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TEKSING TOWARD STAAR © 2014 TEKS/STAAR-BASED LESSONS PARENT GUIDE Six Weeks 4 ® MATHEMATICS TEKSING TOWARD STAAR

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TEKSING TOWARD STAAR © 2014

TEKS/STAAR-BASED

LESSONS

PARENT GUIDESix Weeks 4

®MATHEMATICS

TEKSING TOWARD STAAR

TEKSING TOWARD STAAR2014

TEKSING TOWARD STAARSix Weeks 4 Scope and Sequence

Grade 4 Mathematics

Lesson TEKS/Lesson Content

Lesson 1 4.6B/interpret and draw one or more lines of symmetry, if they exist, for a two-dimensional figure

Lesson 24.7D/draw an angle with a given measure

4.7E/determine the measure of an unknown angle formed by two non-overlapping adjacentangles given one or both angle measures

Lesson 34.8C/solve problems that deal with measurements of length, intervals of time, liquid volumes,mass, and money using addition, subtraction, multiplication, or division as appropriate

Lesson 44.9A/represent data on a…stem-and-leaf plot with whole numbers and fractions

4.9B/solve one- and two-step problems using data in whole number, decimal, and fraction formin a…stem-and-leaf plot

Lesson 5 4.10E/describe the basic purpose of financial institutions, including keeping money safe,borrowing money, and lending.

Review

Assessment

NOTES:

STAAR Category 3 GRADE 4 TEKS 4.6B

TEKSING TOWARD STAAR 2014 Page 1

LESSON 1 - 4.6B

Lesson Focus

For TEKS 4.6B students are expected to identify and draw one or more lines ofsymmetry, if they exist, for a two-dimensional figure.

For this TEKS students should be able to apply mathematical process standards toanalyze geometric attributes in order to develop generalizations about their properties.

For STAAR Category 3 students should be able to demonstrate an understanding ofhow to represent and apply geometry and measurement concepts.

Process Standards Incorporated Into Lesson

4.1B Use a problem-solving model that incorporates analyzing given information,formulating a plan or strategy, determining a solution, justifying the solution,and evaluating the problem-solving process and the reasonableness of asolution.

4.1C Select tools, including real objects, manipulatives, paper and pencil, andtechnology as appropriate, and techniques, including mental math, estimation,and number sense as appropriate, to solve problems.

4.1E Create and use representations to organize, record, and communicatemathematical ideas.

4.1F analyze mathematical relationships to connect and communicate mathematicalideas.

4.1G display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication.

Vocabulary for Lesson

PART Isymmetryline symmetryline of symmetryvertical line of symmetryhorizontal line of symmetrydiagonal line of symmetrysymmetrical

STAAR Category 3 GRADE 4 TEKS 4.6B

TEKSING TOWARD STAAR 2014 Page 2

Math Background Part I - Line Symmetry

Grade 4 students are expected to identify and draw one or more lines of symmetry, ifthey exist, for a two-dimensional figure.

Some figures can be folded, or turned, in such a way that the two parts of the figureare the same size and the same shape. These figures have symmetry.

If you can fold a figure so that it has two parts that have the same size and the sameshape, the figure has line symmetry. The line where you fold the figure is called aline of symmetry.

Understanding Line Symmetry

Some figures can be folded, or turned, in such a way that the halves of the figuresmatch. A figure has symmetry when it can be folded in half, or turned, in such a waythat the two halves are the same size and the same shape.

The line at which a figure can be folded so that its two halves have the same size andthe same shape is called a line of symmetry.

A vertical line goes up and down. A vertical line of symmetry divides a figure intoa left side and a right side that are the same size and the same shape.

A horizontal line goes left and right. A horizontal line of symmetry divides afigure into a top and a bottom that are the same size and the same shape.

A diagonal line goes through vertices of a polygon that are not next to each other.A diagonal line of symmetry can go up and down and left and right and divides afigure into two parts that are the same size and the same shape.

Line of Symmetry

STAAR Category 3 GRADE 4 TEKS 4.6B

TEKSING TOWARD STAAR 2014 Page 3

EXAMPLES: Each of these figures has symmetry. Each figure can be folded in half,or turned, in such a way that the two halves have the same size and the same shape.

The triangle has a horizontal line of symmetry.

The heart has a vertical line of symmetry.

The star has a horizontal line of symmetry.

The letter "A" has a vertical line of symmetry.

Figures With More Than One Line of Symmetry

Some figures have more than one line of symmetry.

EXAMPLE 1: This star has a vertical line of symmetry, a horizontal line of symmetry,and two diagonal lines of symmetry.

You can fold the star on any of these lines of symmetry and the two halves will havethe same size and the same shape exactly.

EXAMPLE 2: Each of these figures is a square.

A square has a vertical line of symmetry, a horizontal line of symmetry, and twodiagonal lines of symmetry.

You can fold a square on any of these lines of symmetry and the two halves will havethe same size and the same shape.

