Hidden Treasure: A Coordinate Game. Assessment Management. Matching Number Stories to Graphs

Transcription

1 Hidden Treasure: A Coordinate Game Objective To reinforce students understanding of coordinate grid structures and vocabulary. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Translate numbers written in scientific notation into standard notation and number-and-word notation. [Number and Numeration Goal ] Use ordered pairs of numbers to name, locate, and plot points in the first quadrant of a coordinate grid. [Measurement and Reference Frames Goal ] Key Activities Students 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 ] Key Vocabulary coordinate grid axes perpendicular origin ordered pair of numbers vertical axis horizontal axis coordinate Materials Math Journal, pp. and Student Reference Book, pp. and Math Masters, p. transparencies of Math Masters, pp.,, and Class Data Pad slate straightedge red pencil or crayon Matching Number Stories to Graphs Math Journal, p. Students match number stories to line graphs and explain their solution strategies. Math Boxes Math Journal, p. Geometry Template compass Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. straightedge Students practice and maintain skills through Study Link activities. READINESS Finding Locations on a Map Math Masters, p. Students locate points on a map. ENRICHMENT Finding Distances Math Masters, p. straightedge computer with Internet access Students use gridlines to identify point-to-point distances on a grid. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. Students write, define, and illustrate the terms horizontal axis and vertical axis. Advance Preparation For Part, make transparencies of Math Masters, pages,, and. Copies of Math Masters, page 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, ). Teacher s Reference Manual, Grades pp., Unit Coordinates, Area, Volume, and Capacity

2 Getting Started Mental Math and Reflexes Have 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:,; thousand ; hundred,; hundred thousand,,; million.,;. ten thousand.,;. hundred thousand Mathematical Practices SMP, SMP, SMP, SMP, SMP Content Standards.NBT.,.NF.a,.G.,.G. Math Message Plot the following points on the small coordinate grid on journal page : (,); (,); (,); (, _ ); (.,.) 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 ] Teaching the Lesson Math Message Follow-Up (Math Journal, p. ; Student Reference Book, p. ; Math Masters, p. ) WHOLE-CLASS Use a transparency of Math Masters, page 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 points. The two number lines are perpendicular. The point where the lines meet (,) 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. Date Plotting a Turtle 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 (,). Interactive whiteboard-ready epresentations are available at to help you teach the lesson. Sample answer: (,) (,) XXXXXXXXX, Math Journal p., XXX p. -_EMCS_S_G_MJ_U_.indd // : PM Lesson

3 Measurement Check Your Understanding Plotting Ordered Number Pairs A rectangular coordinate grid is used to name points in the plane. It is made up of two number lines, called axes, that meet at right angles at their zero points. The point where the two lines meet is called the origin. Every point on a rectangular coordinate grid can be named by an ordered number pair. The two numbers that make up an ordered number pair are called the coordinates of the point. The first coordinate is always the horizontal distance of the point from the vertical axis. The second coordinate is always the vertical distance of the point from the horizontal axis. For example, the ordered pair (,) names point A on the grid at the right. The numbers and are the coordinates of point A. Example Plot the ordered pair (,). Step : Locate on the horizontal axis. Draw a vertical line. Step : Locate on the vertical axis. Draw a horizontal line. Step : The point (,) is located at the intersection of the two lines. The order of the numbers in an ordered pair is important. The pair (,) does not name the same point as the pair (,). Example Locate (,), (, ), and (,). For each ordered pair: Locate the first coordinate on the horizontal axis and draw a vertical line. Locate the second coordinate on the vertical axis and draw a horizontal line. The two lines intersect at the point named by the ordered pair. Draw a coordinate grid on graph paper and plot the following points.. (,). (, ). (,). (,) Check your answers on page. Student Reference Book, p. A (,) (,) The ordered pair (,) names the origin. A (,) (,) (,) 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, 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 (,) and (,) 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. Date Hidden Treasure Gameboards Each player uses Grids and. Grid : Hide your point here. Grid Use this set of grids to play another game. Grid : Hide your point here. Grid : Guess other player s point here. Grid Grid : Guess other player s point here. Graphing a Picture (Math Journal, p. ; Math Masters, p. ) WHOLE-CLASS Tell students that they are going to graph a representation of the turtle shown at the top of journal page as a class. Use the transparency of Math Masters, page to model plotting and connecting points. Begin the picture by having students mark and label the point at (,), 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 points on their graphs. Grid Grid Math Journal, p. Unit Coordinates, Area, Volume, and Capacity

