Hidden Treasure: A Coordinate Game€¦ · LESSON9 Hidden TreasureGameboards 1 1 Date Time Each player uses Grids 1 and 2. Grid 1:Hide your point here. Grid 2:Guess other player’s

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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

704 Unit 9 Coordinates, Area, Volume, and Capacity

Advance PreparationFor Part 1, make transparencies of Math Masters, pages 437, 438, and 485. Copies of Math Masters,

page 485 can be used as additional Hidden Treasure gameboards. For a mathematics and literacy connection,

obtain a copy of G Is for Googol: A Math Alphabet Book by David M. Schwartz (Tricycle Press, 1998).

Teacher’s Reference Manual, Grades 4–6 pp. 249, 250

Key Concepts and Skills• Translate numbers written in scientific

notation into standard notation and

number-and-word notation.

[Number and Numeration Goal 1]

• Use ordered pairs of numbers to

name, locate, and plot points in the

first quadrant of a coordinate grid.

[Measurement and Reference Frames Goal 4]

Key ActivitiesStudents review coordinate grids, ordered

number pairs, and coordinates. They use

coordinate grids to graph a picture by

choosing and connecting ordered number

pairs. Students practice naming and

plotting ordered number pairs by playing

Hidden Treasure.

Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Number and Numeration Goal 1]

Key Vocabularycoordinate grid � axes � perpendicular �

origin � ordered pair of numbers � vertical

axis � horizontal axis � coordinate

MaterialsMath Journal 2, pp. 292 and 293

Student Reference Book, pp. 208 and 319

Math Masters, p. 485

transparencies of Math Masters, pp. 437,

438, and 485 � Class Data Pad � slate �

straightedge � red pencil or crayon

Matching Number Stories to GraphsMath Journal 2, p. 294

Students match number stories

to line graphs and explain their

solution strategies.

Math Boxes 9�1Math Journal 2, p. 295

Geometry Template � compass

Students practice and maintain skills

through Math Box problems.

Study Link 9�1Math Masters, p. 254

straightedge

Students practice and maintain skills

through Study Link activities.

READINESS

Finding Locations on a MapMath Masters, p. 255

Students locate points on a map.

ENRICHMENTFinding DistancesMath Masters, p. 256

straightedge

Students use gridlines to identify

point-to-point distances on a grid.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 142

Students write, define, and illustrate the

terms horizontal axis and vertical axis.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Hidden Treasure:A Coordinate Game

Objective To reinforce students’ understanding of coordinate

grid structures and vocabulary.g

��

Common Core State Standards

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Student Page

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Student Page

Math Journal 2, p. 292

Student Page

Plotting a TurtleLESSON

9 �1

Date Time

Points on a coordinate grid are named by ordered number

pairs. The first number in an ordered number pair locates

the point along the horizontal axis. The second number

locates the point along the vertical axis. To mark a point on

a coordinate grid, first go right or left on the horizontal

axis. Then go up or down from there.

Plot an outline of the turtle on

the graph below. Start with the

nose, at point (8,12).

00 1 2 3

(3,4)

4 5

1

2

3

4

5

(8,12)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

1

2

3

4

5

6

7

8

9

10

11

12

13

Sample answer:

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Lesson 9�1 705

Getting Started

Ongoing Assessment:Recognizing Student Achievement

Mental Math

and �Reflexes

Use the Mental Math and Reflexes problems to assess students’ ability to

translate numbers written in scientific notation into standard notation and

number-and-word notation. Students are making adequate progress if they

correctly write each number in standard notation.

[Number and Numeration Goal 1]

1 Teaching the Lesson

▶ Math Message Follow-Up

WHOLE-CLASS ACTIVITY

(Math Journal 2, p. 292; Student Reference Book, p. 208;

Math Masters, p. 437)

Use a transparency of Math Masters, page 437 to illustrate the following concepts:

� A plane is a flat surface that extends forever. A rectangular coordinate grid is used to name points in a plane.

� The coordinate grid is formed by two number lines called axes.

� The number lines intersect at right angles at their 0 points. The two number lines are perpendicular.

� The point where the lines meet (0,0) is called the origin.

� Every point on a coordinate grid can be named by an ordered pair of numbers. The first number in the pair is always the horizontal distance of the point from the vertical axis. The second number in the pair is always the vertical distance of the point from the horizontal axis.