STAAR Category 3 GRADE 4 TEKS 4.6B

TEKSING TOWARD STAAR 2014 Page 4

Figures With No Line of Symmetry

Some figures do not have symmetry. Figures that do not have symmetry cannot befolded exactly into two equal parts.

EXAMPLES: These figures do not have a line of symmetry.

If you fold each figure along the line, the two parts would not match.

These figures do not have a line of symmetry, so they are not symmetrical.

There is no way to fold the quadrilateral along any line so that the two sides match, sothe figure does not have a line of symmetry.

There is no way to fold the letter "J" along any line so that the two sides match, sothe figure does not have a line of symmetry.

There is no way to fold the triangle along any line so that the two sides match, so thefigure does not have a line of symmetry.

STAAR Category 3 GRADE 4 TEKS 4.7D/4.7E

TEKSING TOWARD STAAR 2014 Page 1

LESSON 2 - 4.7D & 4.7E

Lesson Focus

For TEKS 4.7D students are expected to draw an angle with a given measure.

For TEKS 4.7E students are expected to determine the measure of an unknown angleformed by two non-overlapping adjacent angles given one or both angle measures.

For these TEKS students should be able to apply mathematical process standards tosolve problems involving angles less than or equal to 180 degrees.

For STAAR Category 3 students should be able to demonstrate an understanding ofhow to represent and apply geometry and measurement concepts.

Process Standards Incorporated Into Lesson

4.1A Apply mathematics to problems arising in everyday life, society, and theworkplace.

4.1B Use a problem-solving model that incorporates analyzing given information,formulating a plan or strategy, determining a solution, justifying the solution,and evaluating the problem-solving process and the reasonableness of asolution.

4.1C Select tools, including real objects, manipulatives, paper and pencil, andtechnology as appropriate, and techniques, including mental math, estimation,and number sense as appropriate, to solve problems.

4.1E Create and use representations to organize, record, and communicatemathematical ideas.

4.1F analyze mathematical relationships to connect and communicate mathematicalideas.

4.1G display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication.

Vocabulary for Lesson

PART I PART Iangle measureray unknown anglevertex non-overlapping anglesangle measure adjacent anglesprotractor (angle symbol)

m (the measure of angle)complementary anglessupplementary anglesangle bisector

STAAR Category 3 GRADE 4 TEKS 4.7D/4.7E

TEKSING TOWARD STAAR 2014 Page 2

Math Background Part I - Draw an Angle With a Given Measure

Grade 4 students are expected to use a protractor to draw an angle with a givenmeasure. Your teacher will give you a protractor and a sheet of white paper for Part Iof this lesson. Use your protractor to follow the instructions for drawing angles as yourteacher projects EXAMPLE 1 and EXAMPLE 2.

EXAMPLE 1: Draw ABC with a measure of 82°.

Step 1: Use the straight edge of the protractor to draw and label ray BC.

Step 2: Place the center point of the protractor on point B.Align ray BC with the 0º mark on the protractor.

Step 3: Using the same scale, mark a point at 82º.Label the point A.

Step 4: Use the straight edge of the protractor to draw ray BA.

EXAMPLE 2: Mr. Cochran is building a wheelchair ramp outside his barber shop. Theangle of the ramp must be 5°. Draw and label a picture to show a model of the ramp.

Step 1: Use the straight edge of the protractor to draw the first ray of the angle.

Step 2: Draw a point on the ray to show the vertex of the angle.

Place the center point of the protractor on the point you drew on the ray.Align this ray of the angle with the 0º mark on the protractor.

B C

STAAR Category 3 GRADE 4 TEKS 4.7D/4.7E

TEKSING TOWARD STAAR 2014 Page 3

Step 3: Using the same scale, mark a point at 5°.

Step 4: Use the straight edge of the protractor to draw the second ray of the anglefrom the vertex to the point marked at 5°.

STAAR Category 3 GRADE 4 TEKS 4.7D/4.7E

TEKSING TOWARD STAAR 2014 Page 4

Math Background Part II - Determining Unknown Angle Measures

Grade 4 students are expected to determine the measure of an unknown angleformed by two non-overlapping adjacent angles given one or both angle measures.

EXAMPLE 1: PQS and SQR are adjacent angles.

The mPQR is the sum of PQS and SQR. 37° + 43° = 80°.

So, mPQR is 80°.

EXAMPLE 2: JKM and MKL are adjacent angles. The mJKL is 100°. Find themeasure of MKL.

mJKL = mJKM + mMKL

100° = 90° + mMKL

100° 90° = mMKL

100° 90° = 10°

So, the measure of MKL is 10°.

Complementary Angles

Two angles are complementary if the sum of their measures is 90°.So, if two adjacent angles form a right angle, they are complementary.

EXAMPLE 1: BCE and ECD are complementary angles because 30° + 60° = 90°.

