Practice 7 (CWB p. 12) numbers in their computation. In this example, students learn to estimate the sum of two numbers by rounding Class practice (For Print-based Program): the numbers to the nearest hundred. Task 1 requires students to round a whole number to –– Write ‘Estimate the value of 523 + 608’ on the nearest hundred with the help of a number line. the board. Remediation –– Tell students that when we want to estimate the Task 1(a): Draw the number line on the board and value of a sum, we are finding the approximate guide students to mark the position of 8390 on the value of the sum. To find the approximate value number line. Guide students to conclude that 8390 is of 523 + 608, we can round 523 and 608 to the nearer to 8400 than to 8300, so 8390 is approximately nearest hundred. 8400 when rounded to the nearest hundred. –– Have two students to each round 523 and 608 Task 1(b): Draw the number line on the board and to the nearest hundred. They should be able to guide students to mark the position of 79 023 on the round 523 to 500 and 608 to 600. number line. Guide students to conclude that 79 023 is nearer to 79 000 than to 79 100, so 79 023 is approximately –– Write ‘523 + 608 ≈ 500 + 600’ on the board. 79 000 when rounded to the nearest hundred. Highlight to students the use of the approximate sign to indicate that we are finding the Teaching tips estimated value, and not the exact value of Task 1 the sum of 523 and 608. ¾¾ Highlight to students that when a number is –– Have a student find the sum of 500 and 600 halfway between two hundreds, we take the and conclude that the estimated value of greater hundred as the nearest hundred to 523 + 608 is about 1100. the number. –– Write ‘523 + 608 ≈ 500 + 600 = 1100’ on the Independent practice (For Print-based Program): board. Highlight to students the use of the equal sign to indicate that we are finding the Task 2 requires students to round a whole number to exact value of the sum of 500 and 600. the nearest hundred. –– Guide students to understand that the For answers, go to CW Manual p. 159. estimated value of the sum of 523 and 608 is given by the exact value of the sum of the two Blended Learning Program rounded numbers, 500 and 600. Scholastic (b) Stage: Abstract Representation In this example, students learn to estimate the difference between two numbers by rounding the numbers to the nearest hundred. From PR1ME Mathematics Interactive Edition: –– Write ‘Estimate the value of 855 − 297’ on the Let’s Learn (CB pp. 27–28) board. Go through the teaching examples with students for concept development. Use the detailed lesson plan –– To find the approximate value of 855 − 297, we given in the corresponding lesson notes to carry out can round 855 and 297 to the nearest hundred. the teaching. –– Have two students to each round 855 and 297 Learn to the nearest hundred. They should be able to Estimating sums and differences (CWB p. 13) round 855 to 900 and 297 to 300. Learning Outcome: –– Write ‘855 − 297 ≈ 900 − 300’ on the board. •• Estimate an answer in addition or subtraction Highlight to students the use of the approximate sign to indicate that we are finding the Materials: estimated value, and not the exact value of •• 1 copy of Think About It Worksheet (WS1.4) per the difference between 855 and 297. group –– Have a student find the difference between Vocabulary: 900 and 300 and conclude that the estimated •• estimate value of 855 − 297 is about 600. (a) –– Write ‘855 − 297 ≈ 900 − 300 = 600’ on the board. Stage: Abstract Representation Highlight to students the use of the equal sign In this section, students apply their knowledge of to indicate that we are finding the exact value rounding numbers to learn to estimate sums and of the difference between 900 and 300. differences. Estimating sums and differences enables students to check the reasonableness of their answers –– Guide students to understand that the estimated quickly. This is useful when students work with large value of the difference between 855 and 297 is given by the exact value of the difference between the two rounded numbers, 900 and 300. 14 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
Blended Learning Program ThinkAbout It From PR1ME Mathematics Interactive Edition: Blended Learning Program Let’s Do (CB p. 28) Assign the tasks to students as classwork for From PR1ME Mathematics Interactive Edition: formative assessment. Use the corresponding lesson Think About It (CB p. 28) notes to identify the objectives of each task and Assign the task to students as classwork. Have them address remediation needs. complete the task in groups. Facilitate discussions using the corresponding lesson notes. Exercise 8 (PB p. 18) Assign the tasks to students as classwork for further Have students get into groups. Distribute a copy of formative assessment. Use the corresponding lesson Think About It Worksheet (WS1.4) to each group. Have notes to identify the objectives of each task and them discuss the question presented. Ask a student address remediation needs. from each group to present their answers before proceeding with the questions below. From