Mental Math and ReflexesHave students write numbers in standard notation and number-and-word notation. Ask students to explain how they determined the number of zeros to attach when writing the number in standard notation. Suggestions:

3 ∗ 103 3,000; 3 thousand

5 ∗ 102 500; 5 hundred

9 ∗ 105 900,000; 9 hundred thousand

7 ∗ 106 7,000,000; 7 million

6.5 ∗ 104 65,000; 6.5 ten thousand

3.9 ∗ 105 390,000; 3.9 hundred thousand

Math MessagePlot the following points on the small coordinate grid on journal page 292:

(4,0); (0,4); (0,0); (5,1 1 _ 2 ); (1.25,4.75)

�

Interactive whiteboard-ready

ePresentations are available at

www.everydaymathonline.com to

help you teach the lesson.

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Student Reference Book, p. 208

Student Page


Student Page

Check Your UnderstandingCheck Your Understanding

Draw a coordinate grid on graph paper and plot the following points.

1. (2,4) 2. (�1,�3) 3. (0,5) 4. (�2,2)

Plotting Ordered Number Pairs

A rectangular coordinate grid is used to name points in theplane. It is made up of two number lines, called axes, that meetat right angles at their zero points. The point where the two linesmeet is called the origin.

Every point on a rectangular coordinate grid can be named by anordered number pair. The two numbers that make up anordered number pair are called the coordinates of the point. Thefirst coordinate is always the horizontal distance of the point fromthe vertical axis. The second coordinate is always the verticaldistance of the point from the horizontal axis. For example, theordered pair (3,5) names point A on the grid at the right. Thenumbers 3 and 5 are the coordinates of point A.

Measurement

ExampleExample Plot the ordered pair (5,3).

Step 1: Locate 5 on the horizontal axis. Draw a vertical line.

Step 2: Locate 3 on the vertical axis. Draw a horizontal line.

Step 3: The point (5,3) is located at the intersection of the two lines.

The order of the numbers in an ordered pair is important. Thepair (5,3) does not name the same point as the pair (3,5).

ExampleExample Locate (�2,3), (�4,�1), and (3�12�,0).

For each ordered pair:

Locate the first coordinate on the horizontal axis and draw avertical line.

Locate the second coordinate on the vertical axis and draw ahorizontal line.

The two lines intersect at the point named by the ordered pair.

55

4

3

2

1

10 2 3 4 5

A (3,5)

(0,0)

55

4

3

2

1

10 2 3 4 5

A (5,3)

(0,0)

Check your answers on page 440.

The ordered pair (0,0) names the origin.

55

4

3

2

1

10 2 3 4 5

(3 ,0)1 2

Hidden Treasure Gameboards 1LESSON

9 �1

Date Time

Each player uses Grids 1 and 2.

Grid 1: Hide your point here. Grid 2: Guess other player’s point here.

Use this set of grids to play another game.


0

10

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1

0 1 2 3 4 5 6 7 8 9 10Grid 1

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0 1 2 3 4 5 6 7 8 9 10Grid 2

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0 1 2 3 4 5 6 7 8 9 10Grid 1

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0 1 2 3 4 5 6 7 8 9 10Grid 2


� The numbers in an ordered pair are the coordinates of the corresponding point. To plot the coordinates of a point, first move left or right along the horizontal axis, and then move up or down along the vertical axis.

� One or both coordinates may be a whole number, fraction, decimal, or mixed number.

� When one of the coordinates is 0, the point lies directly on an axis.

Ask volunteers to use the transparency to demonstrate and explain how to plot the Math Message points. Encourage students to make use of the Key Vocabulary terms in their explanations.

Write (3,4) and (4,3) on the board. Ask: Do these coordinates name the same point? No Why? The position of the numbers in an ordered pair determines the axis to be used for each of the coordinates. Unless the numbers are in the same positions in both ordered pairs, they will name different points.

Ask students to suggest ways to remember which axis the coordinates refer to in an ordered number pair. Write their suggestions on the Class Data Pad. For example:

� Alphabetically, horizontal comes before vertical.

� Think about painting the side of a house. You must move the ladder to where you want to paint before climbing up.

� Think about an elevator building. You go across the ground floor first and find the elevator to take you up to where you want to go.

� Think of the proverb: You must crawl before you can walk. Crawling is horizontal. Walking is vertical.

▶ Graphing a Picture

WHOLE-CLASS ACTIVITY

(Math Journal 2, p. 292; Math Masters, p. 438)

Tell students that they are going to graph a representation of the turtle shown at the top of journal page 292 as a class. Use the transparency of Math Masters, page 438 to model plotting and connecting points. Begin the picture by having students mark and label the point at (8,12), which is the tip of the turtle’s nose.

