Compacted Math 4 Q3W1

7/27/2019 Compacted Math 4 Q3W1

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COMPACTEDMATH4/5Quarter 3 * Week 1

Enduring Understandings Fractions and decimals allow us to solve problems that are not possible

with just whole numbers. Just as every whole number is obtained by combining ones, every

fraction can be obtained by combining unit fractions. Relationships exist among larger and smaller measurement units within

a system. The size of a fractional part is relative to the size of the whole. There are relationships among the four operations.

Essential Questions How are units of measure within one system related? How can you apply understandings of operations on whole numbers

to operations on fractions? How can you model, represent, and interpret addition, subtraction,

multiplication, and division situations? How can you represent, interpret, and solve problem situations

involving fractions and decimals? What strategies can be used to represent and compare two

decimals?


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USEDECIMALNOTATIONTOREPRESENTFRACTIONSWITHDENOMINATORS10 OR100 Q3W1D1

Explore: Coin Box. Click on the penny in the bluebox at the bottom of the screen; select collect.The large square represents one dollar.

Answer: What does each small square represent?

What fraction of a dollar is one cent and why? What fraction of a dollar is a dime and how do you

know?

Drag the dime and penny tiles to collect therequired amount of money.

Answer: How many dimes are there in your collection?

How many pennies?

What fraction of a dollar did you collect?

How would you write this amount of money using adollar sign and decimal point?
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USEDECIMALNOTATIONTOREPRESENTFRACTIONSWITHDENOMINATORS10 OR100

Note: Fractions with a denominator of 100 can also berepresented using decimal notation; is written as 0.46.The decimal is read as forty-six hundredths and thedecimal point separates the whole number amount fromthe fractional part of a whole.

Answer: How many hundredths of a dollar is 46 cents? For additional examples, click on the New button at

the top of the page and use dimes and pennies tocollect the new amount shown.

Answer and discuss:

What fraction of a dollar is represented? How can you write this number as a decimal?

What fraction of a dollar is 6 cents ?

How would you represent 6 hundredths as a decimal?

What fraction of a dollar is 60 cents?

How would you represent 60 hundredths as a decimal?


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Examine models of thedecimals 18 hundredths and 1 and 8 hundredths(Modeling Hundredths).

Answer: What decimal does each model represent and how do you know?

How would you represent these numbers as fractions with denominators of 100?

Represent and explain a variety of other decimals.

Discuss the relationships among the representations.

Use the tenths squares to represent 1 6/10 (Decimal Squares: Tenths andHundredths). Explain why your representations are correct.

Note: 1 and 6 tenths can also be represented as the decimal 1.6

Discuss how the representations are related.

Answer: How would you represent 12/10 using Decimal Squares and as a decimal?

Use Decimal Squares: Tenths and Hundredths and decimal notation torepresent additional fractions with denominators of 10 or 100.

Synthesize: How does applying your understanding of fractions help youunderstand decimals?

The Visual Learning Animation, Fractions and Decimals, is an additionalresource that explains and models using decimal notation to representfractions with denominators of 10 or 100.
https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19391&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19391&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19394&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19394&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19392https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19391&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19391&ViewPage=1


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MODELANDADDTENTHSANDHUNDREDTHSQ3W1D2

We are working on the creative thinking skill of flexibility.This means being open and responsive to new anddiverse ideas, representations, and strategies and movingfreely among them.

0.3 0.03 Answer: How do you read these numbers?

Discuss the sizes of these decimals.

View (page 1): Tenths and Hundredths

Answer: How can you represent 3 tenths? How can you represent 3 hundredths?

Shade 30 hundredths in one color and 3 hundredths inanother color on the hundredths square.
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MODELANDADDTENTHSANDHUNDREDTHSQ3W1D2

View (page 2): Tenths and Hundredths

Discuss relating the 3 equations to the shadedhundredths square.

Complete Adding Tenths and Hundredths. Model

addition of tenths and hundredths on decimalsquares.

Answer: How did you model the addends and sums?

For B, what is another equation that represents the same

addition? How do you read the equation for C?

How many tenths are in the sum for E and why?

