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Getting Started: Unit 12 student edition pages 114–116
GSE Focus: ELAGSE1RI4
5 Unpacking the StandardMeanings of Words and Phrases – Students in Grade 1 are expected to use questioning strategies to determine meanings of words and phrases in a text.
Authors use words and phrases in informational texts to teach the reader ideas and concepts associated with the topics of the texts. The reader should ask and answer questions in order to determine definitions of words and phrases.
When teaching students to determine meanings of unknown words, model asking and answering questions such as the following: Do I know the meaning of this word? Have I seen this word in another text? What do I think the word means? Does my idea of the word’s meaning make sense in the sentence? Which print or digital source(s) can help me verify the meaning? Prompt students to ask and answer these questions when they encounter unknown words during independent reading.
6 Instructional Activities Use the following activities to provide instruction and practice for the GSE Focus Standard.
Ask and Answer – Display the passage-specific words. Have students answer the following questions about the words.
• What words do I know?• What words have word parts I know?• What words are similar in spelling?• What words are similar in meaning?• What words have I seen in other texts?• What words can I use correctly in sentences?Guide student responses to the questions as they determine the word meanings.
Sticky Words – Lead discussions with students about habits of skilled readers. Emphasize that skilled readers acknowledge when they encounter words they do not know during reading. Provide students with informational texts and sticky notes. As students read the texts, direct them to use the sticky notes to flag words with unknown meanings. Prompt students to ask and answer questions about the flagged words and the words around them. Allow students to debrief with partners to share what they learned about the words based on their questions and answers.
7 Formative Assessment Provide students with several sentences that contain passage-specific vocabulary words and instruct students to record questions and answers that would help them determine the meanings of words. Use student responses to clarify misconceptions and to plan further instruction or interventions.
Unit 11 Use >, <, or = to Represent Fraction Comparisons 4.3(D) – R . . . . . . . . . . . . . . . . . . . . . 141
Unit 12 Represent and Solve Problems: +/− of Fractions with Equal Denominators 4.3(E) – R . . 151
Unit 13 Use Benchmark Fractions to Evaluate Sums and Differences of Fractions 4.3(F) – S . . . 161
Unit 14 Represent Fractions and Decimals as Distances on Number Lines 4.3(G) – S . . . . . . . . 171
Unit 15 Add and Subtract Whole Numbers and Decimals 4.4(A) – R . . . . . . . . . . . . . . . . . . . . . . 181
Unit 16 Determine Products of a Number x 10 or 100 4.4(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . 191
Unit 17 Use Arrays, Area Models, or Equations to Represent Products 4.4(C) – S. . . . . . . . . . . . 201
Unit 18 Use Strategies and Algorithms to Multiply 4.4(D) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
motivationmath™
Table of Contents
ELA | LEVEL 1Teacher Edition Sample Page
mentoringminds.com
Unit 1
2
mentoringminds.com totalmotivationELA™LEVEL 1 ILLEGAL TO COPY 115
Getting Started: Unit 12 student edition pages 114–116
GSE Focus: ELAGSE1RI4
5 Unpacking the StandardMeanings of Words and Phrases – Students in Grade 1 are expected to use questioning strategies to determine meanings of words and phrases in a text.
Authors use words and phrases in informational texts to teach the reader ideas and concepts associated with the topics of the texts. The reader should ask and answer questions in order to determine definitions of words and phrases.
When teaching students to determine meanings of unknown words, model asking and answering questions such as the following: Do I know the meaning of this word? Have I seen this word in another text? What do I think the word means? Does my idea of the word’s meaning make sense in the sentence? Which print or digital source(s) can help me verify the meaning? Prompt students to ask and answer these questions when they encounter unknown words during independent reading.
6 Instructional Activities Use the following activities to provide instruction and practice for the GSE Focus Standard.
Ask and Answer – Display the passage-specific words. Have students answer the following questions about the words.
• What words do I know?• What words have word parts I know?• What words are similar in spelling?• What words are similar in meaning?• What words have I seen in other texts?• What words can I use correctly in sentences?Guide student responses to the questions as they determine the word meanings.
Sticky Words – Lead discussions with students about habits of skilled readers. Emphasize that skilled readers acknowledge when they encounter words they do not know during reading. Provide students with informational texts and sticky notes. As students read the texts, direct them to use the sticky notes to flag words with unknown meanings. Prompt students to ask and answer questions about the flagged words and the words around them. Allow students to debrief with partners to share what they learned about the words based on their questions and answers.
7 Formative Assessment Provide students with several sentences that contain passage-specific vocabulary words and instruct students to record questions and answers that would help them determine the meanings of words. Use student responses to clarify misconceptions and to plan further instruction or interventions.
