hundred and 1 ten 11 hundreds = 1thousand 1 hundred The other probems wi be done simiar to the exampe used above. Ministry of Education Sampe Lessons copyedits-juy.indd 27 8/27/12 7:38 PM

28 PLENARY Engage students in a discussion about the need for renaming when adding numbers. Suggested questions incude: When does it become necessary to rename? Can you think of some addition probems where renaming woud be necessary (or not necessary)? ASSESSMENT Pay Addition Reay Game Pace students in teams of no more than seven. The first person in each team wi compete the first probem on the worksheet. Then he/she wi pass the worksheet and a penci to the next person in his/her row. This wi continue unti a probems are sequentiay competed by the team. Rues of the Game Each payer must contribute to the team by working a probem when it is his/her turn. Discussion of answers shoud ony be done after the game. The team that finishes first with the most correct responses wi be the winner. Students wi discuss their chaenges and share their successes/attempts. 28 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 28 8/27/12 7:38 PM

29 Work Sheet answer: 2. Tony has $17,052 in his bank account. His brother Mark has $23,459. How much do they have atogether? Answer: Answer: Answer: Answer: 5. John has 4,375 marbes. His brother gave him some more marbes, and he now has 4,500 marbes. How many groups of 25 marbes shoud he add to his origina number to get 4,500 marbes? Answer: 6. A baker baked 567 oaves of bread. Another baker baked twice as many. How many did they bake atogether? Answer: 7. There were 2,325 footba fans in the Nationa Stadium for the game on Friday night. On Saturday there were 3,627 fans. What is the tota number of footba fans that came to both games? Answer: Ministry of Education Sampe Lessons copyedits-juy.indd 29 8/27/12 7:38 PM

30 LESSON 07 FRACTIONS SUB-TOPIC: Addition of fractions with unike denominators GRADE LEVEL: Grade 4 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson, students wi be abe to: appy equivaence to the addition of fractions PREREQUISITE KNOWLEDGE Students shoud aready a) have a conceptua understanding of a fraction b) have an understanding of equivaent fractions c) be abe to Identify ike fractions d) have an understanding of mutipes e) be famiiar with the use of fraction pieces MATERIALS/MANIPULATIVES fraction pieces CONTENT OUTLINE addition of two or more fractions is the combination of the fractions which resuts in a sum that is greater than the addends. To add fractions with different denominators, the concept of equivaence is appied so that a the addends can have a common denominator. PROCEDURE Menta/Ora Starters Students wi be paced in groups to pay a game fraction match Up. o each group wi be given a stack of cards face down, each card bearing different fractions o Students wi take turns to fip cards eaving the fipped card face up on the desk o on recognizing two fractions that are equivaent, a student wi ye match up and take the pair Rue: One student wi be designated in each group as a judge. The judge wi be given the answer card with a possibe pairs. Chidren are aowed three wrong answers before being eiminated from the game. 30 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 30 8/27/12 7:38 PM

31 Main Activity Students wi remain in groups and wi be given a probem: Mary has haf of a chocoate and John has a third. How much chocoate do they have atogether? Using fraction pieces, students wi mode the probem. Students wi be questioned in order to ascertain the probems they have with adding the two fractions and then they wi generate conjecture on how they coud sove the probem. (Exampe is given beow using a diagram.) It is possibe that in modeing the probem students wi join the pieces in an attempt to represent the soution as iustrated beow. Students wi be questioned to find out what name coud be given to the fraction formed. They wi then be guided through a process of fitting smaer fraction pieces (for exampe, sixths, eighths, etc.) exacty over the sum. The aim is for the students to identify how many pieces of which fractiona part wi fit exacty over the sum. Students wi then determine the number of smaer parts that cover each fraction in the addends. For exampe, in the iustrations above, 1 / 2 is equivaent to three sixths and 1 / 3 is equivaent to two sixths. Through questioning, students wi highight the reationship between the denominators in the addends and the equivaent fractions formed. Students wi be given the foowing additiona probems to sove using the method described in previous steps: 1 1 a) + c) b) + 2 d) Ministry of Education Sampe Lessons copyedits-juy.indd 31 8/27/12 7:38 PM