Ask volunteers to suggest whole-number coordinates for the next point on the turtle graph. Have students mark that point on their own graphs and then use a straightedge to connect it to the previous point.

Continue until an outline of the turtle has been drawn on the graph. Remind students that it is not important that their graphs exactly match the picture. Rather, they should choose points that will be a close representation of the picture.

Ask students to label the coordinates of 4 points on their graphs.


Student Reference Book, p. 319

Student Page

Player 1 marks a hiddenpoint at (2,5).

• Player 1 guesses that Player 2’s hidden point is at (1,2) and marks it on Grid 2 in pencil.

• Player 2 marks the point (1,2) in pencil on Grid 1 and tells Player 1 that (1,2) is 7 units(square sides) away from the hidden point.

• Player 1 writes “7” next to the point (1,2) on his or her Grid 2. Player 1’s turn is over, and Player 2 makes a guess.

Player 2 marks a hiddenpoint at (3,7).

Grid 1 Grid 2 Grid 1 Grid 2

Player 1 Player 21 2 3 4 5 6 7 8 9 10

12

43

56789

10

00 1 2 3 4 5 6 7 8 9 10

12

43

56789

10

00

(2,5)

7(1,2)

1 2 3 4 5 6 7 8 9 10

12

43

56789

10

00 1 2 3 4 5 6 7 8 9 10

12

43

56789

10

00

(1,2)

(3,7)

Hidden Treasure

Materials � 1 sheet of Hidden Treasure Gameboards for each player(Math Masters, p. 485)

� 2 pencils� 1 red pen or crayon

Players 2Skill Plotting ordered pairs, developing a search strategyObject of the game To find the other player’s hidden point on acoordinate grid.Directions1. Each player uses 2 grids. Players sit so they cannot see what

the other is writing.2. Each player secretly marks a point on his or her Grid 1. Use the red

pen or crayon. These are the “hidden” points. 3. Player 1 guesses the location of Player 2’s hidden point by naming

an ordered pair. To name the ordered pair (1,2), say “1 comma 2.”4. If Player 2’s hidden point is at that location, Player 1 wins.5. If the hidden point is not at that location, Player 2 marks the

guess in pencil on his or her Grid 1. Player 2 counts the leastnumber of “square sides” needed to travel from the hidden point to the guessed point and tells it to Player 1. Repeat Steps 3–5 with Player 2 guessing and Player 1 answering.

6. Play continues until one player finds the other’s hidden point.

Games

Guess the otherplayer’s point here.

Hide your point here.1 2 3 4 5 6 7 8 9 10

12

43

56789

10

00

Grid 1

1 2 3 4 5 6 7 8 9 10

12

43

56789

10

00

Grid 2


Study Link Master

Matching Graphs to Number StoriesLESSON

9 �1

Date Time

1. Draw a line matching each graph below to the number story that it best fits.

a. Juanita started with $350. She saved another $25 every week.

b. Meredith received $350 for her birthday. She deposited the entire amount in the bank. Every week, she withdrew $50.

c. Julian started a new savings account with $50. Every week after that, he deposited $75.

2. Explain how you decided which graph matches each number story.

3. Circle the rule below that best fits the number story in Problem 1a above.

Savings � $350 � (25 � number of weeks)

Savings � $350 � (25 � number of weeks)

Savings � $350 � number of weeks

Sample answer: Number story b must go with the only graph that shows a decrease. Number stories a and c go with a graph that shows an increase, but Graph B starts at a higher amount.

$0

$300$400$500

$200$100

0 1 2 3 4 5

Graph AAm

ount

Weeks

0$0

$300$400$500

$200$100

1 2 3 4 5

Graph B

Amou

nt

Weeks

$0

$300$400$500

$200$100

0 1 2 3 4 5

Graph C

Amou

nt

Weeks

Lesson 9�1 707

▶ Playing the Hidden PARTNER ACTIVITY

Treasure Game(Math Journal 2, p. 293; Student Reference Book, p. 319;

Math Masters, p. 485)

Ask students whether they have ever played Hot and Cold. It is a game where Player A leaves the room while the others hide some object. Then Player A returns and has to locate the object. The others provide clues by saying whether Player A is “hot” or “cold.” The farther away from the object, the “colder” Player A becomes. The closer to the object, the “warmer” Player A becomes. The game continues until Player A locates the object.

Tell students that Hidden Treasure is a game that is similar to Hot and Cold. Go over the rules on page 319 of the Student Reference Book. Be sure students understand the directions.

Use a transparency of the gameboard (Math Masters, p. 485) to play a sample round showing students how to complete the grids and how to answer a player’s guesses.