MATH | LEVEL 4Teacher Edition Table of Contents
Unit 19 Use Arrays, Area Models, or Equations to Represent Quotients 4.4(E) – S . . . . . . . . . . . 225
Unit 20 Use Strategies and Algorithms to Divide 4.4(F) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
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Graph points in all four quadrants
Vocabulary FocusThe following are essential vocabulary terms for this unit.
axis/axes horizontal quadrant x-coordinate
coordinate plane ordered pair vertical y-axis
coordinates origin x-axis y-coordinate
Vocabulary ActivitySwat the Term
The teacher reads The Fly on the Ceiling by Dr. Julie Glass. The teacher displays an unlabeled, large coordinate plane (with all four quadrants). The large coordinate plane can be a poster, a wall-mounted dry erase or chalkboard, a coordinate plane that is projected, or a coordinate plane created using painter’s tape. Students form two teams. The first player from each team receives a fly swatter from the teacher. The teacher calls a vocabulary term, and the players swat a corresponding location on the grid (e.g., terms include the following: origin, x-axis, y-axis, Quadrant I, Quadrant II, Quadrant III, Quadrant IV, horizontal axis, vertical axis). The player who first swats a correct location wins a point for his/her team. The players are then replaced with the next player from each team, and play continues. The activity can be expanded to include instructions such as the following.
• Swat the quadrant in which the x- and y-coordinates are both positive. (Quadrant I)• Swat the quadrant in which the x- and y-coordinates are both negative. (Quadrant III)• Swat the quadrant in which the x-coordinate is positive and the y-coordinate is negative. (Quadrant IV)• Swat the quadrant in which the x-coordinate is negative and the y-coordinate is positive. (Quadrant II)• Swat the quadrant that contains the ordered pair (-3, -4). (Quadrant III)• Swat the quadrant that contains the ordered pair (2, -6). (Quadrant IV)• Swat the quadrant that contains the ordered pair (- 1 __
2 , 2). (Quadrant II)
• Swat the quadrant that contains the ordered pair (2, 3.5). (Quadrant I)
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4.5(C), 4.5(D) Unit 25 Use Formulas and Models to Solve Problems with Perimeter and Area
Prepare for the Unit Student Pages 199–206
Review the following information to clarify the TEKS before planning instruction.
Reporting Category 3 – Geometry and Measurement
The student will demonstrate an understanding of how to represent and apply geometry and measurement concepts.
Domain – Algebraic Reasoning
TEKS 4.5 – The student applies mathematical process standards to develop concepts of expressions and equations.
Standard – 4.5(C)Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w).
Readiness Standard – 4.5(D)Solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
Mathematical Process TEKS Addressed in This Unit4.1(A), 4.1(B), 4.1(C), 4.1(D), 4.1(F), 4.1(G)
Unpacking the TEKS
Grade 3Students found the perimeters of polygons or found a missing side length when given the perimeter and the remaining side lengths. While students did not formally work with formulas to calculate perimeter or area, they used multiplication of whole numbers related to the number of rows times the number of square units in each row to find the areas of rectangles and reported areas in square units. They also used an additive model for area as they decomposed figures formed by up to three non-overlapping rectangles and understood that the total area of the composite figure could be calculated by finding the sum of the areas of the smaller rectangles.
Grade 4In grade 4, students investigate formulas for perimeter and area using models and tools (e.g., geoboards, tiles, grid paper) and record the findings in whole number measures. Students reason about the relationship between side lengths of rectangles and their perimeters and areas. They will use P = l + w + l + w or P = 2l + 2w for perimeter. Students will also use the formula P = 4s for the perimeter of a square and A = l × w to find the area of a rectangle. Students show their understandings of finding perimeter and area by applying derived formulas to real-world problems. Problems may require students to find a missing side length before computing area, or use a given area and the measure of length or width to determine the missing measure of a side in order to compute perimeter. All calculations to find area and perimeter in grade 4 are limited to whole numbers.
