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Multiplication and Division 21_Overview of Learning Plan (Year 5) ACMNA098, NSW MA3-4NA Equivalent division calculations result if both numbers are divided by a common factor. Resources: playing cards, pencils, paper Children: Simplify divide numbers by a common factor to simplify a division division by calculation, for example, dividing each 148 ÷ 8 = number by a 74 ÷ 4 = common 37 ÷ 2 = factor. 1 18 2 Simplify multiplication by multiply and dividing by the same number. Children ask one another questions about simplifying division and multiplication, for example: divide and multiply numbers by the same number to simplify a multiplication calculation, for example, 6x4= 3x8 6x4= 12 x 2 Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach How could we divide 148 by 8? Do 148 and 8 have any common factors? Is 2 a common factor of 148 and 8? Could we divide both number by 2 to simplify the calculation? Could we divide 74 and 4 by 2 to continue to simplify the calculation? What is 37 divided by 2? How could we simplify 6 times 4? Could we double 4 and halve 6? Is 6 times 4 equal to 3 times 8? Could we double 6 and halve 4? Is 6 times 4 equal to 12 times 2? YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 1 Multiplication and Division 21_Explicit Learning Plan (Year 5) ACMNA098, NSW MA3-4NA Explain that equivalent division calculations result if both numbers are divided by a common factor. Create and solve equivalent number sentences involving multiplication and division. Resources: Playing cards, pencil, paper EXPLICIT LEARNING What could we do? What language could we use to explain and ask questions? Children think about, talk and listen to a friend about, then have the Focuses opportunity to share what they already know. children’s thoughts on the concept, exposing current understanding and any misconceptions ► Today brings an investigation about using common factors to divide. ► What do you know about using common factors to divide? ► Talk about using common factors to divide with a friend. ► Is anyone ready to share what they are thinking about using common factors to divide? We’ve investigated factors. Record, for example, factor: a number that can be multiplied to get another number And we found that a factor is a number that can be multiplied to get another number. Record, for example, 4 is a factor of 12 We found that 4 is a factor of 12 because if we multiply 4 by 3, we get 12. So we also know that 3 is a factor of 12. We’ve investigated common factors. Reviews factors Reviews common factors Record, for example, 4 x 3 = 12 Record, for example, 3 is a factor of 12 Record, for example, Highest Common Factors Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 2 And we found that a common factor is a factor of more than one number. We found that 1 and 3 are common factors of 12 and 15. We’ve investigated highest common factors. And we found that the highest common factor is the highest number that is a factor of more than 1 number. We found that 3 is the highest common factor of 12 and 15. Today we’re going to investigate how we can make division more efficient if we divide both numbers by a common factor. Let’s record a division number sentence, 148 divided by 8. We could use the distributive property to divide 148 by 8. But we already understand that! Let’s look at our division number sentence. Could we divide both numbers by a common factor? Let’s investigate! So let’s find a common factor of 148 and 8. Both 148 and 8 are even numbers. Record, for example, Factors of 12 = 1, 12, 2, 6, 3, 4 Reviews highest common factors Factors of 15 = 1, 15, 3, 5 Common factors of 12 and 15: 1, 3 Introduces making Record, for example, highest common factor of 12 and 15 = 3 division more efficient by dividing both numbers by a common factor (top) Display a division number sentence, for example, 148 ÷ 8 = Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 3 Divide both numbers by 2, for example, 148 ÷ 8 = 74 ÷ 4 = Divide both numbers by 2, for example, 148 ÷ 8 = 74 ÷ 4 = 37 ÷ 2 = 1 Record, for example, 148 ÷ 8 = 74 ÷ 4 = 37 ÷ 2 = 18 2 Allow children time now to engage in guided and independent investigation of dividing numbers by the common factor 2 to create equivalent division number sentences. Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach So 2 must be a common factor of 148 and 8. Let’s divide both numbers by 2. Have we created an equivalent number sentence? Will 74 divided by 4 be equal to 148 divided by 8? Let’s look at our equivalent division number sentence. Could we divide both 74 and 4 by a common factor? Let’s investigate! So let’s find a common factor of 74 and 4. Both 74 and 4 are even numbers. So 2 must be a common factor of 74 and 4. Let’s divide both numbers by 2. Have we created another equivalent number sentence? Will 37 divided by 2 be equal to 84 divided by 4 and 148 divided by 8? What is 37 divided by 2? Is 37 divided by 2, 18 and a half? Did we divide 148 by 8, by dividing both numbers by common factors? YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 4 Reviews making division more efficient by dividing both numbers by a common factor. Display another division number sentence, for example, 114 ÷ 6 = Record, for example, Factors of 6 = 2, 3 Circle the factors of 6 that are also factors of 114, for example, Factors of 6 = 2, 3 Display the division number sentence, for example, 114 ÷ 6 = Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach Let’s record a division number sentence, 114 divided by 6. We could use the distributive property to divide 114 by 6. But we already understand that! So let’s find the common factors of 114 and 6. Let’s start with the lower number because it will have fewer factors. Besides 1 and 6, what are the factors of 6? Now let’s check if any of the factors of 6 are also factors of 114. Is 2 a factor of 114? Yes, 114 is an even number so 2 is a factor. Is 3 a factor of 114? 