Before solving, what is a good estimate for the sum of F?

How do models help you understand adding tenths andhundredths?
https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19395&ViewPage=1https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19396https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19396https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19396https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.HOME/ResourceView.aspx?&ResourceId=19395&ViewPage=1


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MODELANDADDTENTHSANDHUNDREDTHS


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SOLVEMEASUREMENTPROBLEMSINVOLVINGTIMETOTHENEARESTTENTHANDHUNDREDTHOFASECOND

Q3W1D3

Think: What do you know about seconds and minutes?

Examine an analog clock with a second hand to determine the length of time ofone second.

Give impressions of how long 1/100 of a second is. (Use a digital timer to helpstudents appreciate units of time smaller than a second.)

View (page 1): 100 Meter Records. The 100 Meter race is a sprint race and that theworld record holder is referred to as the Fastest Man or Woman in the World. 100

meters is the length of many soccer fields and a bit longer than a regulationfootball field.

Discuss: What do you notice about the times?

How do you read the times?

How much time separates the record set in 2002 and the record set in 2009 and explain?

What equation using fractions represents the comparison of the records set in 2002 and2009?

Complete 100 Meter Records. Answer:

What equation did you use to solve A and explain your solution?

How did you solve D?

About how much faster is the mens record than the womens record and how do youknow?

How did you solve G?

How does thinking of decimals as common fractions help you solve problems involving

tenths and hundredths?
https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19397


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SOLVEMEASUREMENTPROBLEMSINVOLVINGTIMETOTHENEARESTTENTHANDHUNDREDTHOFASECOND


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SOLVEMEASUREMENTPROBLEMSINVOLVINGDISTANCES(KILOMETERSTOHUNDREDTHS) Q3W1D4

View: map of the Mount Vernon Trail.

Note: This scenic, paved trail from Mount Vernon to Theodore RooseveltIsland is about 28 kilometers long and is used by walkers, runners, andcyclists.

Evaluate the problem on Page 1 of the resource, The Mount Vernon Trail.

Discuss: What strategies can you use to solve the problem?

What equation can you write to represent the problem? What is a reasonable answer for the problem and how do you know?

With a partner, solve the problem and share strategies and solutions (TheMount Vernon Trail Sample Solutions).

Note: You will use information from Problem A to solve Problems BD onPages 2 and 3. As you work, read your equations aloud.

Answer:

How do you know that your answer is reasonable? Why did you decide to subtract?

How did thinking about money help you solve the problem?

How can you represent your answer as a decimal?

How does adapting strategies for adding and subtracting fractions help you solveproblems involving addition and subtraction of decimals?

Additional Practice: Biking Word Problemengages students in solving ameasurement problem involving distances (miles to tenths).
https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19398https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19399https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19400https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19400https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19400https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19401https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19401https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19400https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19400https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19399https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19399https://mymcps-instruction.mcpsmd.org/sites/ic/elementary/grade4/_layouts/MCPS.OLC.Home/ResourceView.aspx?viewpage=1&ResourceId=19398


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SOLVEMEASUREMENTPROBLEMSINVOLVINGDISTANCES(KILOMETERSTOHUNDREDTHS)


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SOLVEMEASUREMENTPROBLEMSINVOLVINGLIQUIDVOLUME(LITERSTOHUNDREDTHS) Q3W1D5

Generate a list of drink containers that are common in oureveryday lives.

Discuss the different units of measurement used to expressthe liquid volume of each and the challenges presentedwhen comparing the relative sizes of the containers.

Note: The metric system is based on units of ten, and theunit of liquid volume is the liter.

View: Common Drink Containers

Answer: How can you use the information in the table to help you

compare the liquid volume of different containers?

What strategies could you use to add and subtract thevolumes? How will you decide which operation to use? How do you know that your answer is reasonable? How does thinking about tenths and hundredths help you

solve problems involving the addition and subtraction ofdecimals?
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SOLVEMEASUREMENTPROBLEMSINVOLVINGLIQUIDVOLUME(LITERSTOHUNDREDTHS)

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Compacted Math 4 Q3W1