Use whole number multiplication to express equivalent measurements 30 10 300 100 3000 1000 5000 1000 50 10 500 100 5000 100 ID: 735167
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Slide1
Engage NY Math Module 2
Lesson 13:
Use whole number multiplication to express equivalent measurements.Slide2
30 ÷ 10 =
300
÷ 100 = 3,000 ÷ 1,000 =5,000 ÷ 1,000 =50 ÷ 10 =500 ÷ 100 = 5,000 ÷ 100 =3,000 ÷ 100 =30,000 ÷ 1,000 =50,000 ÷ 1,000 = 40 ÷ 10 =400 ÷ 10 =4,000 ÷ 10 =40,000 ÷ 10 = 700 ÷ 100 =7,000 ÷ 100 =70,000 ÷ 100 =700,000 ÷ 100 = 7,000,000 ÷ 1,000 =
Divide by 10, 100, and 1000Slide3
Multiply Using the Area Model
Use the area model to solve the following in your math notebook. Check your answer with the standard algorithm.
5.21 x 34177.148.35 x 73609.55Slide4
Unit Conversions
1
ft = _____ inI foot is the same as how many inches?122 ft = _____ in243 ft = _____ in364 ft = _____ in48 Slide5
Unit Conversions
10
ft = _____ in1205 ft = _____ in607 ft = _____ in8412 ft = _____ in144 Slide6
Unit Conversions
100 cm = _____ m
I00 centimeters is the same as how many meters?1200 cm = _____ m2300 cm = _____ m3600 cm = _____ m6 Slide7
Unit Conversions
800 cm = _____ m
8400 cm = _____ m41,200 cm = _____ m12500 cm = _____ m5 Slide8
Application Problem
Hands-on conversion reading activity
Every string has an exact match.Measure your string using the following directions.Blue strings = measure your string to the nearest FOOTOrange strings = measure your string to the nearest INCHTan strings = measure your string to the nearest METERGreen strings = measure your string to the nearest CENTIMETERAfter you measure your string, you will find your string’s match which will be a different color.Record your equivalent measures in your math journal. In a few sentences, explain how the same sized piece of string can have two different measurements.Slide9
Concept Development
Distribute a copy of the Grade 5 Mathematics Reference Sheet to each student.
Turn and talk with your tablemates. How might this document help us solve problems?Today we’ll be using this Reference Sheet to help us convert between various units of measure. Discuss with your table the types of measurement units you see on this sheet.Turn to a new page in your journal. Divide your page into three sections labeled Length, Weight, and Volume/Capacity. Talk with your table about which units are used for each type of measurement and record those units in the appropriate column in your journal.Slide10
Concept Development
LENGTH
CentimeterMillimeterMeterKilometerFeetYardsMileWEIGHTGramMilligramKilogramPoundOunceTonVOLUME/CAPACITYCupFluid ouncesPintQuartGallonLiterMilliliterKiloliterSlide11
Concept Development – Problem 1(a):
15 feet = _____ inches
How can we use the patterns we just saw in our Application Problem to help us convert from feet to inches?Visualize the tape measure we just used to measure in feet and inches. How many inches did we see in each foot?12Let’s draw a number line to show what we saw. You draw your own number line in your journal.Slide12
Concept Development – Problem 1(a):
15 feet = _____ inches
If one foot, or one unit, is equal to 12 inches, how can I find what 15 feet is equal to?We can add 12 inches 15 times.We can skip count by twelves 15 times.We can multiply 12 times 15.If one unit is 12 inches, then 10 units is 120 inches, and 5 more units would be 60 inches, so that’s 180 inches.Therefore, we could use repeated addition, skip counting, or multiplication. If I wanted to express this conversion as a multiplication equation, what would it look like? Would this method work for any situation in which I wanted to name feet as inches?15 ft x 12 = 180 inchesSlide13
Concept Development – Problem 1(a):
15 feet = _____ inches
We just converted from feet to inches. Which unit is larger, feet or inches?FeetThink back to our Application Problem. Remind me why we need so many inches to make just 15 feet. Discuss this with your tablemates.Inches are a smaller unit; we need more of them to make the larger units, feet.Slide14
Concept Development –
Problems 1(b/c):
150 feet = _____ inches1800 inches152 feet = _____ inches1824 inches21 feet = ______ inches252 inches210 feet = _____ inches2520 inchesUse the same procedure to solve the following problems in your math journal.Slide15
Concept Development – Problem
2(a
):3 tons 140 pounds = _____ poundsLet’s use our thinking about multiplication to solve this one. At your table, discuss which part of the Reference Sheet will help us solve this one.1 ton = 2,000 poundsHow is this problem slightly different from the first one we solved?We are converting tons and pounds to just pounds.Let’s start with the 3 tons. In your journal draw a double number line showing tons and pounds.Look at your drawing. How many pounds are equal to 3 ton? 1 ton 2 ton 3 ton4,000 pounds 6,000 pounds2,000 poundsSlide16
Concept Development – Problem
2(a
):3 tons 140 pounds = _____ poundsAre we finished? Have we found a weight equal to what we started with?No.Why not?We have 140 more pounds.What do we need to do with those 140 pounds?3 tons 140 pounds equals how many pounds altogether?6,140 pounds 1 ton 2 ton 3 ton 2,000 pounds 4,000 pounds 6,000 poundsSlide17
Concept Development – Problem
2(b):
42 feet 9 inches = _____ inchesLet’s use our thinking about multiplication to solve this one. At your table, discuss the conversion factor we will use to solve this problem. Add this to your Reference Sheet.1 foot = 12 inchesLet’s start with the 42 feet. In your journal draw a double number line showing feet and inches.Look at your drawing. How many inches are equal to 42 feet?504 inches 1 foot 2 feet . . . 42 feet24 inches 504 inches12 inchesSlide18
Concept Development – Problem
2(b):
42 feet 9 inches = _____ inchesAre we finished? Have we found a weight equal to what we started with?No.Why not?We have 9 more inches.What do we need to do with those 9 inches?42 feet 9 inches equals how many inches altogether?513 inches 1 foot 2 feet . . . 42 feet24 inches 504 inches12 inchesSlide19
Concept Development – Problem
3:
_____ ounces = 9 pounds 11 ouncesLook at your Reference Sheet. Tell your neighbor the conversion factor that you’ll use to solve this problem.1 pound = 16 ouncesIn your journal draw a double number line showing pounds and ounces. Use multiplication and addition to solve. Compare your answer with your neighbor’s work as you go.How many ounces are equal to 9 pounds 11 ounces?155 ounces 1 pound 2 pounds . . . 9 pounds32 ounces 144 ounces16 ouncesSlide20
Concept Development – Problem
4:
155 gallons = _____ quarts = _____ pintsUse your Reference Sheet to help you solve this problem independently. If you’d like you may draw a double number line.1 gallon = 4 quarts1 quart = 2 pints155 gallons equals how many quarts? Find the number of quarts mentally.100 gallons is 400 quarts, 50 gallons is 200 quarts and 5 gallons is 20 quarts. So, 155 gallons is 620 quarts. 155 gallons x 4 = 620 quartsFind the number of pints in 620 quarts mentally.There are 2 pints in every quart so just double every place value.620 x 2 = 1,240 pintsSlide21
Concept Development – Problem
4:
57 gallons 1 quart = _____ quarts57 x 4 = 228 + 1 = 229 quarts 63 quarts 3 pints = ______ pints63 x 2 = 126 + 3 = 129 pintsUse your Reference Sheet to help you solve these problems independently in your journal. Slide22
Exit TicketSlide23
Problem Set
Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.