PR1ME Mathematics Coursework Book: Coursework Book Practice 8 (CWB p. 13) –– What are the children supposed to find? Assign all tasks to students as homework. Use the (Estimated value of 341 + 2138) following notes to identify the skills needed for each task and address remediation needs. –– How can we round 341 and 2138? (Round it to the nearest ten or to the nearest hundred) Practice 8 (CWB p. 13) –– How did Yen round the numbers? (She rounded Class practice (For Print-based Program): the numbers to the nearest hundred) Task 1 requires students to round each number in each –– How did Sam round the numbers? (He rounded set of numbers to the nearest hundred before adding the numbers to the nearest ten) or subtracting to find the estimated value. Explain that when a question asks for the estimated Remediation sum or difference, students can choose to round Task 1(a): Guide students to round 118 and 621 to the the numbers to their preferred place value if it is not nearest hundred before adding the rounded numbers specified in the question. Have students work out the to get the estimated sum of 118 and 621. exact value of the sum, and see that both methods give them an estimate that is close to the exact value. Conclude that both children are correct. Scholastic Task 1(b): Guide students to round 485 and 103 to Blended Learning Program the nearest hundred before subtracting the rounded numbers to get the estimated difference between From PR1ME Mathematics Interactive Edition: 485 and 103. Let’s Learn (CB p. 29) Go through the teaching examples with students for Teaching tips concept development. Use the detailed lesson plan Task 1 given in the corresponding lesson notes to carry out the teaching. ¾¾ Highlight to students that the question requires them to round each number to the Learn nearest hundred. If there is no specification Using estimation to check sums and differences in the question, it is not incorrect to round (CWB p. 14) the numbers to the nearest ten to find an estimated value of the sum or difference Learning Outcome: though it is easier to calculate using numbers •• Check reasonableness of an answer in addition that are rounded to the nearest hundred. or subtraction Independent practice (For Print-based Program): Vocabulary: •• reasonable Task 2 requires students to round each number in each set of numbers to the nearest hundred before adding Stage: Abstract Representation or subtracting to find the estimated value. In this section, students will learn the usefulness of estimation in checking the reasonableness of their For answers, go to CW Manual p. 159. answers when working on addition and subtraction involving large numbers. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 15
–– Have students find the sum of 339 and 574. Independent practice (For Print-based Program): Then write ‘339 + 574 = 913’ on the board. Task 2 requires students to find the sum or difference –– Next, guide students to check if the answer is between two numbers, then check the reasonableness reasonable by using estimation. of the answer by using estimation. –– Have two students to each round 339 and 574 For answers, go to CW Manual p. 159. to the nearest hundred. They should be able to round 339 to 300 and 574 to 600. Blended Learning Program –– Write ‘339 + 574 ≈ 300 + 600’ on the board. From PR1ME Mathematics Interactive Edition: Reiterate to students that we use the Practice 2 (CB p. 29) approximate sign to indicate that we are Assign the tasks to students as classwork for finding the estimated value, and not the exact summative assessment. Use the corresponding lesson value of the sum of 339 and 574. notes to identify the objectives of each task and address remediation needs. –– Have a student find the sum of 300 and 600 and conclude that the estimated value of Lesson 3: Factors 339 + 574 is about 900. Duration: 3 h –– Write ‘339 + 574 ≈ 300 + 600 = 900’ on the board. Reiterate to students that we use the equal sign to indicate that we are finding the exact value of the sum of 300 and 600. –– Guide students to see that 913 is about 900, and since the actual sum is close to the estimated value of the sum, the answer of 913 is reasonable. Blended Learning ProgramScholastic Blended Learning Program From PR1ME Mathematics Interactive Edition: From PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 29) Let’s Learn (CB pp. 30–31) Assign the tasks to students as classwork for Go through the teaching examples with students for formative assessment. Use the corresponding lesson concept development. Use the detailed lesson plan notes to identify the objectives of each task and given in the corresponding lesson notes to carry out address remediation needs. the teaching. Exercise 9 (PB p. 19) Learn Assign the tasks to students as classwork for further formative assessment. Use the corresponding lesson Finding factors of a whole number (CWB p. 15) notes to identify the objectives of each task and address remediation needs. Learning Outcome: •• List all factors of a whole number up to 100 From PR1ME Mathematics Coursework Book: Coursework Book Practice 9 (CWB p. 14) Vocabulary: Assign all tasks to students as homework. Use the •• factor following notes to identify the skills needed for each task and address remediation needs. (a) Stage: Pictorial Representation Practice 9 (CWB p. 14) Students are introduced to the term ‘factors’ for the first time although these are not entirely new concepts Class practice (For Print-based Program): to them. They will learn to understand factors as numbers that are multiplied to get a product. In this Task 1 requires students to find the sum or difference stage, pictures are used to guide students in writing between two numbers, then check the reasonableness multiplication sentences that will help them find the of the answer by using estimation. factors of a product. Remediation –– Have students look at the picture of the row of Task 1: Guide students to round each number to the flowers on CWB p. 15. Have them identify that nearest hundred before adding or subtracting the there is 1 row and 10 columns of flowers. rounded numbers to get the estimated value. –– Guide students to write a multiplication Teaching tips sentence to find the total number of flowers in Task 1 the set. Then write ‘1 × 10 = 10’ on the board. ¾¾ Highlight to students that it is not incorrect to –– Next, have students look at the picture of the round the numbers to the nearest ten to find two rows of flowers on the page. Similarly, an estimated value of the sum or difference have them identify that there are 2 rows and though it is easier to calculate using numbers 5 columns of flowers. that are rounded to the nearest hundred. 16 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
–– Guide students to write another multiplication Scholastic From PR1ME Mathematics Coursework Book: sentence to find the total number of flowers in Coursework Book Practice 10 (CWB p. 16) the set. Then write ‘2 × 5 = 10’ on the board. Assign all tasks to students as homework. Use the following notes to identify the skills needed for each Stage: Abstract Representation task and address remediation needs. In this stage, students are introduced to the definition of the term ‘factors’. Through the multiplication Practice 10 (CWB p. 16) sentences that they derived from the pictures of flowers earlier, students will learn that factors are Class practice (For Print-based Program): numbers that are multiplied to get the product. Task 1 requires students to list all the factors of a whole –– Guide students to see that the numbers that number up to 100. are multiplied in a multiplication sentence are called factors and the result of the Remediation multiplication is called the product. Hence, 1 Task 1: Guide students to identify the number of rows and 10 are factors of 10, and 10 is the product and columns of corn in each picture and write the of 1 and 10. Similarly, 2 and 5 are also factors of multiplication sentences to find the number of corn in 10, and 10 is also the product of 2 and 5. the each sets. (b) Teaching tips Stage: Pictorial Representation Task 1 In this stage, pictures are used to guide students to write a multiplication sentence that will help them learn ¾¾ Reiterate to students that factors are numbers that a product can have more than two factors. that are multiplied to get a product. –– Have students look at the picture of the leaves Independent practice (For Print-based Program): on CWB p. 15. Have them identify that there are 3 sets of leaves and there are 4 rows and Task 2 requires students to write the missing factor of a 5 columns of leaves in each set. number up to 100. –– Guide students to write a multiplication sentence Task 3 requires students to list all the factors of a whole to find the total number of leaves in the 3 sets. number up to 100. Then, write ‘3 × 4 × 5 = 60’ on the board. For answers, go to CW Manual p. 159. Stage: Abstract Representation Through the multiplication sentence that they derived Blended Learning Program from the picture of leaves earlier, students will learn that a product can have more than two factors. From PR1ME Mathematics Interactive Edition: Let’s Learn (CB p. 32) –– Guide students to conclude from the Go through the teaching examples with students for multiplication sentence that 60 is the product concept development. Use the detailed lesson plan of 3, 4 and 5. given in the corresponding lesson notes to carry out the teaching. –– Reiterate to students that numbers that multiply to form a product are called factors. Hence, 3, 4 and 5 are factors of 60. –– Get students to conclude that a number can have more than two factors. Blended Learning Program Learn Finding out if a number is a factor of another From PR1ME Mathematics Interactive Edition: number (CWB pp. 16–17) Let’s Do (CB pp. 31–32) Assign the tasks to students as classwork for Learning Outcome: formative assessment. Use the corresponding lesson •• Find out if a 1-digit number is a factor of a notes to identify the objectives of each task and given whole number address remediation needs. (a) Exercise 10 (PB pp. 20–21) Stage: Abstract Representation Assign the tasks to students as classwork for further In this section, students will learn that a factor is a formative assessment. Use the corresponding lesson number that divides another number exactly without notes to identify the objectives of each task and any remainder. In this example, students are to divide address remediation needs. a number by its factor. –– Write ‘Is 5 a factor of 30?’ on the board. –– Reiterate to students that numbers that multiply to form a product are the factors of the © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 17
