Engage NY Module 14 Lesson 14- Objective: Divide decimals with a remainder using place value understanding and relate to a written method

Fluency Practice – Multiply & Divide Exponents Millions Hundred Thousands Ten Thousands One Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Write 65 tenths as a decimal on the place value chart. Now multiply by 10 2 and display your result on the place value chart. Write 87 thousandths on the place value chart. Now multiply by 10 3 and display on the place value chart. Write 5,472 on the place value chart. Now divide by 10 2 and display on the place value chart

Fluency Practice – Round to Different Place Value Write in unit form on your board starting with ones and then tenths. Round to the nearest tenth on your board. ▫6.385 = 6.4 Round to the nearest ones on your board. ▫6.385 = 6 Write in unit form on your board starting with hundreds and then hundredths. Round to the nearest hundreds on your board. ▫ = 300 Round to the nearest hundredths on your board. ▫ =

Fluency Practice – Find the Quotient How would you write the division statement for 14 ÷ 2? ▫14 ÷ 2 = 7 How would you write the above division statement in unit form? ▫14 ones ÷ 2 = 7 ones What is the division statement for 1.4 ÷ 2 and how would it be written in unit form? ▫1.4 ÷ 2 = 0.7, 14 tenths ÷ 2 = 7 tenths What is the division statement for 0.24 ÷ 3 and how would it be written in unit form? ▫0.24 ÷ 3 = 0.08, 24 hundredths ÷ 3 = 8 hundredths

Application Problem A bag of potato chips contains 0.96 grams of sodium. If the bag is split into 8 equal servings, how many grams of sodium will each serving contain? Bonus: What other ways can the bag be divided into equal servings so that the amount of sodium in each serving has 2 digits to the right of the decimal and the digits are greater than zero in the tenths and hundredths place?

Application Problem Problem – 0.96 ÷ 8 = 0.12 What is another way (form) you could set the problem up to make the math a little easier? ▫96 hundredths ÷ 8 = 12 hundredths Bonus - Students could run thru division problems until you start to repeat a factor. ▫96 hundredths ÷ 2 = 48 hundredths ▫96 hundredths ÷ 3 = 32 hundredths ▫96 hundredths ÷ 4 = 24 hundredths ▫96 hundredths ÷ 5 = 19 hundredths 2 thousandths (.192) ▫96 hundredths ÷ 6 = 16 hundredths ▫96 hundredths ÷ 7 = 13 hundredths 7 thousandths (.137 and continues) ▫96 hundredths ÷ 8 = 12 hundredths (original problem) ▫96 hundredths ÷ 9 = 10 hundredths 6 thousandths (.106 and continues) ▫96 hundredths ÷ 10 = 9 hundredths 6 thousandths (.096)

Concept Development - Problem 1-3 Solve 672 ÷ 3 What ways can we look at this problem to make it easier to solve? ▫Unit form ▫Expanded form What form would be easier unit form, standard form, or expanded form? Why? Let’s look at each form. ▫Standard ÷ 3 ▫Unit – 6 hundred, 72 ones ÷ 3 ▫Expanded – 600 ÷ ÷ ÷ 3 Pick one form and solve

Concept Development - Problem 1 Solve 672 ÷ 3 What ways can we look at this problem to make it easier to solve? ▫Unit form ▫Expanded form What form would be easier unit form, standard form, or expanded form? Why? Let’s look at each form. ▫Standard ÷ 3 ▫Unit – 6 hundred, 72 ones ÷ 3 ▫Expanded – 600 ÷ ÷ ÷ 3 Pick one form and solve

Concept Development – Problem 1 StandardUnitExpanded hundred 72 ones ÷ 3 = 2 hundred 24 ones 6 hundred 7 tens 2 ones ÷ 3 = 2 hundred 2 tens 1 ten 2 ones (now combine 1 ten 2 ones and then divide by 3 and add it to 2 hundred 2 tens) 12 ones ÷ 3 = 4 ones 2 hundred 2 tens 4 ones = 224 (6 x 100) + (7 x 10) + (2 x 1) ÷ 3 = ? (600 ÷ 3) + (70 ÷ 3) + (2 ÷ 3) (10 (remainder) + 2) ÷ 3 = = 224

Concept Development – Problem 1 Now lets look at dividing 6.72 by 3 (6.72 ÷ 3) Draw a place value chart with 3 rows and show 6.72 on your place value chart with disk. Note do the algorithm with each step

Concept Development - Problem 1 Starting in the ones column, how many equal groups of 3 can we make? As you place a disk cross off one. Keep going until you have used them all or have some remaining and cannot make even groups. How many disk are in each group of 3? Now repeat for tenths? How many are in each group? Do we have any left over?

▫Yes 1 disk. What can we do with the left over disk? Why 10 hundredths? How many hundredths will we know have? Now repeat for hundredths? How many disk are in each group of 3? Concept Development - Problem 1 Exchange it in for 10 hundredths. It takes 10 hundredths to make 1 tenth. 12 4

Do we have any hundredths left over? What is our answer? How many groups of 3 do we have in each place value column? What is our answer in standard form? Concept Development - Problem 1 2 ones 2 tenths 4 hundredths No.

Concept Development - Problem 1 How is the division we did with decimal units like whole number division? It’s the same as dividing whole numbers except we are sharing units smaller than ones. Our quotient has a decimal point because we are sharing fractional units. The decimal shows where the ones place is. Sometimes we have to change the decimal units just like changing the whole number units in order to continue dividing. Now lets try 5.16 ÷ 4

Concept Development - Problem ÷ 4 Ones. TenthsHundredths

Concept Development - Problem 6

Concept Development - Problem 7-8

Concept Development - Problem 9-10

Concept Development - Problem 11-13

End of Lesson Problem Set Debrief Exit Ticket