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MATH | LEVEL 6Teacher Edition Sample Page
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Unit 33
TEKS 6.11(A) – Readiness
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Graph points in all four quadrants
Suggested Formative Vocabulary AssessmentOn a sheet of paper, each student draws two perpendicular lines to represent the x- and y-axes, dividing the paper into fourths. The student labels the x-axis, the y-axis, the origin, and each of the four quadrants. In each quadrant, the student records three facts (using complete sentences) about that quadrant. The teacher reviews student work to assess student learning and plans additional instruction as needed.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)5.B, (c)5.G)
Suggested Instructional Activities
1. In pairs, students play Coordinate Plane Battleship. Provide a handout of a coordinate plane for each student. Players mark four points on their planes without showing their partners. In turn, players try to guess the locations of the points by naming coordinates until they have scored four “hits” by guessing the four points marked on the partner’s coordinate plane.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.E)
2. Students work with partners and play a modified version of Connect Four using a coordinate grid and different colors of pencils or markers. In turn, each player names an ordered pair and points to the location to claim a point on the coordinate grid. If the ordered pair is correct, the player records the point in his/her designated color. The first player to correctly name and locate four coordinates in a horizontal, vertical, or diagonal row is the winner. A variation of this game can be played using a coordinate grid marked in fractional units.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)3.D, (c)3.F)
3. Students complete the Get the Picture? Motivation Station activity on page 269 in the student edition. Then students use a full-page coordinate grid to create their own dot-to-dot picture, listing the coordinates in order. Students trade their coordinate lists and complete one another’s dot-to-dot pictures. The teacher displays student creations.(DOK: 3, Bloom’s/RBT: Synthesis/Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E)
4. Students work in groups of three to create a flow chart describing how to graph an ordered pair in a four-quadrant coordinate plane. Each group records their work on a large poster or sheet of butcher paper and presents the flow chart to the class. For each flow chart, the teacher displays an ordered pair, and the students follow the directions on the flow chart to graph the point.(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)5.B)
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Use Formulas and Models to Solve Problems Unit 25 4.5(C), 4.5(D)with Perimeter and Area
Introduction
Activity: (10–15 minutes)
The teacher reads Spaghetti and Meatballs for All by Marilyn Burns. Student pairs use Color Tiles ® to represent the square tables and also use paper clips to represent chairs. Note that the individual tables in the model are all unit squares so a table can be used as a unit of area. Each table can accommodate one chair per side, so the number of chairs (paper clips) is equivalent to the perimeter of a table arrangement. Next, the teacher leads the students to informally define area as the number of square units required to cover a region (as represented by the number of tables or tiles in the models) and perimeter as the distance around the figure (as represented by the number of chairs in the model). The teacher may opt to introduce these ideas as questions, since students may remember the concepts from third grade.
As an extension, students brainstorm methods of finding the areas and perimeters of the models without counting all the tiles or paper clips. Students work together to develop the formulas for area of a rectangle (A = l × w) and perimeter of a rectangle (P = l + w + l + w or P = 2 × (l + w) or P = 2l + 2w). (DOK: 3, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)5.B)
Formative Assessment (5–10 minutes) The teacher asks probing questions to determine students’ understanding of area and perimeter.
• When Mrs. Comfort’s relatives push the tables together, what happens to the total number of people who can eat at the tables? Why? • Is it possible for two rectangles to have the same area but diff erent perimeters? Justify your answer. • In the story, what table arrangement seated the greatest number of people? Why? • How can you prove that the formula A = l × w can be used to calculate the area of a table? • What is a general rule you can use for finding the perimeter of a rectangle? How can you express this rule using numbers and symbols, in which l represents length and w represents width? • Suppose you know that the width of a table is 7 units and the area is 42 square units. How can you find the length? • Suppose a table is square and its area is 25 square units. How can you find its length and width?
Connect to the Student Edition: Introduction, page 199
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MATH | LEVEL 6Teacher Edition Sample Page
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Unit 33
TEKS 6.11(A) – Readiness
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Graph points in all four quadrants
Suggested Formative AssessmentThe teacher reads statements such as those shown below. Students give a thumbs-up if the statement is true and a thumbs-down if the statement is false. The teacher notes areas of misunderstanding and plans additional instruction and/or intervention activities as needed.
• On a coordinate plane, the x-axis is horizontal. (true)• On a coordinate plane, the y-axis is diagonal. (false)• The x- and y-axes are perpendicular. (true)• When plotting a point, always begin at the origin. (true)• When plotting the point (-2, -4), move down 2 spaces and then move left 4 spaces. (false)• When plotting the point (2, -4), move right 2 spaces and then move down 4 spaces. (true)• The ordered pairs (2, -2) and (-2, 2) name the same location on a coordinate plane. (false)• The ordered pair (0, 3) names a point on the y-axis. (true)• The ordered pair (3, 0) names a point on the x-axis. (true)(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I)
Suggested Reflection/Closure Activity
Students reflect on the concepts addressed in the lesson and, in turn, each student shares one new fact or idea learned.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)3.F)
Suggested Formative AssessmentStudents complete the following information as an exit ticket. The teacher provides each student with a slip of paper like the one shown below. Students complete the ticket and give it to the teacher as they leave. The teacher reviews the answers and determines if additional instruction or interventions are needed.
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4.5(C), 4.5(D) Unit 25 Use Formulas and Models to Solve Problems with Perimeter and Area
Vocabulary FocusThe following are essential vocabulary terms for this unit.
area length rectangle square unitdimension model side widthformula perimeter square
Vocabulary Activities
Activity: Word Web (10–15 minutes) The teacher provides a topic for the middle space of a word web. Students complete the webs connecting vocabulary words to everyday activities. An example follows.
installingbaseboardsin a room
installing afence around
a garden
placing aborder arounda bulletin board
completing ahome run in
baseball
decorating theedges of a cake
with frosting
Activities thatInvolve Perimeter
using aweedeateraround the
edges of a yard
Other topics for word webs might include:
• Activities that Involve Area • Activities in Which Dimensions Must be Measured • Objects Measured in Square Units
Formative Assessment (5–10 minutes) Students write short stories about situations in which they would need to determine the area or perimeter of an object or space. Students use a minimum of four vocabulary words in the stories. The teacher gathers and evaluates evidence of understanding demonstrated by student stories and plans additional vocabulary activities as needed. (DOK: 2, RBT: Apply, ELPS: (c)1.E, (c)1.H, (c)5.B, (c)5.G)
Connect to the Student Edition: Vocabulary Activity, page 204
Literature ConnectionsThese literature titles provide additional connections that support the focus standard of the unit. The books may be used as part of an introductory activity, an instructional activity, or a reflection/closure activity to enhance or extend unit concepts. Books may be placed in the classroom library or in a math center for student access.
