Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 9.7 x 7 = 9 + 0.7 67.9 9 x 7 = 63 Change the decimal to a fraction, multiply. Multiply the decimal by 10, multiply, then divide the product by 10. OR 7 x 7 x 𝟏 𝟏𝟎 = 49 x 𝟏 𝟏𝟎 = 49 ÷ 10 = 4.9 7 x 0.7 = 7 x 𝟕 𝟏𝟎 = 𝟒𝟗 𝟏𝟎 𝟒𝟗 𝟏𝟎 = 4 ones + 9 tenths = 4.9 63 + 4.9 = 67.9 Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 9.7 x 7 = 9 + 0.7 67.9 Multiply the number by 10, multiply, then divide the product by 10 97 x 7 = 9 + 07 Using the area model 9 x 7 = 63 7 x 7 x 𝟏 𝟏𝟎 = 49 x 𝟏 𝟏𝟎 = 49 ÷ 10 = 4.9 63 + 4.9 = 67.9 97 x 7 = 9 + 07 OR 9.7 x 7 = 9.7 x 7 = 7 x 9.7 x 10 ÷ 10 9.7 x 7 = 7 x 97 ÷ 10 x 90 + 7 7 630 49 630 + 49 = 679 679 ÷ 10 = 67.9 Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Using the area model 9.3 x 74 9.3 x 74 = 688.2 Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Using the distributive property in the area model 9.3 x 74 9.3 x 10 x 74 ÷ 10 Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Investigation: Select cards to make whole numbers and decimals that you are ready to multiply. Multiply the decimal by the whole number by either: keeping the decimal as a decimal and multiplying, or multiplying the decimal by powers of 10 to make a whole number, multiplying the whole numbers, then dividing the product by the power of 10. Explain your strategy to a friend. Reflection: How can we multiply decimals by whole numbers and powers of 10? Problem Solving I multiplied a decimal number by 15 and got an answer less than 15. What might the decimal number be? Problem Solving The product of 2 numbers is 14.4. What could the 2 numbers be? Problem Solving What might the missing numbers be? x . = . Problem Solving There are 2 number cards. Use the number cards to make this number sentence true: . x 9 = 43.2 Problem Solving There are 2 number cards. She makes a two-digit number that includes decimals and multiplies it by 9. What products could Jenna make?             8 4 2 3 Place Value 29, Multiplication Division 25, Fractions Decimals 26    

Place Value 29, Multiplication Division 25, Fractions Decimals 26 35.7 ÷ 4 = 32 + 3.7 3.6 + 0.1 8.925 32 ÷ 4 = 8 𝟏 𝟒 x 32 = 8 Change the decimal to a fraction, divide. Multiply the decimal by 10, divide, then divide the product by 10. OR 3.6 ÷ 4 = 0.9 𝟏 𝟒 x 3.6 = 0.9 0.1 ÷ 4 = 𝟏 𝟒 x 0.1 = 𝟏 𝟏𝟎 ÷ 4 = 𝟏 𝟒 x 𝟏 𝟏𝟎 = 𝟏 𝟏𝟎 ÷ 4 = 𝟏 𝟒 x 𝟏 𝟏𝟎 = 𝟎.𝟐𝟓 𝟏𝟎 0.1 ÷ 4 = 𝟏 𝟒 x 0.1 = 1 ÷ 4 ÷ 10 = 𝟏 𝟒 x 1 ÷ 10 = 0.25 ÷ 10 = 0.25 ÷ 10 = 0.25 ÷ 10 = 0.025 0.25 ÷ 10 = 0.025 Place Value 29, Multiplication Division 25, Fractions Decimals 26 8 + 0.9 + 0.025 = 8.925

Place Value 29, Multiplication Division 25, Fractions Decimals 26 35.7 ÷ 4 = 32 + 3.7 3.6 + 0.1 8.925 357 ÷ 4 = 𝟏 𝟒 x 357 = 300 + 57 300 + 57 40 + 17 40 + 17 16 + 1 16 + 1 300 ÷ 4 = 75 𝟏 𝟒 x 300 = 75 40 ÷ 4 = 10 𝟏 𝟒 x 40 = 10 16 ÷ 4 = 4 𝟏 𝟒 x 16 = 4 1 ÷ 4 = 𝟏 𝟒 𝟏 𝟒 x 1 = 𝟏 𝟒 75 + 10 + 4 + 𝟏 𝟒 = 89.25   89.25 ÷ 10 = 8.925 Divide the decimal by 10, divide, then divide the product by 10. Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Investigation: Select cards to make whole numbers and decimals that you are ready to divide. Multiply the decimal by the whole number by either: keeping the decimal as a decimal and dividing, or multiplying the decimal by powers of 10 to make a whole number, dividing the whole numbers, then dividing the product by the power of 10. Explain your strategy to a friend. Reflection: How can we divide decimals by whole numbers and powers of 10?   Problem Solving What number makes this number sentence correct? 1.6 × ? = 4. 8 Problem Solving What number, when divided by 9, would have a quotient of 0.7? Problem Solving I divided a decimal by a whole number and got 6.2. What number might I have divided by? Problem Solving I divided 2.4 by a whole number and got 1.2. What number did I divide by? Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Investigation: Select cards to make decimals and whole numbers that you are ready to multiply. Estimate the product of multiplying the decimals by a whole number. Use a calculator to multiply and check your estimate. With a partner, discuss whether your estimate was close to the correct answer and why. Reflection: What strategies did you use to estimate? Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Investigation: Select cards to make decimals and whole numbers that you are ready to divide. Estimate the quotient of dividing the decimals by a whole number. Use a calculator to divide and check your estimate. With a partner, discuss whether your estimate was close to the correct answer and why. Reflection: What strategies did you use to estimate? Place Value 29, Multiplication Division 25, Fractions Decimals 26

Place Value 29, Multiplication Division 25, Fractions Decimals 26 Investigation: In pairs have a decimal ‘target’ number and a calculator. Make your calculator show the target number using multiplication or division. For example, if your target number is 12.36, it could be made by multiplying 6.18 by 2, multiplying 3.09 by 4, dividing 24.72 by 2, dividing 49.44 by 4 etc.  Record your answers. Reflection: What strategies can you use when multiplying and dividing decimals by a whole number? Place Value 29, Multiplication Division 25, Fractions Decimals 26