C

30°60°

B

D

E

Q43°

P

R

S

37°

J

90°

L

K

M

STAAR Category 3 GRADE 4 TEKS 4.7D/4.7E

TEKSING TOWARD STAAR 2014 Page 5

EXAMPLE 2: DEG and GEF are complementary angles because 40° + 50° = 90°.

Supplementary Angles

Two angles are supplementary if the sum of their measures is 180°.If two adjacent angles form a straight angle, then the angles are supplementary.

EXAMPLE 1: BCE and ECD are supplementary angles.

120° + 60° = 180°

EXAMPLE 2: DEG and GEF are supplementary angles.

70° + 110° = 180°

Angle Bisectors

An angle bisector is a ray that separates an angle into two congruent angles. Thetwo new angles have the same measure.

EXAMPLE: The measure of ABC is 60°. BD

is the angle bisector of ABC.

The measure of each of the two equal angles formed by the angle bisector is 30°.

D

40°

50°

F

E

G

B30°

30°

A

C

D

C

60°

B D

E

120°

G

E

110°

D F

70°

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 1

LESSON 3 - 4.8C

Lesson Focus

For TEKS 4.8C students are expected to solve problems that deal with measurementsof length, intervals of time, liquid volumes, mass, and money using addition,subtraction, multiplication, or division as appropriate.

For this TEKS students should be able to apply mathematical process standards toselect appropriate customary and metric units, strategies, and tools to solve problemsinvolving measurement.

For STAAR Category 3 students should be able to demonstrate an understanding ofhow to represent and apply geometry and measurement concepts.

Process Standards Incorporated Into Lesson

4.1A Apply mathematics to problems arising in everyday life, society, and theworkplace.

4.1B Use a problem-solving model that incorporates analyzing given information,formulating a plan or strategy, determining a solution, justifying the solution,and evaluating the problem-solving process and the reasonableness of asolution.

4.1C Select tools, including real objects, manipulatives, paper and pencil, andtechnology as appropriate, and techniques, including mental math, estimation,and number sense as appropriate, to solve problems.

4.1D Communicate mathematical ideas, reasoning, and their implications usingmultiple representations, including symbols, diagrams, graphs, and languageas appropriate.

4.1F analyze mathematical relationships to connect and communicate mathematicalideas.

4.1G display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication.

Vocabulary for Lesson

PART I PART II PART IIIlength intervals of time liquid volumeequivalent measurements equivalent measurements capacityestimation elapsed time standard unitsreasonable metric units

equivalent measurements

PART IV PART Vmass moneyamount of matter balanceequivalent measurements withdrawal

deposit

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 2

Math Background Part I - Problems That Deal With Measurements of Length

Grade 4 students are expected to solve problems that deal with measurements oflength using addition, subtraction, multiplication, or division as appropriate.

Appropriate tools and equivalent measurements must be used to measure and tosolve problems that deal with measurements of length.

Use the Grade 4 Mathematics Reference Materials as a tool to solve problemsinvolving equivalent measurements for length.

The answer to any measurement problem can be estimated before finding the exactanswer by rounding the numbers in the problem before working it out. The estimatetells approximately what the answer will be. If estimation is done first, a decisioncan be made whether the actual calculated answer is reasonable.

Estimation is used when actually solving some measurement problems. For example,measurement problems that deal with measurements of length might askapproximately how long, or whether a certain number is a reasonable answer toa problem. Estimation is actually required to solve these types of problems.

EXAMPLE 1: Eric built a new picnic table for his patio. The picnic table is 5 feet 10inches long. How long is the picnic table in inches?

Use estimation before working the problem out.The mixed measure is greater than 5 feet and less than 6 feet.The mixed measure is closer to 6 feet than 5 feet.

The Grade 4 Mathematics Reference Materials shows 1 foot (ft) = 12 inches (in.)

Think of 5 ft 10 in. as 5 ft + 10 in.

Regroup the feet into inches.1 ft = 12 in.

5 ft = 5 × 12 in.

5 ft = 60 in.

Solve the problem.5 ft = 60 in.

+ 10 in. + 10 in.70 in.

So, the picnic table is 70 inches long.

Decide if the answer is reasonable.The original mixed measure of 5 feet 10 inches is closer to 6 feet than 5 feet.

6 ft = 6 × 12 in.

6 ft = 72 in.

So, the answer of 70 inches long is a reasonable answer.

EXAMPLE 2: Hector built a deck at the back of his house in 2 days. At the end of thefirst day he worked his deck was 12 feet 6 inches wide. During the second day heworked he made the deck 8 feet 4 inches wider. How wide is the deck that Hectorbuilt?

Add the mixed measures to find the width of the deck.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 3

Step 1: Add the inches.

12 ft 6 in.+ 8 ft 4 in.

10 in.

Step 2: Add the feet.

12 ft 6 in.+ 8 ft 4 in.

20 ft 10 in.

So, the deck Hector built was 20 feet 10 inches wide.

EXAMPLE 3: Avery is building a fence around a picnic area at the city park. She hasa pole that is 6 feet 6 inches long. She cuts off 1 foot 7 inches from one end of thepole. How long is the pole now?