number. Thus, a product can be divided by its ScholasticLearn factor exactly and there will be no remainder. –– Have a student divide 30 by 5 in the vertical Prime and composite numbers (CWB p. 18) form on the board. Conclude that 30 can be divided by 5 exactly. So, 5 is a factor of 30. Learning Outcomes: •• Differentiate prime numbers from composite (b) numbers Stage: Abstract Representation In this example, students are to divide a number by Vocabulary: another number that is not a factor. •• composite number •• prime number –– Write ‘Is 5 a factor of 53?’ on the board. –– Have a student divide 53 by 5 in the vertical (a) Stages: Pictorial representation and Abstract form on the board. Conclude that 53 cannot Representation be divided by 5 exactly and there is a In this example, students are introduced to prime remainder of 3. So, 5 is a not factor of 53. numbers. Have students recall that the numbers that are multiplied in a multiplication sentence are called Blended Learning Program factors. Representing the factors of a number in a pictorial form allows students to visualize the two From PR1ME Mathematics Interactive Edition: factors of a prime number; 1 and itself. Students then Let’s Do (CB p. 32) learn the definition of a prime number. Assign the tasks to students as classwork for formative assessment. Use the corresponding lesson –– Have students look at the picture in (a) on notes to identify the objectives of each task and CWB p. 18. address remediation needs. –– Get students to notice that there is 1 row of Exercise 11 (PB p. 22) 7 counters. Explain that we can represent this Assign the tasks to students as classwork for further by using the multiplication sentence 1 × 7 = 7. formative assessment. Use the corresponding lesson notes to identify the objectives of each task and –– Write ‘1 × 7 = 7’ on the board. address remediation needs. –– Guide students to see that 7 does not have any From PR1ME Mathematics Coursework Book: other factors. Coursework Book Practice 11 (CWB p. 17) –– Point out that a prime number is a number that Assign all tasks to students as homework. Use the following notes to identify the skills needed for each has only two factors, 1 and the number itself. task and address remediation needs. Explain that since the number 7 has only two factors, 1 and 7, we can say that 7 is a prime Practice 11 (CWB p. 17) number. Class practice (For Print-based Program): (b) Stages: Pictorial representation and Abstract Task 1 requires students to find out if a 1-digit number is Representation a factor of a given whole number. In this example, students are introduced to composite numbers. The arrangements of counters to represent Remediation the two sets of factors for a composite number helps Task 1: Guide students to divide the numbers in the students visualize that a composite number has more vertical form and check if they can be divided exactly. than 2 factors. Students then learn the definition of a composite number and compare the difference Teaching tips between a composite number and a prime number. Task 1 –– Have students look at the picture in (b) on ¾¾ Reiterate to students that a factor is a number CWB p. 18. that divides another number exactly without any remainder. –– Get students to notice the number of counters in each set. Independent practice (For Print-based Program): –– Guide students to write the multiplication Task 2 requires students to find out if a 1-digit number is sentence representing the counters on the left. a factor of a given whole number. –– Write ‘1 × 6 = 6’ on the board. For answers, go to CW Manual p. 160. –– Guide students to write the multiplication sentence representing the counters on the right and write ‘2 × 3 = 6’ on the board. –– Have students list the factors of 6 and have them notice that the number 6 has more than two factors. Point out that a number that has more than two factors is a composite number. So, the number 6 is a composite number. –– Ask students whether the number 1 is a prime or a composite number. 18 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