Chickens on the Move – Pam Pollack and Meg Belviso
Perimeter and Area at the Amusement Park – Dianne Irving
Perimeter, Area, and Volume: A Monster Book of Dimensions – David A. Adler
Racing Around: Perimeter – Stuart J. Murphy
Sam’s Sneaker Squares – Nat Gabriel
Sir Cumference and the Isle of Immeter – Cindy Neuschwander
Spaghetti and Meatballs for All!: A Mathematical Story – Marilyn Burns
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MATH | LEVEL 6Teacher Edition Sample Page
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Unit 33
TEKS 6.11(A) – Readiness
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Graph points in all four quadrants
Interventions
1. The teacher creates a coordinate plane on the floor, marking the x- and y-axes with painter’s tape. The teacher writes ordered pairs of integers on index cards, one ordered pair per card, and gives one card to each student. In turn, each student must walk from the origin to the point designated by the ordered pair on his/her card, explaining the move (e.g., “I am starting at the origin. I am moving 3 spaces to the right and 2 spaces up.”). When a student arrives at the designated point, he/she reads the ordered pair. The teacher continues the activity using ordered pairs of rational numbers.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)3.H)
2. Each student writes his/her initials in large block letters on a coordinate plane. Students place points and label the ordered pairs at significant locations (e.g., the vertices of the angles of a letter) so that the ordered pairs of the points can be used to recreate the points and trace the letters. (DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.H, (c)2.I)
3. Students play a game in groups of four. Each group uses two dice (red and white) and a 1–4 spinner. Each player in the group receives a blank coordinate grid. In turn, each player rolls the dice to determine an ordered pair. (The red die indicates the x-coordinate, and the white die indicates the y-coordinate.) Then the player spins the spinner to determine the quadrant and resulting signs for the ordered pair. The player locates, marks, and labels the correct point on the coordinate grid. Other players must confirm correct placement before play passes to the next player. The object of the game is to be the first player to correctly plot an ordered pair in all four quadrants of his/her coordinate plane.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I, (c)3.E)
4. Students use interactive online sources to play games that involve locating ordered pairs on a coordinate plane.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.F)
Suggested Formative AssessmentThe teacher individually interviews each student in the intervention group. The teacher gives the student a coordinate plane and displays an ordered pair. The student explains how to plot the point. The teacher repeats this several times so the student plots points in all four quadrants. Based on student responses, the teacher modifies instruction and/or plans additional interventions.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I)
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Use Formulas and Models to Solve Problems Unit 25 4.5(C), 4.5(D)with Perimeter and Area
Instructional Activities
Activity 1: (20–30 minutes)
Students use painter’s tape or other colored tape to outline rectangles and squares found on tile floors or walls of the classroom or hallway. The teacher guides students as they identify the lengths and widths of the rectangles in units. Then, the teacher identifies the perimeter of an outlined rectangle and students work together to discover the formula for finding the perimeter of a rectangle. Next, the teacher identifies the area of the same outlined rectangle. The teacher and students work together, as a class, to discover the formula used to calculate the area of a rectangle. The teacher records the formulas on the board and students use them to find the areas and perimeters of the other outlined rectangles and squares. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)4.C)
Activity 2: (20–30 minutes) Given a perimeter, area, and one dimension (e.g., perimeter = 30 units, area = 50 square units, and length = 10 units), small groups work to find and record a rectangle that meets all given specifications. Students use the information to show how the formulas for area and perimeter can be used in reverse to determine the missing dimensions (e.g., A = l × w, so A ÷ l = w). Students then write real-world scenarios that could be applied to the given parameters. Groups exchange and solve problems, using the appropriate formulas. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G, (c)3.H, (c)4.F, (c)4.J, (c)5.B, (c)5.G)
Formative Assessment (5–10 minutes) Students form agreement circles to demonstrate understanding of applying the area and perimeter formulas for rectangles. The teacher develops three or four statements about this concept. Students form a circle in the classroom. The teacher reads the statements one at a time, allows think time, and students then move toward the center of the circle to show agreement with the statement or remain on the circumference of the circle to show disagreement. The teacher then groups students into small groups and provides time for students to discuss and solidify understandings. The teacher uses the results from this assessment to plan additional instruction and/or provide interventions. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G)
Connect to the Student Edition: Guided Practice, page 200, Independent Practice, page 201
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MATH | LEVEL 6Teacher Edition Sample Page
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Unit 33
TEKS 6.11(A) – Readiness
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Graph points in all four quadrants
Extending Student Thinking
Students use grade-appropriate Internet and library resources to research the life and accomplishments of René Descartes, the mathematician credited with the development of the Cartesian plane. Students prepare a presentation for the class by organizing information and graphics on a tri-fold board or by developing a dramatic monologue in which a student poses as Descartes and tells about his life.(DOK: 4, Bloom’s/RBT: Synthesis/Create, ELPS: (c)1.E, (c)4.G, (c)5.G)
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4.5(C), 4.5(D) Unit 25 Use Formulas and Models to Solve Problems with Perimeter and Area
Interventions
Activity 1: (15–20 minutes) The teacher provides pairs or small groups of students with an assortment of Color Tiles® and assigns each group an area, for example, 36 square units. Each group uses the tiles to make as many squares and rectangles as possible with the given area. Repeat the activity with perimeter. The teacher asks students probing questions.