32 PLENARY In journas, students wi describe how to add fractions with unike denominators. ASSESSMENT Students wi remain in groups and each group wi be given a set of questions to mode using fractiona pieces. In soving the probems they wi try to rename the addends using equivaent fractions with common denominators. Groups wi share their efforts with the cass. 32 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 32 8/27/12 7:38 PM

33 LESSON 08 FRACTIONS SUB-TOPIC: Appying equivaence to addition and subtraction of fractions GRADE LEVEL: Grade 4 DURATION: 1 hour SPECIFIC OBJECTIVES By the end of the esson, students wi be abe to: appy the concept of equivaence to the addition of fractions PREREQUISITE KNOWLEDGE Students shoud aready have: a) a conceptua understanding of a fraction b) an understanding of equivaent fractions c) the abiity to Identify ike fractions MATERIALS/MANIPULATIVES mutipication tabes, pain paper, crayons and fraction cards (cards with fractions written on them) CONTENT OUTLINE one method of adding fractions with different denominators is to rename the fractions by appying equivaence, so that the fractions to be added have the same denominator. PROCEDURE Menta/Ora Starters Students wi pay the game equivaent hopscotch. a diagram of the reguar hopscotch wi be drawn in which teacher wi pace fraction cards. The fractions wi be strategicay paced so that at east four of them are equivaent to the one that the teacher wi highight. The aim of the game is to hop ony on those which are equivaent. fractions may be repaced for each round. ministry of education Sampe Lessons copyedits-juy.indd 33 8/27/12 7:38 PM

34 ⁶ ₂₄ ⁸ ₁₂ ⁴ ₁₂ ⁵ ₂₀ ⁶ ₉ ⁴ ₁₆ ³ ₁₂ ⁴ ₆ ² ₈ ² ₃ ¹ ₄ Main Activity Using two fractions from the hopscotch, 2 ₃ and ¹ ₄, students wi be provided with pre-cut, equa sized rectanges to represent the two fractions. Vertica ines wi be used to divide one rectange to show thirds whie horizonta ines wi be used to divide the other rectange to show fourths as iustrated beow. 2 ₃ ¹ ₄ 34 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 34 8/27/12 7:38 PM

35 Students wi be instructed to modify their drawings so that each third is divided into quarters and each quarter is divided into thirds as iustrated beow. ⁸ ₁₂ ³ ₁₂ Through questioning, students attention wi be drawn to the number of equa parts that both rectanges are divided into, and they wi aso see that the new fractions formed are equivaent to the origina addends. Students attention wi be drawn to a mutipication tabe paced on the chak board. With teacher s hep students wi be ed to observe patterns of equivaence on the chart. The students wi be guided to see how they coud use the pattern of equivaence on the mutipication chart to sove addition of fractions with different denominators. The mutipication tabe wi aow students to identify a common mutipe of the denominators. This wi be done by identifying one denominator in a row and the other denominator in a coumn, thereby ocating a number where a pointer woud point if moved downward and across (as indicated beow). Students wi then identify a pair of equivaent fractions that have this common denominator. Ministry of Education Sampe Lessons copyedits-juy.indd 35 8/27/12 7:38 PM

36 mutipication Tabe PLENARY Students wi be engaged in an activity in which a house wi be drawn on cartridge paper and paced on the chakboard. This house wi have some pockets (for exampe doors, windows, roof) where probems invoving addition of fractions with different denominators wi be paced. each group wi be given a card with the soution to one of the probems. as a group, the students wi work the probems in the sots to identify the correct sot in which to pace their soution. 36 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 36 8/27/12 7:38 PM