4 Playing the Hidden Treasure Game (Math Journal, p. ; Student Reference Book, p. ; Math Masters, p. ) PARTNER 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 of the Student Reference Book. Be sure students understand the directions. Use a transparency of the gameboard (Math Masters, p. ) 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. Note that a gameboard consists of two grids. Hidden Treasure Player marks a hidden point at (,). Grid Grid Materials sheet of Hidden Treasure Gameboards for each player (Math Masters, p. ) pencils red pen or crayon Players Skill Plotting ordered pairs, developing a search strategy Object of the game To find the other player s hidden point on a coordinate grid. Directions. Each player uses grids. Players sit so they cannot see what the other is writing.. Each player secretly marks a point on his or her Grid. Use the red pen or crayon. These are the hidden points.. Player guesses the location of Player s hidden point by naming an ordered pair. To name the ordered pair (,), say comma.. If Player s hidden point is at that location, Player wins.. If the hidden point is not at that location, Player marks the guess in pencil on his or her Grid. Player counts the least number of square sides needed to travel from the hidden point to the guessed point and tells it to Player. Repeat Steps with Player guessing and Player answering.. Play continues until one player finds the other s hidden point. Player marks a hidden point at (,). Grid Student Reference Book, p. Grid Games Hide your point here. Grid Guess the other player s point here. Grid (,) (,) (,) (,) Player Player EMCS_S_SRB_G_GAM_.indd Player guesses that Player s hidden point is at (,) and marks it on Grid in pencil. Player marks the point (,) in pencil on Grid and tells Player that (,) is units (square sides) away from the hidden point. Player writes next to the point (,) on his or her Grid. Player s turn is over, and Player makes a guess. // : PM Grid : Hide your point here. Grid : Guess other player s point here. Grid Grid Circulate and assist. Pass out copies of Math Masters, page if additional gameboards are needed. Ongoing Learning & Practice Matching Number Stories to Graphs (Math Journal, p. ) PROBLEM SOLVING Students match number stories to line graphs and explain their solution strategies. They also identify the rule that describes one of the stories. Date Matching Graphs to Number Stories. Draw a line matching each graph below to the number story that it best fits. a. Juanita started with $. She saved Graph A another $ every week. $ $ $ $ $ $ Weeks b. Meredith received $ for her birthday. She deposited the entire amount in the bank. Every week, she withdrew $. c. Julian started a new savings account with $. Every week after that, he deposited $.. Explain how you decided which graph matches each number story. 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.. Circle the rule below that best fits the number story in Problem a above. Savings = $ + ( number of weeks) Savings = $ - ( number of weeks) Savings = $ number of weeks Math Journal, p. Amount Amount Amount Graph B $ $ $ $ $ $ Weeks Graph C $ $ $ $ $ $ Weeks -_EMCS_S_G_MJ_U_.indd // : PM Lesson

5 Date Math Boxes cm. Draw a circle with a radius of centimeters.. Multiply. What is the diameter of the circle? _ a. _ = (unit). What is the volume of the rectangular prism? Circle the best answer. A units B units C units D units. Write a number sentence to represent the story. Then solve. Alex earns $. per hour when he babysits. How much will he earn in _ hours? Number sentence:. _ =. $. Solution: Math Journal, p. -_EMCS_S_G_MJ_U_.indd cm _, or b. _ _ = _ c. _ _ = _ d. _ _ =. If you picked a number at random from the grid below, what is the probability that it would be an odd number? Fraction Percent. Write the prime factorization of each number. a. = b. = c. = d. = e. = _ -. %, or, or, or, or // : PM Math Boxes (Math Journal, p. ) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit content. Writing/Reasoning Have students write a response to the following: Explain how you solved Problem d. How might you check your answer? Sample answer: I renamed _ as _ and renamed _ as _. I multiplied _ _ = _. Then I divided by to rename the product as a mixed number. = _. To check my answer, I would use my calculator to divide _ _ = _. Ask students to write a number story for Problem d. Answers vary. Study Link (Math Masters, p. ) Home Connection Students practice plotting points on a coordinate grid. Differentiation Options READINESS Finding Locations on a Map (Math Masters, p. ) Min Study Link Master Name Date STUDY LINK Plotting Points. 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! (,); (,); (,); (,); (,); (,); (,); (,) Draw a line segment connecting (,) and (,). Draw a line segment connecting (,) and (,). 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.. What -dimensional shape could this drawing represent? Rectangular prism. a. What ordered pair would name the missing vertex to represent a prism? (,) b. Draw the missing vertex, and then add dashed lines for the missing edges. Practice., +, + =, =. _, or. _ + _ =. _ + _ = ENRICHMENT Finding Distances (Math Masters, p. ) 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. Math Masters, p. - EMCS_B_MM_G_U_.indd // : PM Unit Coordinates, Area, Volume, and Capacity

6 When students have finished, ask them to connect the points they plotted in Problem. 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 Name Date A Botanical Garden Map A fifth-grade class is visiting a botanical garden. They plan to see every attraction and have lunch in the picnic area. Each student has a copy of the map below. They want to use ordered pairs of numbers to label each attraction and the picnic area. N Teaching Master Welcome Center Rose Garden Scale.... km Sample answers: Entry Road Garden Cafe Parking Lot (,) Picnic Area W S Exit Road E Prairie Plants ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. ) SMALL-GROUP Min To provide language support for coordinate grids, have students use the Word Bank Template found on Differentiation Handbook, page. 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. Specimen Pine Forest Forest Japanese Gardens Paved Road Trail Find and plot the ordered pairs of numbers for each location. School Bus (,) Sample answers: Welcome Center (,) Prairie Plants (,) Rose Garden (,) Pine Forest (,) Picnic Area (,) (,) Specimen Forest Japanese Gardens (,) Math Masters, p. Teaching Master Name Date Traveling the Grid by Bus 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. Sample answers:. Choose where the class should go and connect the points. Skateboard Park. Think of the grid lines as streets. The class must take the bus, and the bus can travel along the grid lines only. Which location is closer to the museum now? aquarium aquarium museum planetarium Is it the same as your first choice? Answers vary. Why or why not? Answers vary. Scale:. cm represents block At the museum, the class learned about plans for the new Skateboard Park. Everyone thought that it should be located an equal distance from the aquarium, museum, and planetarium by bus.. Draw and label a point on the grid that shows where the new Skateboard Park should be located. Maggie said the city should have built Skateboard Park first. You could just draw a circle using Skateboard Park as the center. Then there would be many locations that were the same distance away. Sample answer:. 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 from Skateboard Park.. Do you agree or disagree with Maggie? Explain your answer on the back of this page. disagree Skateboard Park Math Masters, p. Lesson