–– Guide students to see that the number 1 is –– Write on the board the following: neither a prime nor a composite number since 12 = 2 × 6 12 = 3 × 4 it has only one factor, itself. =2×2×3 =3×2×2 –– Reiterate that to determine whether a number is a prime number or a composite number, –– Explain to students that when we write a students will first need to list the factors of composite number as a product of its prime that number. If the only factors are 1 and factors, it is called prime factorization. the number itself, then the number is a prime number. However, if the number has more than (b) two factors, then the number is a composite Stage: Abstract Representation number. In this example, students learn to perform prime factorization using a factor tree and continuous Practice 12 (CWB p. 18) division. Class practice (For Print-based Program): Scholastic Method 1: Using a factor tree –– Explain to students that when using a factor Task 1 requires students to identify the prime and tree to carry out prime factorization, we need composite numbers. to express the number as a product of its smallest prime factor and another number. Remediation –– Have students look at Method 1 on CWB p. 19. Task 1: Have students list the factors of each number. –– Guide students to see that 2 is the smallest Then have students recall the definition of a prime prime factor of 36. Have them see that the number and a composite number. Guide students product of 18 and 2 gives 36. to see if the number has more than two factors, it is a –– Demonstrate how to write the first two rows of composite number. If it has only two factors, which are the factor tree of 36 on the board. 1 and itself, then it is a prime number. –– Write on the board the following: Independent practice (For Print-based Program): 36 Task 2 requires students to list the first six prime numbers. 2 × 18 For answers, go to CW Manual p. 160. –– Get students to see that since 18 is not a prime number, we then have to find the smallest Learn possible prime factor of 18. Prime factorization (CWB pp. 19–20) –– Guide students to see that 2 is the smallest Learning Outcome: prime factor of 18 and that the product of •• Use prime factorization to write a given number 2 and 9 gives 18. as a product of its prime factors –– Continue on the factor tree by writing the Vocabulary: following on the board: •• prime factorization 36 (a) Stage: Abstract Representation 2 × 18 Students are introduced to the concept of prime factorization. They build upon the knowledge of prime 2 ×2×9 numbers and factors to express a composite number as a product of its prime factors. –– Get students to see that since 9 is not a prime number, we then have to find the smallest –– Guide students to express 12 as a product of its prime factor of 9. factors in 3 different multiplication sentences. –– Guide them to see that 3 is the smallest prime –– Write ‘12 = 1 × 12’, ‘12 = 2 × 6’ and ‘12 = 3 × 4’ factor of 9 and that the product of 3 and 3 on the board. gives 9. –– Highlight to students that since 12 has more –– Complete the factor tree on the board: than two factors, it is a composite number. 36 –– Point out to students that two of the factors are 2 and 3, which are prime numbers. 2 × 18 –– Guide students to write 12 as a product of its 2 ×2×9 prime factors, 2 and 3. 2 ×2×3×3 –– Referring to the factor tree on the board, explain to students that we can obtain the prime factorization by looking at the last row of the completed factor tree. –– Write on the board ‘36 = 2 × 2 × 3 × 3’. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 19
Method 2: Using continuous division Scholastic Blended Learning Program –– Explain that when using continuous division to From PR1ME Mathematics Interactive Edition: carry out prime factorization, we need to first Practice 3 (CB p. 33) divide the number by its smallest prime factor. Assign the tasks to students as classwork for summative assessment. Use the corresponding lesson –– Have students look at Method 2 on CWB p. 20. notes to identify the objectives of each task and –– Guide students to see that 2 is the smallest address remediation needs. prime factor of 36. Lesson 4: Multiples –– Write on the board ‘2 36’. –– Ask what 36 divided by 2 is and have students Duration: 3 h provide the response. Blended Learning Program –– Write ‘18’ below ‘36’ on the board. –– Tell students that we will divide 18 by its smallest From PR1ME Mathematics Interactive Edition: Let’s Learn (CB p. 34) prime factor. Ask students what the smallest Go through the teaching example with students for prime factor of 18 is and get them to divide concept development. Use the detailed lesson plan 18 by 2. given in the corresponding lesson notes to carry out –– Write ‘2’ to the left of ‘18’ on the board as the teaching. shown on the page. Guide students to see that 18 divided by 2 is 9. Learn –– Write ‘9’ below ‘18’. Finding multiples of a whole number (CWB p. 21) –– Ask students what the smallest prime factor of 9 is and lead them to divide 9 by 3. Learning Outcome: –– Write ‘3’ to the left of ‘9’ on the board as shown •• List the multiples of a whole number up to 10 on the page. Guide students to see that 9 divided by 3 is 3. Vocabulary: –– Write ‘3’ below ‘9’ on the board. •• multiple –– Ask students what the smallest prime factor of 3 is and lead them to divide 3 by 3. Stage: Pictorial Representation –– Write ‘3’ to the left of ‘3’ on the board as shown Students are introduced to the term ‘multiples’ for the on the page. Guide students to see that 3 first time although it is not an entirely new concept to divided by 3 is 1. them. They will learn to understand that a multiple of a –– Explain to students that we stop the