Have partners play two or more games. Players write in their own journals, using one of the two gameboards on journal page 293. Note that a gameboard consists of two grids.

00

10987654321

1 2 3 4 5 6 7 8 9 10Grid 1

00

10987654321

1 2 3 4 5 6 7 8 9 10Grid 2


Circulate and assist. Pass out copies of Math Masters, page 485 if additional gameboards are needed.

2 Ongoing Learning & Practice

▶ Matching Number Stories

INDEPENDENT ACTIVITY

to Graphs(Math Journal 2, p. 294)

Students match number stories to line graphs and explain their solution strategies. They also identify the rule that describes one of the stories.

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BBBBBBBBBBBBBBBBBBLELEELEMMMMMMMMMOOOOOOOOOBLBLBLBLBLBLBLBBLBLROOOOROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINNVINVINVINVINVINVV GGGGGGGGGGGOLOOOLOOOLOOLOO VINVINVVLLLLLLLLVINVINVINNVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLOLLOOO VVVVLLLLLLLLLLLVVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOOOSOOSOSOSOSOSOSOSOOOSOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING



Student Page

Math Boxes LESSON

9 �1

Date Time

1. Draw a circle with a radius of 2 centimeters.

What is the diameter of the circle?

2 cm

2. Multiply.

a. 3

_ 8 ∗ 4 _ 7 =

b. 1 1 _ 8 ∗ 2

3

_ 4 =

c. 2 2 _ 3 ∗ 1

3

_ 5 =

d. 2 1 _ 6 ∗ 3 1

_ 4 =

(unit)

4. If you picked a number at random from

the grid below, what is the probability

that it would be an odd number?

3. What is the volume of the rectangular

prism? Circle the best answer.

A 32 units3

B 160 units3

C 130 units3

D 80 units3

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

Fraction

Percent

5. Write a number sentence to represent

the story. Then solve.

Alex earns $8.00 per hour when he

babysits. How much will he earn in

4 1 _ 2 hours?

Number sentence:

Solution:

6. Write the prime factorization of

each number.

a. 38 =

b. 92 =

c. 56 =

d. 72 =

e. 125 =

153 162

197

219

77

128 129

12

4 cm 12

_ 56

, or 3

_ 14

3 3

_ 32

4 4

_ 15

7 1

_ 24

8

_ 15

8.00 × 4 1

_ 2 = 36.00

$36.00

2 ∗ 19

2 ∗ 2 ∗ 23, or 22 ∗ 23

2 ∗ 2 ∗ 2 ∗ 7, or 23 ∗ 7

2 ∗ 2 ∗ 2 ∗ 3 ∗ 3, or 23 ∗ 32

5 ∗ 5 ∗ 5, or 53

53.3 -

%

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STUDY LINK

9 �1 Plotting Points

149 208

Name Date Time

1. Plot the following points on the grid below. After you plot each point,

draw a line segment to connect it to the last point you plotted.

Reminder: Use your straightedge!

(3,6); (11,11); (15,11); (15,7); (7,2); (3,2); (3,6); (7,6)

Draw a line segment connecting (7,6) and (7,2).

Draw a line segment connecting (7,6) and (15,11).

0

1

2

4

3

5

6

7

8

9

10

11

12

13

14

15

1 2 3 4 5 6 7 80 9 10 11 12 13 14 15

2. What 3-dimensional shape could this drawing represent? Rectangular prism

3. a. What ordered pair would name the missing vertex to represent a prism? (11,7) b. Draw the missing vertex, and then add dashed lines for the missing edges.

Practice

4. 3,745 + 8,761 + 791 = 13,297 5. 3.745 + 87.61 + 781 = 872.355

6. 4 3

_ 8 + 5 7 _ 8 = 7. 1

_ 5 + 3

_ 4 = 10 2

_ 8 , or 10

1

_ 4 19

_ 20

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Study Link Master


▶ Math Boxes 9�1


(Math Journal 2, p. 295)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-3. The skill in Problem 5 previews Unit 10 content.

Writing/Reasoning Have students write a response to the following: Explain how you solved Problem 2d. How might you check your answer? Sample answer: I renamed 2 1 _ 6

as 13 _ 6 and renamed 3 1 _ 4 as 13 _ 4 . I multiplied 13 _ 6 ∗ 13 _ 4 = 169 _ 24 . Then I divided 169 by 24 to rename the product as a mixed number. 169 ÷ 24 = 7 1 _ 24 . To check my answer, I would use my calculator to divide 7 1 _ 24 ÷ 3 1 _ 4 = 2 1 _ 6 . Ask students to write a number story for Problem 2d. Answers vary.