37 ASSESSMENT Students wi sove the foowing addition probems using either the mutipication tabe or rectanguar grid. Students wi share soutions with cass. a) John has two thirds of a cake; Mary gave him another one fifth of the same size cake. How much cake does John now have? b) Pau s friend ate three eighths of a pizza and Sue ate one third of the same pizza. How much of the pizza was eaten? Ministry of Education Sampe Lessons copyedits-juy.indd 37 8/27/12 7:38 PM

38 LESSON 09 SUBTRACTION OF FRACTIONS WITH UNLIKE DENOMINATORS GRADE LEVEL: Grade 5 DURATION: 1 hour SPECIFIC OBJECTIVES At the end of the esson students shoud be abe to: subtract proper fractions with renaming sove probems which require operations on fractiona numbers PREREQUISITE KNOWLEDGE Students shoud aready a) have knowedge of mutipication of whoe numbers b) have a conceptua understanding of fractions c) be famiiar with equivaent fractions d) have knowedge of comparing and ordering fractions MATERIALS/MANIPULATIVE fraction pieces, fraction charts, bank papers, crayons, and chocoate bar CONTENT OUTLINE Subtracting fractions with different denominators incudes rewriting each fraction with a common (same) denominator. This invoves finding an equivaent fraction with the same denominator to represent the fractions to be subtracted. PROCEDURE Menta/Ora Starters Students wi be arranged in pairs. each pair wi be given a diagram of a proper fraction. at the teacher s instruction, each pair wi move about to find matching equivaent fractions. foowing this activity, the students wi share what they have observed about equivaent fractions. 38 Sampe esson pans - number Sampe Lessons copyedits-juy.indd 38 8/27/12 7:38 PM

39 Main Activity Students in their groups wi be given a fraction kit, containing a whoe, haves, fourths, eighths, twefths. Teacher wi ask the foowing questions: 0 How many fourths make a whoe? 0 How many haves make a whoe? 0 What is another fraction for two quarters? Simiar activity wi be done with the other fractions. Students wi be guided into finding common fractiona pieces to represent both ³/₄ and ¹/₃ to get ⁹/₁₂ and ⁴/₁₂. Students wi show other fractions as equivaent fractions using fractiona pieces. Students, as whoe cass, wi then be given the probem situation beow and wi be guided through the steps of subtracting fractions using the fractiona pieces: Mr. Smith needs to move haf of the ibrary books into the ibrary s new addition. Yesterday he moved ¹/₅ of the books. What fraction of the books does he sti need to move? Using fractiona pieces, the students wi be guided through the foowing task: Students wi be asked to te what they noticed about the denominators of the fractions in 1 1 the probem (. (They are not the same denominator) 2 5) Students wi be asked to identify from their fraction kit, a piece that can represent each fraction Students wi be guided into finding common fractiona pieces to represent both 1/2 and 1/5 to get 5/10 and 2/10 respectivey Therefore, the new question becomes 5/10-2/10 = 3/10 PLENARY Students wi be paced into two groups and asked the foowing questions in competition format. The group to score 10 points first wi be the winning team; 2 points wi be given for suitabe responses. a) Using fraction pieces, what is the difference between ⁵/₆ and ¹/₄? b) What must be done to fractions with unike denominators before we subtract? 1 2 c) Expain how to find equivaent fractions for and. 2 5 Ministry of Education Sampe Lessons copyedits-juy.indd 39 8/27/12 7:38 PM

40 ASSESSMENT Students wi be asked to use the appropriate fraction pieces to assist them in determining the difference for the foowing fractions: 1. a) b) minus = minus = c) minus = a) Without using the fraction pieces, what is the difference between and 6 2? 15 4 b) Is ess than, equa to, or greater than 1? Find the difference for the foowing: 3 1 a) b) c) Nataie studied hour for a mathematics test whie Janet studied 4 6 hour. Who studied onger? How much onger? 40 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 40 8/27/12 7:38 PM