• How many diff erent squares and rectangles were you able to make? • Why does the perimeter of each shape change? • Why doesn’t the area of each shape change? • How would this activity change if you were given a perimeter instead of area? Explain your answer.
Activity 2: (15–20 minutes) The teacher wraps a length of string around the rim of a rectangle to measure the perimeter. The teacher cuts the length of the string to match the perimeter. Then, the teacher straightens the string and measures its length with a ruler. The teacher emphasizes that perimeter is a linear measure. Students use strings to find the perimeters of rectangles on an activity sheet. The teacher emphasizes the connection between the string activity and the formulas for the perimeters of rectangles and squares.
Next, the teacher uses Color Tiles® to cover as much of the surface of a book in rows and columns as possible, and then counts the number of tiles used to cover the surface. The teacher emphasizes that area is a measure of the number of square units contained in a space. Students use Color Tiles® to find the areas of rectangles on an activity sheet. The teacher emphasizes the connection between the tiles and formulas for the areas of rectangles and squares. (DOK: 1, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I)
Formative Assessment (5–10 minutes)
The teacher gives each student three note cards. On the first note card, students draw a rectangle or square and label its length and width or show the length and width using centimeter squares. On the second note card, students write an equation to show how to determine the perimeter of the drawn shape. On the third card, students write an equation to show how to determine the area of the drawn shape. The teacher collects, shuff les, and distributes three cards to each student. Students trade cards with classmates until they have a set of three matched cards. The teacher observes students as they match cards and plans additional instruction and/or interventions as needed. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)4.C, (c)4.F, (c)5.B)
P = 5 + 5 + 3 + 3 A = 5 × 3
5
3
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MATH | LEVEL 6Teacher Edition Sample Page
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Unit 33
TEKS 6.11(A) – Readiness
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Use Formulas and Models to Solve Problems Unit 25 4.5(C), 4.5(D)with Perimeter and Area
Extending Student ThinkingActivity: (complete outside of regular class time)
Students investigate the relationship of the formula for finding the area of a rectangle to the formula for finding the area of a triangle. Students use tangrams to form rectangles. Using their knowledge of area, students generalize and justify a formula for finding the area of a triangle. Students create models using grid paper and/or geoboards to support their generalizations and share their results with the class. (DOK: 3, RBT: Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.G, (c)3.H)
Connect to the Student Edition: Critical Thinking, page 203
Reflection/Closure Activity
Activity: (10–15 minutes) Students draw rectangles and squares on centimeter grid paper. The teacher displays a four-column table on the board with the headings Length, Width, Perimeter, and Area. Student volunteers describe the rectangles by length, width, perimeter, and area. The teacher records students’ measurements on the table. As a class, discuss patterns between the columns. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)2.I, (c)3.D)
Connect to the Student Edition: Journal, page 204, Assessment, page 202, Motivation Station, page 205, Homework, page 206
Critical Thinking TraitsStudents may demonstrate multiple critical thinking traits as they participate in the instructional activities for this unit. For example, on the Critical Thinking page, students should experience the following critical thinking traits: Problem 1—Adapt, Link, Strive; Problem 2—Communicate, Link, Reflect.On the Motivation Station page, students should experience the following critical thinking traits: Adapt, Collaborate, Strive. (See Critical Thinking Traits information in Teacher Resources.)
PartnersIndividual
Key for Recommended Groupings
Groups Whole Class
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Unit 33 IntroductionStandard 6.11(A) – Readiness
1 Which points are located in Quadrant IV?
2 Which point is located at (–4, 0)?
3 What are the coordinates for point D?
4 Which points have a y-value greater than 4?
5 Which points are located in Quadrant II?
6 Which points have an x-value of 0?
7 What is the ordered pair that is located 2 whole units to the right and 3 whole units down from point E?
8 Which points have negative values for both x and y?
9 If points F and I are connected to form a line segment, name another ordered pair on the line segment.
Use the coordinate grid to answer questions 1–9.
x
y
A
E
B
C
D
G
I
L
K
H
J
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6
6
5
4
3
2
1
–1
–2
–3
–4
–5
–6
F
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Introduction
1 Makesha’s rectangular tabletop is 5 feet long and 3 feet wide as shown by the model.
What is the perimeter of Makesha’s tabletop?