▶ Study Link 9�1


(Math Masters, p. 254)

Home Connection Students practice plotting points on a coordinate grid.

3 Differentiation Options

READINESS


▶ Finding Locations on a Map 5–15 Min


To provide experience with coordinate grids, have students identify locations on a map using ordered pairs of numbers. Students used a similar map structure to name points using ordered pairs of numbers in Fourth Grade Everyday Mathematics.

When students have finished, ask volunteers to share their solution strategies. Discuss which locations could be named with more than one point and why. Some locations are areas that contain several points, and other locations are a single place at a single point.

ENRICHMENT


▶ Finding Distances 15–30 Min


To apply students’ understanding of coordinate grids, have them use a grid to compare and analyze distances. Students compare distances across diagonals with distances where only lines along the grid and square corners are allowed.


LESSON

9�1

Name Date Time

A Botanical Garden Map

A fifth-grade class is visiting a botanical garden. They plan to see every attraction and havelunch in the picnic area. Each student has a copy of the map below. They want to useordered pairs of numbers to label each attraction and the picnic area.

Find and plot the ordered pairs of numbers for each location.

School Bus (6,8) Sample answers: Welcome Center

Prairie Plants Rose Garden

Pine Forest Picnic Area

Specimen Forest Japanese Gardens (9,2)(7,3)(7,5)(3,3)(2,7)(11,9)(2,9)

PineForest

WelcomeCenter

Entry Road

Parking Lot

SpecimenForest

JapaneseGardens

Picnic Area

RoseGarden

GardenCafe

Exit Road

PrairiePlants

0 1 2 3 4 5 6 7 8 9 10 11 120

1

2

3

4

5

6

7

8

9

10

11

12

TrailPaved Road

0 0.2 0.4 0.6 0.8 1 km

Scale

(6,8)

N

W E

S

Sample answers:


Teaching Master

Mrs. Thrasher’s fifth-grade class is taking a fieldtrip to two different locations: the aquarium,museum, or planetarium, depending on which two places are closest to each other.

1. Choose where the class should go andconnect the points.

2. Think of the grid lines as streets. Theclass must take the bus, and the bus cantravel along the grid lines only. Whichlocation is closer to the museum now?aquariumIs it the same as your first choice?Answers vary.Why or why not? Answers vary.

At the museum, the class learned about plans for the new Skateboard Park.Everyone thought that it should be located an equal distance from theaquarium, museum, and planetarium by bus.

3. Draw and label a point on the grid that shows where the new Skateboard Parkshould be located.

Maggie said the city should have built Skateboard Parkfirst. You could just draw a circle using Skateboard Parkas the center. Then there would be many locations thatwere the same distance away.

4. Use the grid to the right to check Maggie’s idea.Remember that the bus can go along the gridlines only.Mark every point that is the same distance fromSkateboard Park.

5. Do you agree or disagree with Maggie?

Explain your answer on the back of this page.

disagree

LESSON

9�1

Name Date Time

Traveling the Grid by Bus

Skateboard Park

Scale: 0.75 cm represents 1 block

aquarium museum

planetarium

SkateboardPark

Sample answer:

Sample answers:


Teaching Master

Lesson 9�1 709

When students have finished, ask them to connect the points they plotted in Problem 4. Ask: What shape was formed? A square Discuss why the points did not form a circle. With a circle drawn on a grid, some of the points would be on a diagonal from the center. Because diagonals are not allowed, the shape couldn’t be a circle. Explain that this shape is a taxicab circle because all of the points are equidistant from the center point.

Taxicab geometry was developed by Russian mathematician, Hermann Minkowski. Consider assigning students to explore the interactive taxicab geometry activity on the Annenberg Foundation Web site at http://www.learner.org/teacherslab/math/geometry/shape/taxicab/.

ELL SUPPORT

SMALL-GROUP ACTIVITY

▶ Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 142)

To provide language support for coordinate grids, have students use the Word Bank Template found on Differentiation Handbook, page 142. Ask students to write the terms horizontal axis and vertical axis, draw pictures relating to the terms, and write other related words. See the Differentiation Handbook for more information. Point out the unusual spelling of the plural, axes, and distinguish this meaning from the plural of the cutting tool, ax.


Documents

Hidden Treasure: A Coordinate Game€¦ · LESSON9 Hidden TreasureGameboards 1 1 Date Time Each player uses Grids 1 and 2. Grid 1:Hide your point here. Grid 2:Guess other player’s