division number is the product of that number and another number. when we get 1 as the quotient. –– Point out to students that we can obtain the –– Have students look at the picture of the first dot prime factorization by looking at the prime card from the left on CWB p. 21. Have them factors on the left hand side of the continuous identify that there is 1 row and 4 columns of dots. division. –– Write on the board ‘36 = 2 × 2 × 3 × 3’. –– Guide students to write a multiplication sentence to find the total number of dots. Practice 13 (CWB p. 20) Then, write ‘1 × 4 = 4’ on the board. Class practice (For Print-based Program): –– Next, have students look at the pictures of the rest of the dot cards on the page. Similarly, Task 1 provides practice in carrying out the prime have them identify that there are 2 rows and factorization of numbers using a factor tree and then 4 columns of dots in the second dot card, 3 rows checking the answers using continuous division. and 4 columns of dots in the third dot card, and 4 rows and 4 columns of dots in the last dot card. Remediation Task 1: First, have students find the smallest prime –– Guide students to write the other multiplication factor of each number. Next, guide them to divide the sentences to find the number of dots on each number by the smallest prime factor. Then, have them dot card. Then, write ‘2 × 4 = 8’, ‘3 × 4 = 12’ and write the two factors in the factor tree or the quotient ‘4 × 4 = 16’ on the board. in the continuous division form. Then, have them find the next smallest prime factor of the quotient you get Stage: Abstract Representation after the division. In this stage, students are introduced to the definition of the term ‘multiples’. Through the multiplication Independent practice (For Print-based Program): sentences that they derived from the pictures of the dot cards earlier, students will learn that a multiple of a Task 2 requires students to carry out the prime number is the product of that number and another number. factorization of numbers using a factor tree or continuous division. For answers, go to CW Manual p. 160. 20 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
–– Have students look at the four multiplication Independent practice (For Print-based Program): sentences and guide them to see that these are multiplication facts of 4. Task 2 requires students to write the next five multiples given the first two multiples. –– Guide students to understand that the product of each of these multiplication sentences, 4, 8, For answers, go to CW Manual p. 160. 12 and 16 are called the multiples of 4. Blended Learning Program –– Point out to students that a multiple of a number is the product of that number and From PR1ME Mathematics Interactive Edition: another number. Let’s Learn (CB p. 35) Go through the teaching examples with students for –– Guide students to identify that each of these concept development. Use the detailed lesson plan multiplication sentence has 4 as a factor, and given in the corresponding lesson notes to carry out highlight that a number is a factor of all its the teaching. multiples. Hence, 4 is a factor of the multiples 4, 8, 12 and 16 in this example. –– Reinforce students’ understanding of multiples by getting them to find the next six multiples of 4. Blended Learning Program Scholastic Learn From PR1ME Mathematics Interactive Edition: Relating factors and multiples (CWB p. 22) Let’s Do (CB p. 34) Assign the tasks to students as classwork for Learning Outcomes: formative assessment. Use the corresponding lesson •• Relate factors and multiples notes to identify the objectives of each task and •• Find out if a whole number is a multiple of a address remediation needs. given whole number up to 10 Exercise 12 (PB p. 23) (a) Assign the tasks to students as classwork for further Stage: Abstract Representation formative assessment. Use the corresponding lesson In this section, students learn about the relationship notes to identify the objectives of each task and between factors and multiples. They will learn that the address remediation needs. multiple of a number has the number as a factor. In this example, students are to divide a number by its factor. From PR1ME Mathematics Coursework Book: Coursework Book Practice 14 (CWB pp. 21–22) –– Lead students to understand that we can use Assign all tasks to students as homework. Use the division to find out if a number is a multiple of following notes to identify the skills needed for each another given number. task and address remediation needs. –– Have a student divide 18 by 2 in the vertical Practice 14 (CWB pp. 21–22) form on the board. Conclude that 18 can be divided by 2 exactly. Hence, 18 is a multiple of Class practice (For Print-based Program): 2, and 2 is a factor of 18. Task 1 requires students to write the first four multiples of –– Reiterate to students that multiples of 2 can be 8 with the help of pictures. divided by 2 exactly and multiples of 2 have 2 as a factor. Remediation Task 1: Guide students to identify the number of balloons (b) in the sets and write the multiplication sentences Stage: Abstract Representation ‘1 × 8 = 8’, ‘2 × 8 = 16’, ‘3 × 8 = 24’ and ‘4 × 8 = 32’. In this example, students are to divide a number by Reiterate to students that a multiple of a number is the another number that is not a factor. product of that number and another number, so the first four multiples of 8 are 8, 16, 24 and 32. –– Have a student divide 45 by 2 in the vertical form on the board. Conclude that 45 cannot Teaching tips be divided by 2 exactly. Hence, 45 is not a Task 1 multiple of 2, and 2 is not a factor of 45. ¾¾ Have students recite the multiplication table From these two examples, lead students to see how of 8 to find the first four multiples of 8. factors and multiples are related. If a number can be divided exactly by a second number, this means that the first number is a multiple of the second number. This also shows that the second number is a factor of the first number. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 21
Blended Learning Program –– Guide students to see that the numbers in this column are both multiples of 2 and multiples of 5. From PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 35) –– Have students also see that the numbers in this Assign the tasks to students as classwork for column can be divided by 10 exactly. Hence, formative assessment. Use the corresponding lesson the numbers are also multiples of 10. notes to identify the objectives of each task and address remediation needs. –– Guide students to notice that the digit in the ones place of the multiples of 10 is 0. Blended Learning Program Blended Learning Program ScholasticFrom PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 37) From PR1ME Mathematics Interactive Edition: Assign the tasks to students as classwork for formative Let’s Learn (CB p. 36) assessment. Use the corresponding lesson notes to Go through the teaching examples with students for identify the objectives of each task and address concept development. Use the detailed lesson plan remediation needs. given in the corresponding lesson notes to carry out the teaching. Exercise 13 (PB p. 24) Assign the tasks to students as classwork for further Learn formative assessment. Use the corresponding lesson notes to identify the objectives of each task and Identifying multiples of 2, 5 and 10 (CWB p. 23) address remediation needs. Learning Outcome: From PR1ME Mathematics Coursework Book: •• Identify multiples of 2, 5 and 10 Coursework Book Practice 15 (CWB p. 24) Assign all tasks to students as homework. Use the Materials: following notes to identify the skills needed for each •• 1 copy of Hundred Chart (BM1.1) task and address remediation needs. (a) Practice 15 (CWB p. 24) Stages: Pictorial Representation and Abstract Representation Class practice (For Print-based Program): In this example, students learn to recognize patterns in numbers that are multiples of 2. Task 1 requires students to find out if the greater number is a multiple of the smaller number and if the –– Enlarge a copy of Hundred Chart (BM1.1) and smaller number is a factor of the greater number. stick it on the board. Have students see that the numbers in the chart are arranged in 10 rows, Remediation with each row having 10 numbers. Task 1(a): Guide students to divide 54 by 9 in the vertical form. Conclude that 54 can be divided by 9 exactly. –– Get students to identify the multiples of 2 and circle Hence, 54 is a multiple of 9 and 9 is a factor of 54. them in black. Remind students that the multiples of 2 are numbers that can be divided by 2 exactly. Task 1(b): Guide students to divide 39 by 9 in the vertical form. Conclude that 39 cannot be divided by 9 exactly. –– Guide students to notice that the digit in the ones Hence, 39 is not a multiple of 9 and 9 is not a factor of 39. place of the multiples of 2 is either 0, 2, 4, 6 or 8. Teaching tips (b) Task 1 Stages: Pictorial Representation and Abstract Representation ¾¾ Have students recite the multiplication table In this example, students learn to recognize patterns in of 9 to list the first ten multiples of 9. numbers that are multiples of 5. Independent practice (For Print-based Program): –– Next, get students to identify the multiples of 5 and cross them out in red. Remind students that Tasks 2 and 3 require students to find out if the greater multiples of 5 are numbers that can be divided number is a multiple of the smaller number and if the by 5 exactly. smaller number is a factor of the greater number. –– Guide students to notice that the digit in the Task 4 requires students to identify which numbers are ones place of the multiples of 5 is either 0 or 5. multiples and which numbers are factors in a multiplication sentence. (c) Stages: Pictorial Representation and Abstract For answers, go to CW Manual p. 160. Representation In this example, students learn to recognize patterns in numbers that are multiples of 10. –– Then, get students to look at the numbers that are both circled in black and crossed out in red in the last column of the chart. 22 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