Answer: ______________
What is the area of Makesha’s tabletop?
Answer: ______________
2 Mr. Carlson wants to carpet the family room of his house as shown in the diagram. He multiplied 10 14 to determine how much carpet to purchase.
10 ft
14 ft
Why did Mr. Carlson multiply 10 14?
Answer: _______________________
_______________________________
_______________________________
3 Nachele measures her rectangular bedroom ceiling and buys exactly 48 feet of wallpaper border to put around the ceiling. If the length of Nachele’s ceiling is 14 feet, what is the width?
Answer: ______________
Explain how you found your answer.
_______________________________
_______________________________
4 Trevor folds a square sheet of paper in half vertically. He then folds the paper in half horizontally to form 4 congruent squares. The model below represents the paper.
The perimeter of each small square is 48 centimeters. What is the perimeter of Trevor’s original sheet of paper?
Answer: ______________
Explain how you found your answer.
_______________________________
_______________________________
_______________________________
Write and solve an equation to find the area of Trevor’s original sheet of paper.
Answer: ________________________
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Standard 6.11(A) – ReadinessUnit 33 Guided Practice
Use the polygon shown on the coordinate grid to answer questions 1–3.
y
x
2
1
–1
–2
–2 –1 1 2
1 Which ordered pair does NOT represent a vertex of the polygon?
A (– 3 _ 4 , – 1 _ 2 )
B ( 1 _ 4 , 2 1 _ 2 )
C (–1 1 _ 2 , 1 3 __ 4 )
D (1, – 3 _ 4 )
2 Which ordered pair lies inside the polygon and is located in Quadrant IV?
F (– 1 _ 2 , – 3 _ 4 )
G ( 3 _ 4 , – 1 _ 2 )
H (– 1 _ 4 , – 1 _ 2 )
J ( 1 _ 2 , – 3 _ 4 )
3 Which point is located on the perimeter of the polygon?
A (– 1 _ 2 , 2 1 _ 4 )
B (1, – 1 _ 2 )
C ( 3 _ 4 , 2 1 _ 4 )
D (1 1 _ 2 , 3 _ 4 )
Use the map to answer questions 4 and 5.
The routes Tia takes from her house to different places are represented on the grid below.
y
x
Tia’shouse
Store
School
Park
8
6
4
2
–2
–4
–6
–8
–8 –6 –4 –2 2 4 6 8
4 Which ordered pair best represents a point on Tia’s route to the store?
F (–5, 6)
G (–2.5, 0)
H (–2, 5)
J (–3.5, –3)
5 Each unit on the grid represents 1 mile. For Tia to travel from the park to the library, she must go 3 miles south and 5 miles west. Which represents the coordinates of the library?
A (0, –8)
B (10, –8)
C (–8, 0)
D (–8, 10)
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Guided Practice
1 Mr. Edison asks his students to design a rectangular garden with a perimeter of 12 units. Which design does NOT show a garden with a perimeter of 12 units?
A
B
C
D
2 Every evening, Candy jogs around her neighborhood. The block she jogs around is in the shape of a square.
Lemon LanePeach S
treet Pear
Ave
nue
Apple Drive
What formula can Candy use to determine how far she jogs each evening?
F P = 4 s H P = 2 s
G A = s s J A = l w
3 City Park has a children’s wading pool that is surrounded by a rectangular fence. The diagram shows the pool and the fence.
10 meters
8 meterswading pool
Which of the following is a true statement about the area of the wading pool?
A The area of the wading pool is equal to 80 square meters.
B The area of the wading pool is less than 80 square meters.
C The area of the wading pool is equal to 36 meters.
D The area of the wading pool is greater than 80 square meters.
4 Mr. Schilling owns a construction company. He pours a concrete patio that is 54 feet long and 18 feet wide.
18 feet
54 feet
Mr. Schilling pays for concrete by the number of square feet. What is the area of the patio he pours?
F 144 sq ft H 942 sq ft
G 972 sq ft J 486 sq ft
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Unit 33 Independent PracticeStandard 6.11(A) – Readiness
Use the grid to answer questions 1–3.
y
x
Q
TV
U
W
X
S
n
m
54321
–1–2–3–4–5
–5 –4 –3 –2 –1 1 2 3 4 5
l
1 Which of the following are NOT coordinates located on line n?
A (4 1 _ 2 , 1 1 _ 2 )
B (1, –1 1 _ 2 )
C (0, –3)
D (–1 1 _ 2 , –4 1 _ 2 )
2 For which point(s) do the x- and y-coordinates have the same value?
F Point S only
G Points S and W only
H Points S, W, and X only
J Points S, W, X, and V only
3 Points T, S, and U represent 3 vertices of a parallelogram. Which best represents point Y, the fourth vertex of the parallelogram?