Subtract to find the length of the pole now.

Step 1: Subtract the inches.6 ft 6 in.

1 ft 7 in.

7 inches is greater than 6 inches, so regroup to subtract.

1 foot = 12 inches

6 ft 6 in.1 ft 7 in.

11 in.Step 2: Subtract the feet.

6 ft 6 in.1 ft 7 in.

4 ft 11 in.

So, the length of the pole is 4 feet 11 inches now.

EXAMPLE 3: Derrik has 5 pieces of plumbing pipe. Each piece is 3 feet 6 incheslong. If Derrik joins the pieces end to end to make one long pipe, how long will thenew pipe be in feet and inches?

Multiply to find the length of the new pipe.

3 ft 6 in. × 4Step 1: Regroup 3 feet into inches.

1 ft = 12 in.

3 ft = 3 × 12 in.

3 ft = 36 in.

Step 2: Combine the inches in the original length of each piece of pipe.

36 in. + 6 in. = 42 in.

5 18

5 18

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 4

Step 3: Find the length of the new pipe in inches.

42 in. × 4 = 168 in.

Step 4: Find the length of the new pipe in feet and inches.

168 in. ÷ 4 = 12 ft. 0 inches

So, the length of the new pipe will be 12 feet.

EXAMPLE 4: Jackson had a length of rope that was 1 meter 8 cm long. He cut therope into 4 equal lengths. What is the length of each of the 4 equal pieces?

Divide to find the length of each of the 4 pieces.

1 m 8 cm ÷ 4

Step 1: Regroup 1 foot into inches.

1 m = 100 cm

Step 2: Combine the inches to find the original length of the rope.

100 cm + 8 cm = 108 in.

Step 3: Solve the problem.

108 ÷ 4 = 27

So, the length of each of the 4 equal pieces is 27 centimeters.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 5

Math Background Part II - Problems That Deal With Intervals of Time

Grade 4 students are expected to solve problems that deal with intervals of timeusing addition, subtraction, multiplication, or division as appropriate.

Appropriate tools and equivalent measurements must be used to measure and tosolve problems that deal with intervals of time.

Use the Grade 4 Mathematics Reference Materials as a tool to solve problemsinvolving equivalent measurements for intervals of time.

Measuring Time

An analog clock has an hour hand, a minute hand, and a second hand to measuretime.

The time shown on this analog clock is 4:30:12.

Read 4:30:12 as 4:30 and 12 seconds, or 30 minutes and 12 seconds after 4.

The Grade 4 Reference Materials compare units of time to one another. In someproblems you may need to convert from one unit to another.

To change from a longer unit of time to a shorter unit of time, you multiply.The new number of units will be larger.

To change from a shorter unit of time to a longer unit of time, you divide. The newnumber of units will be smaller.

EXAMPLE 1: How many minutes are in 4 hours?

1 hour = 60 minutes

Use the operation of multiplication to change from a larger unit (hours) to a smallerunit (minutes).

60 minutes per hour 4 hours = 240 minutes

There are 240 minutes in 4 hours.

EXAMPLE 2: How many years are in 48 months? Find the fact on the Grade 4Reference Materials that relates days to weeks.

1 year = 12 months

TIME

1 year1 year1 week

1 day1 hour

1 minute

======

12 months52 weeks7 days24 hours60 minutes60 seconds

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 6

Use the operation of division to change from a smaller unit (months) to a larger unit(years).

48 months 12 months per year = 4 years

There are 4 years in 48 months.

Amount of Time

You may need to find the amount of time that has been taken for a particular activity.In some problems you may need to convert time from one unit to another.

EXAMPLE 1: Akisha studied for 1 hour 35 minutes on Tuesday, 1 hour 25 minutes onWednesday, and 2 hours 35 minutes on Thursday. How long did she spend studyingon these three days?

Add to find the total amount of time.

1 hour 35 minutes1 hour 25 minutes

+ 2 hours 35 minutes4 hours 95 minutes

Since 95 minutes is greater than one hour, rewrite the answer so that the number ofminutes is fewer than 60.

First convert 95 minutes to hours and minutes.1 hour = 60 minutes95 minutes = 60 minutes + 35 minutes95 minutes = 1 hour 35 minutes

Then convert 4 hours 95 minutes to hours and minutes.4 hours 95 minutes = 4 hours + 1 hour 35 minutes4 hours + 1 hour 35 minutes = 5 hours 35 minutes

Akisha spent 5 hours 35 minutes studying on these three days.

Elapsed Time

Elapsed time is the amount of time that has passed. Elapsed time is found bycounting from the starting time to the finishing time.

EXAMPLE 1: The clocks below show the length of a second, a minute, and an hour.

Start Time: 3:00:00 1 second elapses.

The time is now 3:00:01.

1 minute, or60 seconds, elapses.

The second hand hasmade a full turn

clockwise.

The time is now 3:01:00.