Lesson 5: Number Patterns Scholastic –– Guide students to see that the pattern consists of multiples of 2. Have students say what the Duration: 1 h multiples of 2 are. Learn –– Lead students to see that the multiple of 2 after 14 is 16. Finding the missing term in a number pattern (CWB p. 25) –– Conclude by saying that we can complete a number pattern that consists of multiples of a Learning Outcome: number. •• Find the missing term(s) in a number pattern Practice 16 (CWB p. 25) (a) Stage: Abstract Representation Class practice (For Print-based Program): In this example, students learn to count on in steps of 2 to complete a number pattern. They will also identify Task 1 requires students to complete a number pattern that the numbers in the pattern are odd numbers and by counting backwards in steps of 2 or by recognizing use this information to find the missing number in the that the numbers are even. number pattern. Remediation –– Write ‘3, 5, 7, 9, _____’ on the board. Task 1: Guide students to understand that the pattern –– Guide students to count on in steps of 2 from 3 is made up of even numbers, and that each number is less than the number before it, hence they have to find to 9 and conclude that each number is 2 more the previous even number to find the missing number in than the previous number. the pattern. –– Highlight to students that since each number is 2 more than the previous number, the rule of Teaching tips the pattern is to add 2. Have students say what Task 1 the missing number in the number pattern is by telling them to apply the rule. ¾¾ Highlight to students that they have to –– Write ‘11’ in the blank. determine whether the pattern is made up –– Next, guide students to see that the numbers in of odd or even numbers. Then, they have the pattern are actually odd numbers. to identify if the numbers are increasing or –– Lead students to see that each odd number in decreasing to determine the rule of the the pattern is 2 more than the number before number pattern. it. Guide students to see that the next odd number after 9 is 11 and conclude that the Independent practice (For Print-based Program): missing number in the number pattern is 11. Task 2 requires students to complete a number pattern (b) by counting on or backwards. Stage: Abstract Representation In this example, student learn to count backwards in Task 3 requires students to find the missing number in a steps of 3 to complete a number pattern. number pattern that is made up of multiples of 5. –– Write ’27, 24, 21, 18, ____’ on the board. For answers, go to CW Manual p. 160. –– Guide students to count backwards in steps of Blended Learning Program 3 from 27 and conclude that each number is 3 less than the previous number. From PR1ME Mathematics Interactive Edition: –– Highlight to students that since each number Practice 4 (CB p. 37) is 3 less than the previous number, the rule Assign the tasks to students as classwork for of the pattern is to subtract 3. Have students summative assessment. Use the corresponding lesson conclude that to find the missing number, they notes to identify the objectives of each task and have to apply the rule. address remediation needs. –– Conclude that the missing number in the number pattern is 3 less than 18 which is 15. (c) ChapterWrap-up Stage: Abstract Representation In this example, students learn to complete a number Reiterate the following points: pattern in which the members are multiples of 2. –– We can find the number which is 1, 10, 100, 1000, or 10 000 more than (or less than) a given –– Write ‘12, 14, _____, 18, 20’ on the board. number. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 23
–– We can use a number line to show the order of numbers. –– On a number line, the numbers are arranged in increasing order from left to right. –– We can compare and order numbers within 100 000. –– We can use a number line to help us round numbers. –– A whole number can be rounded to the nearest ten or hundred. –– Estimating sums and differences helps to check the reasonableness of answers. –– When a factor is multiplied by another factor, a product is formed. –– We can find factors of a number by listing. Example: 1 × 6 = 6 2×3=6 The factors of 6 are 1, 2, 3 and 6. –– A number is the factor of a second number if the second number can be divided by the number exactly. –– Prime numbers are numbers that have only two factors, 1 and the number itself. –– Composite numbers are numbers that have more than two factors. Scholastic –– When we write a number as a product of its prime factors, it is called prime factorization. –– A multiple of a number is the product of that number and another number. –– We can find multiples of a number by listing. –– Example: 1 × 5 = 5 2 × 5 = 10 3 × 5 = 15 4 × 5 = 20 The first four multiples of 5 are 5, 10, 15, 20. –– If a number can be divided exactly by the second number, this means that the first number is a multiple of the second number. This also shows that the second number is a factor of the first number. –– We can complete number patterns by counting on and backwards, and listing the multiples of a number. 24 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6
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