A (2, –3 1 _ 2 )
B (1, –3 1 _ 2 )
C ( 1 _ 2 , –3 1 _ 2 )
D (0, –3 1 _ 2 )
Use the grid to answer questions 4 and 5.
y
x
2
1
–1
–2
–2 –1 1 2
4 Which ordered pair represents a point located inside the quadrilateral but outside the pentagon?
F (–0.5, –1.25)
G (–0.25, 0.75)
H (–0.75, –0.5)
J (–1.5, –0.75)
5 Which of the following represents a point in Quadrant III that is located on the perimeter of the pentagon?
A (–1.5, –0.25)
B (–0.75, 0.25)
C (0.75, –1.5)
D (–1.25, –1.25)
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Independent Practice
1 Butch has a square closet in his bedroom. He wants to find the area of the floor of the closet. He measures the length of one side of the floor. What other measurement does Butch need to find the area of the closet floor?
A The width of the closet
B The height of the closet
C The depth of the closet
D He does not need any other measurement.
2 Mrs. Able bought a rectangular rug. The rug has an area of 48 square feet. Which of the following could NOT be the dimensions of Mrs. Able’s new rug?
F Length 16 feet, Width 3 feet
G Length 12 feet, Width 4 feet
H Length 8 feet, Width 6 feet
J Length 9 feet, Width 5 feet
3 Mrs. Gardner is paving the sidewalk in front of her home with square tiles. The perimeter of each tile is 40 inches. Which pair of equations can be used to find the area of each tile in square inches?
A 40 4 10, and 10 10 20
B 40 4 160, and 160 10 1,600
C 40 4 10, and 10 10 100
D 40 4 44, and 44 4 11
4 Melinda has a rectangular flower garden. The width of her garden is 5 feet. Melinda uses 60 feet of edging to go around the garden. What is the length, in feet, of Melinda’s garden?
Record your answer and fill in the bubbles on the grid below. Be sure to use the correct place value.
0123456789
0123456789
0123456789
0123456789
0123456789
5 Brad’s family is building a new house. The carpenter allowed Brad to help him calculate the length of baseboard needed to go around the bases of the walls in the dining room. This figure shows Brad’s dining room.
10 ft16 ft
10 ft
baseboard
Which of the following expressions could be used to find the total length, in feet, of baseboard needed?
A 10 16
B (2 10) (2 16)
C 16 10 10
D 10 (16 10)
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Standard 6.11(A) – ReadinessUnit 33 Assessment
Use the grid to answer questions 1–6.
y
x
A
F G
HJ
C
B 2
1
–1
–2
–2 –1 1 2
1 Which ordered pair represents a point inside both the triangle and the rectangle?
A (0.2, 1)
B (0.8, 0.4)
C (–0.6, 1.2)
D (–0.4, –1.4)
2 Which of the following represents a point in Quadrant IV that is located at a vertex of one of the figures?
F (1.2, –1.2)
G (–2.4, –1.2)
H (2.2, –1.6)
J (–0.6, 1.6)
3 Which best describes the signs of all coordinates located in Quadrant II?
A (–x, –y)
B (–x, y)
C (x, –y)
D (x, y)
4 A right triangle is formed using points C and H as two of the vertices. Which point best represents the coordinates for point X, the third vertex of the triangle?
F (1.2, –1.8)
G (1.8, –2.6)
H (2.2, –1)
J (2.2, –1.2)
5 Which ordered pair represents an intersection of two line segments?
A (0, –1.6)
B (–1.2, 1)
C (–1, –1.2)
D (0.8, –1.2)
6 Which ordered pair represents a point located inside the triangle but outside the rectangle?
F (–0.2, 1.4)
G (–1.2, –0.2)
H (–0.4, –1.4)
J (0.4, –0.8)
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Assessment
1 Travis built a stage for the Summer Theater Company. The area of the stage is 720 square feet.
720 square feet
Which could be the dimensions of the stage?
A Length 40 C Length 35 Width 19 Width 15
B Length 36 D Length 35 Width 20 Width 21
2 Ali bought 2 picture frames. The rectangles represent the sizes of the frames.
16 cm6 cm
19 cm 8 cm
What is the difference, in square centimeters, between the areas of the two picture frames?
Record your answer and fill in the bubbles on the grid below. Be sure to use the correct place value.
0123456789
0123456789
0123456789
0123456789
0123456789
3 Shelby’s parents want to place a fence around a new dog pen in the backyard. The length of the pen is 17 feet, and the width is 15 feet. How many feet of fencing do they need to buy?
A 64 feet C 255 feet
B 32 feet D 510 feet
4 Which equation CANNOT be used to determine the perimeter of the square below?
5 in.
5 in.
F 4 5 P
G 5 5 5 5 P
H (2 5) (2 5) P
J 5 5 P
5 The framed painting in Ping’s room has dimensions of 16 inches wide and 20 inches long. Ping took the painting down and replaced it with a framed painting that is 1 inch longer and 1 inch wider than the old one. What is the area of the new painting?