1 hour, or60 minutes, elapses.

The minute hand hasmade a full turn

clockwise.

The time is now 4:00:00.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 7

EXAMPLE 2: The elapsed time between 8:00 A.M. and 8:30 A.M. is 30 minutes.

Some problems require you to find how long it takes to do something. Someproblems require you to calculate the amount of time that has passed between oneevent and another. For other problems you may need to know how long it has beensince something happened.

EXAMPLE 2: Miguel went on a bicycle ride. He started riding at 11:15 A.M. Hestopped at 2:25 P.M. How much time passed while Miguel was riding?

Count the hours between 11:15 A.M. and 2:15 P.M.

There are 3 hours between 11:15 A.M. and 2:15 P.M.

Count the number of minutes between 2:15 P.M. and 2:25 P.M.

There are 10 minutes between 2:15 P.M. and 2:25 P.M.

Combine the hours and the minutes.

3 hours + 10 minutes

The total time that passed during Miguel’s bike ride was 3 hours 10 minutes.

EXAMPLE 3: Uncle Walt is flying from Chicago to Dallas with a stop in Atlanta. Hisplane leaves Chicago at 8:15 A.M. and arrives in Dallas at 12:05 P.M. Chicago andDallas are in the same time zone. How long is the flight?

1 hour 1 hour1 hour

5 minutes

5 minutes

Starting Time Finishing Time

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 8

Count the whole hours.

From 8:15 A.M. to 11:15 A.M. is 3 hours.

Count the minutes from 11:15 A.M. to 12:05 P.M.

From 11:15 A.M. to 12:05 P.M. is 50 minutes.

Add the hours and minutes.3 hours + 50 minutes

The flight was 3 hours and 50 minutes.

EXAMPLE 4: Reagan goes to tennis practice after school. Practice lasts 1 hour and20 minutes and is over at 4:40 P.M. At what time does tennis practice begin?

Draw a time line to show the end time and the elapsed time.

Tennis practice begins at 3:20 P.M.

Estimating Time

Estimation is used when actually solving some measurement problems. For example,measurement problems that deal with measurements of time might askapproximately how long, or whether a certain number is a reasonable answer toa problem. Estimation is actually required to solve these types of problems.

EXAMPLE 1: Akisha studied 1 hour 55 minutes on Tuesday, 1 hour 45 minutes onWednesday, and 2 hours 15 minutes on Thursday. About how long did she spendstudying on these three days?

8:15

9:15

11:15

10:15

1 h

1 h

1 h

You can’t jump from 11:15 to 12:15 becausethat is past the arrival time in Dallas.

1 hr20 min

End Time4:40 P.M.

Begin Time3:20 P.M.

15 min

5 min

10 min

20 min

25 min

30 min

35 min

40 min

50 min45 min

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 9

Estimate and add to find an estimate for the total number of hours and minutes.

1 hour 55 minutes is about 2 hours1 hour 45 minutes is about 2 hours2 hours 15 minutes is about 2 hours

2 hours + 2 hours + 2 hours = 6 hours

Akisha studied about 6 hours on these three days.

EXAMPLE 2: Uncle Walt is flying from Chicago to Dallas with a stop in Atlanta. Hisplane leaves Chicago at 7:38 A.M. and arrives in Dallas at 12:11 P.M. Chicago andDallas are in the same time zone. About how long is the flight?

Count the whole hours.From 7:38 A.M. to 11:38 A.M. is 4 whole hours.

Estimate the minutes from 11:38 A.M. to 12:11 P.M.

From 11:38 A.M. to 12:00 noon is about 20 minutes. From 12 noon to 12:11 P.M. isabout 10 minutes.

20 minutes + 10 minutes = 30 minutes

Add the estimated hours and minutes.

4 hours + 30 minutes

The flight is about 412

hours.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 10

Math Background Part III - Problems That Deal With Liquid Volumes

Grade 4 students are expected to solve problems that deal with measurements ofliquid volumes using addition, subtraction, multiplication, or division as appropriate.

Appropriate tools and equivalent measurements must be used to measure and tosolve problems that deal with measurements of liquid volumes.

Liquid volume or capacity is a measure of how much a container can hold.

Liquid volume can be measured in customary or metric units.Customary units of liquid volume include gallons, quarts, ounces, pints, and cups.Metric units of liquid volume include liters and milliliters.

Use the Grade 4 Mathematics Reference Materials as a tool to solve problemsinvolving equivalent measurements for liquid volumes.

EXAMPLE 1: James put 10 liters 250 milliliters of water in his aquarium. How manymilliliters of water did he put in his aquarium?

Use addition to find the number of milliliters of water he put in his aquarium.

10 liters (L) + 250 milliliters (mL)

Convert the measures to the same unit.

Convert 10 liters to milliliters.The Grade 4 Reference Materials shows 1 liter (L) = 1,000 milliliters (mL).

1 L = 1,000 mL

10 L = 10,000 mL

So, 1 liter = 10,000 mL.