41 LESSON 10 MULTIPLICATION OF DECIMALS BY A WHOLE NUMBER GRADE LEVEL: Grade 5 DURATION: 1 hour SPECIFIC OBJECTIVES At the end of this esson, students shoud be abe to: find the product of a whoe number and a decima number with no more than 3 decima paces PREREQUISITE KNOWLEDGE Students shoud aready know: a) pace vaue up to thousandths b) mutipication of whoe numbers c) addition of decima numbers d) how to represent decimas using hundred grid MATERIALS/MANIPULATIVES Base ten modes: tenths, hundredths and thousandths grid, crayons, cacuators CONTENT OUTLINE mutipication is an operation that invoves combining equa sized groups. PROCEDURE Menta/Ora Starters Teacher wi draw a 2 1 mutipication tempate on the board for students to copy. Teacher wi ro a die three times. after each ro students wi decide in which box they wi pace the number roed in order to obtain the smaest (or argest) product possibe. ministry of education Sampe Lessons copyedits-juy.indd 41 8/27/12 7:38 PM

42 Main Activity Students wi work in pairs to shade given decima numbers (ess than 1) on grid paper. Exampe: Shade grid paper to show 0.20 Students use another coour to shade 0.20 a second time. Students wi continue to work in pairs to show the vaue of 2, 3 or 4 groups of Students wi write mathematica sentences to represent operation done. Given a bank grid, students wi be asked to shade 0.25 of the grid; they wi aso be asked to shade another 0.25 using another coour. To ensure that students understand the use of the grid in mutipying decimas by whoe numbers, teacher wi ask the foowing questions: o How many squares in a are shaded? o How coud this be found using addition? o How coud this be found using mutipication? o What woud be 3 x 0.25? Students wi be paced in groups of five. each group wi be given a different mutipication probem to mode on arge etter sized grids: a) b) c) d) e) f) Sampe esson pans - number Sampe Lessons copyedits-juy.indd 42 8/27/12 7:38 PM

43 PLENARY each group wi mount its soution on the wa for a cass discussion. possibe questions for discussion are: What chaenges did you encounter? Why were two grids used? Can you think of questions that woud require three grids? ASSESSMENT assessment wi be continuous throughout the esson using the foowing checkist: Checkist Areas Yes No Comments Were students abe to shade the grid correcty? Were students abe to mode mutipication questions on the grid? Were students abe to identify mutipication probems represented on a grid? Were students abe to use two grids when necessary? Were students abe to identify soutions using the grid? ministry of education Sampe Lessons copyedits-juy.indd 43 8/27/12 7:38 PM

44 LESSON 11 MULTIPLICATION OF DECIMALS BY POWERS OF TEN GRADE LEVEL: Grade 5 DURATION: 1 hour SPECIFIC OBJECTIVES At the end of this esson students shoud be abe: to mutipy a decima number by 10, 100, 1000 PREREQUISITE KNOWLEDGE Students shoud aready know how to: a) represent pace vaue up to thousandths b) mutipy whoe numbers by 10, 100,1000 c) mode decimas on grid paper MATERIALS/MANIPULATIVES Cacuators, dice and pace vaue chart CONTENT OUTLINE When a number is mutipied by ten, each digit in the answer becomes ten times arger, and therefore its position shifts one pace to the eft on the pace vaue chart. Simiar concusions can be drawn about mutipying by 100 and PROCEDURE Menta/Ora Starters Students wi be engaged in a game entited circes and stars. In this game, students wi work in pairs and wi use two dice of different coours to mutipy numbers. one coour wi represent the number of circes to be drawn and the other coour wi represent the number of stars to be drawn in each circe. each pair wi pay five rounds. The pair of students whose products give the arger sum after three rounds is the winner. Main Activity Students wi be asked to use their cacuators to evauate the foowing: o o o Sampe esson pans - number Sampe Lessons copyedits-juy.indd 44 8/27/12 7:38 PM