114 is 90 plus 24 – so 3 must be a factor of 114 So both 2 and 3 are factors of 114 and 6. Let’s look at our division number sentence. Could we divide both numbers by a common factor? Let’s investigate! Dividing 114 by 3 is not really much easier than dividing 114 by 6. So let’s divide 114 and 6 by 2. What does 114 divided by 2 equal? YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 5 Record, for example, 114 ÷ 6 = 57 ÷ 3 = Record, for example, 114 ÷ 6 = 57 ÷ 3 = 19 Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach Does 114 divided by 2 equal 57? What does 6 divided by 2 equal? Does 6 divided by 2 equal 3? Have we created an equivalent number sentence? Will 57 divided by 3 be equal to 114 divided by 6? Now we could divide 57 by 3 using the distributive property and preferred multiples. Is 3 a factor of 57? Is 57, 30 and 27? Are 30 and 27 multiples of 3? Is 57, 3 less than 60? Is 60 a multiple of 3? What is 57 divided by 3? Is 57 divided by 10 plus 9? Is 57 divided by 3, 20 minus 1? Is 57 divided by 3, 19? YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 6 Introduces making Display another division number sentence, for example, 354 ÷ 6 = division more efficient by dividing both numbers by a common factor. Let’s record a division number sentence, 354 divided by 6. We could use the distributive property to divide 354 by 6. But we already understand that! So let’s find the common factors of 354 and 6. Let’s start with the lower number because it will have fewer factors. Besides 1 and 6, what are the factors of 6? Now let’s check if any of the factors of 6 are also factors of 354. Circle the factors of 6 that are also factors of 354, for example, Is 2 a factor of 354? Factors of 6 = 2, 3 Yes, 354 is an even number so 2 is a factor. Is 3 a factor of 354? 354 is 300 plus 54 – so 3 must be a factor of 354 So both 2 and 3 are factors of 354 and 6. Let’s look at our division number sentence. Could we divide both numbers by a common factor? Let’s investigate! Let’s divide 354 and 6 by 3. What does 354 divided by 3 equal? Is 354 300 plus 30 plus 24? Does 354 divided by 3 equal 100 plus 10 plus 8? Record, for example, Factors of 6 = 2, 3 Display the division number sentence, for example, 354 ÷ 6 = Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 7 Record, for example, 354 ÷ 6 = 118 ÷ 2 = Record, for example, 354 ÷ 6 = 118 ÷ 2 = 59 Does 354 divided by 3 equal 118 What does 6 divided by 3 equal? Does 6 divided by 3 equal 2? Have we created an equivalent number sentence? Will 118 divided by 2 be equal to 354 divided by 6? Now we could divide 118 by 2 by halving. What is half of 118? Is half of 118, 59? Is 118 divided by 2, 59? Is 354 divided by 6, 59? Allow children time now to engage in guided and independent investigation of dividing numbers by a common factor to create equivalent division number sentences. Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 8 Children think about, talk and listen to a friend about, then have the Introduces equivalent number opportunity to share what they already know. sentences involving division using common factors (top) ► Today brings an investigation about using common factors to create equivalent multiplication and division number sentences. ► What do you know about using common factors to create equivalent multiplication and division number sentences? ► Talk about using common factors to create equivalent multiplication and division number sentences with a friend. ► Is anyone ready to share what they are thinking about using common factors to create equivalent multiplication and division number sentences? We’ve investigated factors. Record, for example, factor: a number that can be multiplied to get another number And we found that a factor is a number that can be multiplied to get another number. Record, for example, 4 is a factor of 12 We found that 4 is a factor of 12 because if we multiply 4 by 3, we get 12. So we also know that 3 is a factor of 12. We’ve investigated common factors. And we found that a common factor is a factor of more than one number. We found that 1 and 3 are common factors of 12 and 15. Record, for example, 4 x 3 = 12 Record, for example, 3 is a factor of 12 Record, for example, Highest Common Factors Record, for example, Factors of 12 = 1, 12, 2, 6, 3, 4 Factors of 15 = 1, 15, 3, 5 Common factors of 12 and 15: 1, 3 Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 9 Record, for example, 354 ÷ 6 = 118 ÷ 2 = 59 Record, for example, 46 ÷ 8 = Record, for example, 46 ÷ 8 = 23 ÷ 4 6 3 Record, for example, 46 ÷ 8 = 5 8 = 5 4 3 Record, for example, 23 ÷ 4 = 5 4 Allow children time now to engage in guided and independent investigation of creating equivalent division number sentences by dividing both numbers by a common factor. Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach We’ve investigated division by dividing both numbers by a common factor. We found that 354 divided by 6 is equivalent to 118 divided by 2 because we divided 354 and 6 by 3. Today we’re going to investigate using common factors to create equivalent division number sentences. Let’s create a division number sentence, 46 divided by 8 On the other side of the equals sign, let’s create an equivalent number sentence. Do 46 and 8 have any common factors? Is 2 a common factor of 46 and 8? Let’s divide both numbers by the common factor, 2. Have we created an equivalent number sentence? Does 46 divided by 8 equal 23 divided by 4? What does 46 divided by 8 equal? Does 46 divided by 8 equal 5 and three-quarters? What does 23 divided by 4 equal? Does 23 divided by 4 equal 5 and three-quarters? Which number sentence was easier to solve? Was it easier to solve 23 divided by 4, than 46 divided by 8? When we create equivalent number sentences by dividing both numbers by a common factor, does it create an easier number sentence? YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 10 Record, for example, 46 ÷ 8 = 23 ÷ 4 Introduces equivalent number sentences involving multiplication using the same Record, for example, 6 x 4 = factors Record, for example, 6 x 4 = 3 x 8 Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach We’ve investigated division by dividing both numbers by a common factor. We found that 46 divided by 8 is equivalent to 23 divided by 4 because we divided 46 and 8 by 2. Today we’re going to investigate using the same factor to create equivalent multiplication number sentences. Let’s create a multiplication number sentence, 6 times 4. On the other side of the equals sign, let’s create an equivalent number sentence. If we halve one number and double the other number, will we have an equivalent number sentence? Let’s investigate! What is half of 6? Is half of 6, 3? Have we created an equivalent number sentence? Does 6 times 4 equal 3 times 8? What does 6 times 4 equal? Does 6 times 4 equal 24? What does 3 times 8 equal? Does 3 times 8 equal 24? When we divided one number by 2 and multiplied the other number by 2, did we create an equivalent number sentence? Why? Let’s investigate! YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 11 Record, for example, x 4 = half as much as x 8 When we multiply by 4, do we get a number that is 4 times greater? When we multiply by 8, do we get a number that is 8 times greater? So when we multiply by 4, will we have half as much as when we multiply by 8? And when we multiply by 8, will we have twice as much as when we multiply by 4? If we multiply 6 by 4, will we have half as much as 6 times 8? Does 6 times 4 equal half of 6 times 8? Is half of 6 times 8, 3 times 8? If we multiply 3 times 8, will we have twice as much as 3 times 4? Does 3 times 8 equal twice 3 times 4? Is twice 3 times 4, 6 times 4? Let’s create another multiplication number sentence, 46 times 8. On the other side of the equals sign, let’s create an equivalent number sentence. If we double one number and halve the other number, will we have an equivalent number sentence? Let’s investigate! Record, for example, x 8 = twice as much as x 4 Record, for example, 6 x 4 = half of 6 x 8 1 Record, for example, 6 x 4 = half of 6 x 8 = 2 of 6 x 8 1 Record, for example, 6 x 4 = half of 6 x 8 = 2 of 6 x 8 = 3 x 8 Record, for example, 3 x 8 = twice 3 x 4 Record, for example, 3 x 8 = twice 3 x 4 = 2 x 3 x 4 Record, for example, 3 x 8 = twice 3 x 4 = 2 x 3 x 4 = 6 x 4 Record, for example, 46 x 8 = Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 12 Record, for example, 46 x 8 = 92 x 4 Record, for example, 46 x 8 = 40 x 8 + 6 x 8 = 320 x 48 = 368 Record, for example, 92 x 4 = 90 x 4 + 2 x 4 = 360 + 8 = 368 What is double 46? Is double 46, 92? What is half of 8? Is half of 8, 4? Have we created an equivalent number sentence? Does 46 times 8 equal 92 times 4? What does 46 times 8 equal? Does 46 times 8 equal 368? What does 92 times 4 equal? Does 92 times 4 equal 368? When we multiplied one number by 2 and divide the other number by 2, did we create an equivalent number sentence? Why? Let’s investigate! When we multiply by 4, do we get a number that is 4 times greater? When we multiply by 8, do we get a number that is 8 times greater? So when we multiply by 4, will we have half as much as when we multiply by 8? And when we multiply by 8, will we have twice as much as when we multiply by 4? Record, for example, multiply by 4 makes a number 4 times greater Record, for example, multiply by 8 makes a number 8 times greater Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 13 If we multiply 92 by 4, will we have half as much as 6 times 8? Does 92 times 4 equal half of 92 times 8? Record, for example, 92 x 4 = half of 92 x 8 = 2 of 92 x 8 = 46 x 8 Is half of 92 times 8, 46 times 8? Record, for example, 46 x 8 = twice 46 x 4 If we multiply 46 times 8, will we have twice as much as 46 times 4? Does 46 times 4 equal twice 46 times 8? Is twice 46 times 8, 92 times 4? Record, for example, 92 x 4 = half of 92 x 8 1 Record, for example, 92 x 4 = half of 92 x 8 = 2 of 92 x 8 1 Record, for example, 46 x 8 = twice 46 x 4 = 2 x 46 x 4 Record, for example, 46 x 8 = twice 46 x 4 = 2 x 46 x 4 = 92 x 4 Allow children time now to engage in guided and independent investigation of creating equivalent multiplication number sentences by dividing one number and multiplying the other number by the same factor. Website: http://www.alearningplace.com.au Email: [email protected] Twitter: @learn4teach YouTube: A Learning Place A Teaching Place Facebook: A Learning Place 14