Add to find the answer.10,000 mL + 250 mL = 10,250 mL

So, James put 10,250 milliliters of water in his aquarium.

EXAMPLE 2: Freda has a recipe that asks for 1 quart of milk. She has 3 cups of milk.How much more milk does she need?

Use subtraction to find the difference between the amount of milk Freda needs andthe amount of milk she has.

1 quart (qt) ‒ 3 cups (c)

Convert the measures to the same unit.

First, convert 1 quart to pints.The Grade 4 Reference Materials shows 1 quart (qt) = 2 pints (pt).

Next, convert 2 pints to cups.The Grade 4 Reference Materials shows 1 pint (pt) = 2 cups (c).

1 pt = 2 c

1 pt × 2 = 2 c × 22 pt = 4 c

So, 1 quart = 4 cups.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 11

Subtract to find the answer.4 c ‒3 c = 1 c

So, Freda needs 1 more cup of milk.

EXAMPLE 3: Brittney used 5,000 milliliters of water to water her flower garden. Howmany liters of water is that?

The Grade 4 Reference Materials shows 1 liter = 1,000 milliliters.

Milliliters are smaller than liters, so use division to find how many liters are in 5,000milliliters.

5,000 ÷ 1,000 = 5

So, Brittney used 5 liters to water her flower garden.

EXAMPLE 4: Petra needs 3 cups of milk for a recipe. How many ounces of milk doesshe need for the recipe?

The Grade 4 Reference Materials shows 1 cup = 8 fluid ounces.

Cups are larger than ounces, so use multiplication to find how many ounces are in3 cups.

3 × 8 = 24

So, Petra needs 24 ounces of milk for her recipe.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 12

Math Background Part IV - Problems That Deal With Mass

Grade 4 students are expected to solve problems that deal with measurements ofmass using addition, subtraction, multiplication, or division as appropriate.

Appropriate tools and equivalent measurements must be used to measure and tosolve problems that deal with measurements of mass.

Mass is the measure of the amount of matter in an object. A balance is the toolused to measure mass. An object is placed on one of the balance pans. Masses areplaced on the other balance pan so that the two balance pans hold the same amountof matter.

Metric units of mass include kilograms, grams, and milligrams.

Use the Grade 4 Mathematics Reference Materials as a tool to solve problems involvingequivalent measurements for mass.

EXAMPLE 2: Joe bought 600 grams of cayenne pepper and 2 kilograms of blackpepper. How many grams of pepper did he buy?

Joe bought 600 grams of cayenne pepper.

He bought 2 kilograms of black pepper.

Add to find the total amount of pepper Joe bought.

amount of cayenne pepper + amount of black pepper = total amount of pepper

First, convert 2 kilograms of black pepper to grams so you can add.

The Reference Materials shows 1 kilogram (kg) = 1,000 grams (g).

Multiply to find the number of grams in 2 kilograms.

1 kg = 1,000 g

2 kg = 2,000 g

So, 2 kilograms = 2,000 grams of black pepper.

Now, add to find the total amount of pepper Joe bought.

600 grams of cayenne pepper + 2,000 grams of black pepper

600 g + 2,000 g = 2,600 g

So, Joe bought 2,600 grams of pepper in all.

Use a balanceto measure mass.

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 13

Math Background Part V - Problems That Deal With Money

Grade 4 students are expected to solve problems that deal with money using addition,subtraction, multiplication, or division as appropriate.

EXAMPLE 1: The amount of money that is in an account after a deposit orwithdrawal is made is called the balance. A deposit is when money is added to thebalance of an account. A withdrawal is when money is subtracted from the balanceof an account.

The balance in Meisha’s savings account is $423.54. She makes a deposit of $58.95.What is the balance in her savings account now?

Use addition to find the balance after a deposit.

Step 1: Line up the decimal points. Add the hundredths.

$423.54+ $ 58.95

9Step 2: Add the tenths. Regroup as needed.

$423.54+ $ 58.95

49Step 3: Add the ones, tens and hundreds. Regroup as necessary. Place the dollar

sign and the decimal point in the sum.

$423.54+ $ 58.95

$482.49

So, the balance in Meisha's savings account now is $482.49.

Two weeks later, Meisha decides to withdraw $75.34 from her savings account. Whatis the balance now?

Use subtraction to find the balance after a withdrawal.

Step 1: Line up the decimal points. Subtract the hundredths.

$482.49‒$ 75.34

5Step 2: Subtract the tenths.

$482.49‒$ 75.34

15

Step 3: Subtract the ones, tens and hundreds. Regroup as necessary. Place thedollar sign and the decimal point in the difference.

$482.49‒$ 75.34

$407.15

So, the balance in Meisha's savings account now is $407.15.