45 They wi then record their answers in the tabe beow. Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Mutipy by Discuss the foowing questions: What happens to the digits in the number 478 when you mutipy by: 10? 100? 1000? Teacher wi ensure that students understand that when a number is mutipied by ten, each digit in the answer becomes ten times arger, and therefore its position shifts one pace to the eft on the pace vaue chart. Simiar concusions can be drawn about mutipying by 100 and Students wi be asked to use their cacuators to evauate the foowing: They wi then record their answers in the tabe beow. Thousands Hundreds Tens Ones Decima Point Tenths Hundredths Mutipy by Ministry of Education Sampe Lessons copyedits-juy.indd 45 8/27/12 7:38 PM

46 The cass wi have a discussion to hep the students reaise: a) that, ike before, the digits in the answer move to the eft as they become arger by powers of ten b) that each time the number becomes ten times arger, a zero is paced at the end Students wi be asked to compete the foowing without using the cacuator: Thousands Hundreds Tens Ones Decima Point Tenths Hundredths Mutipy by , Students wi be asked to compete the foowing number sentences: a) = b) ,000 = c) = PLENARY Students wi be asked to make a journa entry on how to mutipy decima numbers by powers of ten. ASSESSMENT Compete the foowing mutipication sentences: a) = b) 0.03 = 30 c) ,000 = d) 100 = Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 46 8/27/12 7:38 PM

47 LESSON 12 MULTIPLICATION OF FRACTIONS BY A FRACTION GRADE LEVEL: Grade 5 DURATION: 1 hour SPECIFIC OBJECTIVES At the end of the esson, students shoud be abe to: find the product of two fractiona numbers ess than 1 sove probems which require operations on fractiona numbers PREREQUISITE KNOWLEDGE Students shoud aready: a) have a conceptua understanding of fractions b) know the process of deriving equivaent fractions c) be abe to add and subtract fractions MATERIALS/MANIPULATIVES fraction pieces, fraction cards, bank transparencies CONTENT OUTLINE mutipying a number by a fraction invoves dividing a number into equa pieces and taking out a specified number of equa pieces. mutipying a number by ¾, for exampe, requires that the number be divided into 4 equa pieces and 3 of these parts be taken out for consideration. Menta/Ora Starters Students wi pay the I Have, Who Has game. Cards wi be distributed as students are engaged in answering and asking questions. Exampe: I have 1 Who has 1 2? I have ½ Who has 3 4? I have ¾ Who has 5 9? I have ⁵ ₉ Who has 2 7? I have ²/₇ Who has 4 5? I have ⁴/₅ Who has 7 11? I have ⁷/₁₁ Who has 5 2? I have ⁵/₂ Who has 10 3? I have ¹⁰/₃ Who has 3 8? I have ³/₈ Who has 11 10? I have ¹¹/₁₀ Who has 6 20? I have ⁶/₂₀ Who has 9 9? ministry of education Sampe Lessons copyedits-juy.indd 47 8/27/12 7:38 PM

48 Teacher wi cut card aong the ines. Each card wi be foded and paced in a bag/box. Each student wi randomy seect one piece. Any student can start the game by asking the question on their card. The person with the correct answer wi respond by saying, I have, who has? (Students shoud say the fraction name, for exampe, "a haf", and NOT "one over two".) The game ends when it reaches the student who started the game. Note: The game may be extended to any number of cards desired. Main Activity Students wi be given the probem task beow to write number sentence. Probem Task: In Andrea s garden, ³/₈ is panted with fowers, and ²/₃ of that fower section has red roses. What fraction of the entire garden is panted with red roses? Students wi be guided by teacher in using an area mode to sove the probem 3 2 X 8 3 Students wi be paced in groups of five to shade a rectange (or square), partitioned verticay, to represent ³/₈ (shown in red) and each group wi be given another rectange (or square), partitioned horizontay, to represent ²/₃ (shown beow in bue on transparency). Students wi be guided into superimposing the two squares to show the product of the 2 fractions to be ⁶/₂₄ or ¹/4. N.B. Teacher wi ask students appropriate questions to hep them to recognize that the area that is doube-shaded represents the product 48 Sampe Lesson Pans - number Sampe Lessons copyedits-juy.indd 48 8/27/12 7:38 PM