1

11

starting balancedeposit

starting balancedeposit

starting balancedepositnew balance

127

starting balancewithdrawal

starting balancewithdrawalnew balance

starting balancewithdrawal

STAAR Category 3 GRADE 4 TEKS 4.8C

TEKSING TOWARD STAAR 2014 Page 14

EXAMPLE 2: Mr. Lester wants to buy books for his bookstore. The new mysterybook he wants to buy comes in a case containing 48 books. Each book costs $18.What will Mr. Lester pay for 1 case of the books?

Step 1: Think of 48 as 4 tens and 8 ones. Multiply $18 by 8 ones. Use place valueand regrouping as necessary.

$ 18× 48144

Step 2: Multiply $18 by 4 tens, or 40. Use place value and regrouping as necessary.

$ 18× 4814472

Step 3: Add the partial products. Place a dollar sign in the final product.

$ 18× 48144

+ 72$864

So, Mr. Lester will pay $864 for 1 case of the books.

EXAMPLE 3: Mr. Lester paid $592 for 8 boxes of a popular magazine for hisbookstore. What is the amount he paid for each box of the magazines?

Use division to find the amount he paid for each box of the magazines. $592 ÷ 8

Step 1: Divide the tens.

Step 2: Divide the ones. Regroup 3 tens as 30 ones. Place the dollar sign in thequotient.

So, Mr. Lester paid $74 for each case of magazines.

6

63

63

cost per booknumber of books in 1 case

cost per booknumber of books in 1 case

cost for 1 case of books

cost per booknumber of books in 1 case

87

Divide: 59 tens ÷ 8

Multiply: 8 × 7 tensSubtract: 59 tens ‒ 56 tens 3

$59256

874

Divide: 32 ones ÷ 8Multiply: 8 × 4 ones

Subtract: 32 ones ‒ 32 ones tens

32‒32

0

$59256

$

STAAR Category 4 GRADE 4 TEKS 4.9A/4.9B

TEKSING TOWARD STAAR 2014 Page 1

LESSON 4 - 4.9A/4.9B

Lesson Focus

For TEKS 4.9A students are expected to represent data on a frequency table, dot plot,or stem-and-leaf plot marked with whole numbers and fractions. Focus for this lessonis stem-and-leaf plots.

For TEKS 4.9B students are expected to solve one- and two-step problems using datain whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. Focus for this lesson is stem-and-leaf plots.

For these TEKS students should be able to apply mathematical process standards tosolve problems by collecting, organizing, displaying, and interpreting data.

For STAAR Category 4 students should be able to demonstrate an understanding ofhow to represent and analyze data and how to describe and apply personal financeconcepts.

Process Standards Incorporated Into Lesson

4.1C Select tools, including real objects, manipulatives, paper and pencil, andtechnology as appropriate, and techniques, including mental math, estimation,and number sense as appropriate, to solve problems.

4.1D Communicate mathematical ideas, reasoning, and their implications usingmultiple representations, including symbols, diagrams, graphs, and languageas appropriate.

4.1E Create and use representations to organize, record, and communicatemathematical ideas.

Vocabulary for Lesson

PART I PART IIstem-and-leaf plot stem-and-leaf plotstem stemleaves leaves

STAAR Category 4 GRADE 4 TEKS 4.9A/4.9B

TEKSING TOWARD STAAR 2014 Page 2

Math Background Part I - Stem-and-Leaf Plots

Grade 4 students are expected to represent data on a stem-and-leaf plot.

A stem-and-leaf plot is a graph that displays groups of data arranged by place value.

Representing Data On A Stem-and-Leaf Plot

Follow these steps to create a stem-and-leaf plot:Step 1: Group the data by the tens digits.

Step 2: Order the tens digits vertically from least to greatest.Draw a vertical line to the right of the tens digits (stems).

Step 3: Separate the numbers in each group into stems (tens) and leaves (ones).Write each ones digit (leaves) to the right of the tens digit (stem) in orderfrom least to greatest.

Step 4: Title the stem-and-leaf plot and label a stem and leaves column.

Step 5: Make a key that explains how to read a stem and leaves.

EXAMPLE: A dance teacher recorded the heights in inches of students in a beginnerdance class. The teacher needs to organize the students by height for a dance recital.

57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52, 56, 46, 54, 49, 50

Create a stem-and-leaf plot to organize the data.

Step 1: Group the data by the tens digits.

40: 49, 48, 46, 49

50: 57, 57, 57, 58, 57, 54, 51, 50, 52, 56, 54, 50

60: 61, 61, 68, 64, 65

Step 2: Order the tens digits vertically from least to greatest.Draw a vertical line to the right of the tens digits (stems).

Step 3: Separate the numbers in each group into a stem (tens) and leaves (ones).Write each ones digit (leaves) to the right of the tens digit (stem) in orderfrom least to greatest.

Step 4: Title the stem-and-leaf plot and label stem and leaves.

Heights of Dance Students (in.)Stem Leaves

4 6 8 9 95 0 0 1 2 4 4 7 7 7 7 86 1 1 4 5 6

4 6 8 9 95 0 0 1 2 4 4 7 7 7 7 86 1 1 4 5 6

456

STAAR Category 4 GRADE 4 TEKS 4.9A/4.9B

TEKSING TOWARD STAAR 2014 Page 3

Step 5: Add a key that explains how to read the stem and leaves.

Heights of Dance Students (in.)Stem Leaves

4 6 8 9 95 0 0 1 2 4 4 7 7 7 7 86 1 1 4 5 6

Key: 4 6 represents 46 inches

STAAR Category 4 GRADE 4 TEKS 4.9A/4.9B

TEKSING TOWARD STAAR 2014 Page 4

Math Background Part II - Use Data To Solve Problems

Grade 4 students are expected to solve one-step and two-step problems using data ina stem-and-leaf plot.

The purpose of a stem-and-leaf plot is to organize the numbers in a set of data so thatthe numbers themselves make the display. An advantage of representing data with astem-and-leaf plot is that it easily identifies the greatest and least values in a set ofdata. Also, it gives a quick way of checking how many pieces of data fall in variousgroups. Unlike frequency tables, the stem-and-leaf plot displays the value of everypiece of data.

Sometimes conclusions need to be drawn or convincing arguments need to be madeabout data on a stem-and-leaf plot. To do this, careful review of the data and findingevidence that supports conclusions or arguments is required.

EXAMPLE: Jackson practices basketball free throws almost every day. Each time hepractices, he records the number of free throws he makes in a stem-and-leaf plot.

These are some of the conclusions that can be drawn from the data shown in thestem-and-leaf plot:

Jackson recorded the number of free throws he made on 24 different days.

The least number of free throws Jackson made on any day was 4.

The greatest number of free throws Jackson made on any day was 37.

Jackson made 9 free throws on 2 days.

Jackson made 11 free throws on 2 days.

Jackson made 20 free throws on 2 days.

Jackson made 30 free throws on 2 days.

Jackson made 32 free throws on 4 days.

Jackson made less than 10 free throws on 4 days.

Jackson made between 10 and 20 free throws on 6 days.

Jackson made between from 20 to 29 free throws on 7 days.

Jackson made 30 or more free throws on 7 days.

Jackson made more than 20 free throws on 12 days.

Jackson made less than 10 free throws or more than 26 free throws on 13 days.

Jackson made 20 or more free throws on more than half of the days.

Number of Free Throws MadeStem Leaves

0 4 6 9 91 1 1 2 4 5 92 0 0 4 5 6 8 93 0 0 2 2 2 2 7

Key: 0 4 represents 4 free throws

STAAR Category 4 GRADE 4 TEKS 4.10E

TEKSING TOWARD STAAR 2014 Page 1

LESSON 5 - 4.10E

Lesson Focus

For TEKS 4.10E students are expected to describe the basic purpose of financialinstitutions, including keeping money safe, borrowing money, and lending.

For this TEKS students should be able to apply mathematical process standards tomanage one's financial resources effectively for lifetime financial security.

For STAAR Category 4 students should be able to demonstrate an understanding ofhow to represent and analyze data and how to describe and apply personal financialconcepts.

Process Standards Incorporated Into Lesson

4.1A Apply mathematics to problems arising in everyday life, society, and theworkplace.

4.1D Communicate mathematical ideas, reasoning, and their implications usingmultiple representations, including symbols, diagrams, graphs, and languageas appropriate.

4.1F analyze mathematical relationships to connect and communicate mathematicalideas.

Vocabulary for Lesson

PART Ifinancial institutionsloanborrowerlenderinterest

STAAR Category 4 GRADE 4 TEKS 4.10E

TEKSING TOWARD STAAR 2014 Page 2

Math Background Part I - Financial Institutions

Grade 4 students are expected to describe the basic purpose of financial institutions,including keeping money safe, borrowing money, and lending.

Financial institutions, such as banks and credit card companies, are businesses.They are in the business of keeping money safe, lending money, and borrowingmoney.

When you open a savings account at a bank, the bank is a borrower. This has anadvantage of keeping your money safe. When you take out a loan or credit card, thebank is a lender.

When you borrow money from a financial institution, you will pay interest on the loan.Interest is the additional money paid by a borrower to a lender in exchange for theuse of the lender’s money.

EXAMPLE: Tyrone wants to buy a 4-wheeler that costs $400. Tyrone does not haveenough money to buy the 4-wheeler. He sees this sign at his bank.

Tyrone knows he can borrow the money from a financial institution to buy the4-wheeler, but he also knows he will have to pay interest. He decides to borrow themoney from his bank. How much will Tyrone have to repay the bank to borrow themoney?

Find the total interest on $400.

Think: 4 × $100 = $400

Interest = $10 for every $100 borrowed

Interest = 4 × $10 = $40

So, the total interest Tyrone will have to pay is $40.

Find the total amount Tyrone will have to repay the bank.

Repayment of loan = loan amount + interest

Repayment of loan = $400 + $40 = $440

So, the total amount Tyrone will have to repay the bank to borrow the money is $440.