A 896 square inches
B 357 square inches
C 120 square inches
D 74 square inches
4
MATH | LEVEL 6Student Edition Sample Page
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Standard 6.11(A) – Readiness Unit 33 Critical Thinking
Use the grid to answer the questions that follow.
x
y
10
8
6
4
2
–2
–4
–6
–8
–10
–10 –8 –6 –4 –2 2 4 6 8 10
1 An ordered pair is located in Quadrant III. The x-coordinate is greater than the y-coordinate. List 3 possible ordered pairs that meet this criteria.
__________ __________ __________
2 Draw a line segment on the coordinate plane above using the following criteria:
• One endpoint must be located in Quadrant IV.
• The line segment must intersect the y-axis but must NOT intersect the x-axis.
In which quadrant or quadrants does the line segment lie? ________________________
What are the endpoints of the line segment? ____________________________________
If the x- and y-coordinates of the endpoint located in Quadrant IV are reversed, describe what happens to the point’s location.
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Unit 25 Critical Thinking
1 Dell, Anna, Mason, and Jenna each have their own bedroom. The floor of each bedroom has a different area. The areas are 120 square feet, 121 square feet, 128 square feet, and 132 square feet. Use the clues below to determine which bedroom belongs to each child.
• Mason’s bedroom floor is a perfect square.
• Anna’s bedroom floor has the same width as Mason’s, but its length is longer.
• Jenna’s floor has a length that is twice its width and a perimeter of 48 feet.
• The width of Dell’s bedroom floor is 1 foot less than the width of Mason’s floor, and the length is the same as the length of Anna’s floor.
Complete the table to show which bedroom belongs to each child, and record the dimensions of the rooms.
Bedroom Dimensions
Child Area Length Width
Dell
Anna
Mason
Jenna
Analysis
Analyze
2 Mrs. Davis plans for 2 fourth-grade classes to watch a movie. She arranges 39 carpet squares so that every student has one carpet square to sit on while watching the movie. After Mrs. Davis arranges the carpet squares, Maria counts to find that the perimeter of the sitting area is 32 units. In the space below, draw a diagram to show how the carpet square arrangement might look.
Synthesis
Create
4
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Standard 6.11(A) – ReadinessUnit 33 Journal/Vocabulary Activity
Explain to a younger student what happens when an ordered pair is not plotted in the correct order.
Use the terms in the box to correctly label the picture shown. Each term is used only once.
x-coordinate Quadrant III coordinate plane x-axis
y-axis origin Quadrant I point Quadrant IV
y-coordinate Quadrant II ordered pair
(–3, –4) (1, –4.5)
1.
2.
3.
4.
5.
6.
11.
12.
8.
10.
9.
7.
Vocabulary Activity
Analysis
Analyze
Journal
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Journal/Vocabulary Activity
Think about what you know about the perimeter and area of a rectangle. Draw all possible rectangles with an area of 36 square units. Label the lengths and widths of the rectangles, then find the perimeter of each rectangle.
What generalization can you make about the perimeters of rectangles in relation to the shapes of the rectangles (long and thin versus square)?
Work in groups of 3-5. Write the vocabulary words from the word bank on index cards. Shuffle the cards and place them face down in the middle of the group.
In turn, each player selects the top card and, using a pencil and paper clip, spins the spinner. The player must use the method shown on the spinner to try to get the other players in the group to say the word. The first player to state the correct word scores 1 point, and the person giving the clues scores 1 point. When all words have been used, the cards may be reshuffled, and the game may be replayed.
Vocabulary Activity
JournalAnalysis
Analyze
Usemotions
orgestures.
Draw apicture.
Usewords
todescribe.
Word Bank
area length side
dimension perimeter square
formula rectangle square unit
width
4
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Unit 33 Motivation StationStandard 6.11(A) – Readiness
Get the Picture?
Complete Get the Picture? individually. Plot the ordered pairs listed below, and then connect them in the order they are shown to reveal a picture.
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Unit 25 Motivation Station
Motivation Mike says, “You’ve outdone yourself!”
Capture the Block
Play Capture the Block with a partner. Each player uses a different color to create rectangular blocks on the game board. In turn, players roll two dice. The product of the numbers rolled indicates the number of line segments a player may draw to try to create a rectangular block. For example, if a player rolls 4 and 6, the player marks 24 line segments on the game board. The player may choose to draw a closed figure with a perimeter of 24 units, or the player may choose to simply mark 24 units of a larger block, hoping to complete the block on another turn. The player who closes any rectangular block is the one who captures the block. Blocks created must include whole squares only (no diagonals). When a player closes a block, he/she colors the area and records both the area and perimeter in the space. The winner is the player with the greater total area.
Player 1 Player 2
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Standard 6.11(A) – ReadinessUnit 33 Homework
1. Research jobs that use the coordinate plane. Select 2 different jobs and write one paragraph about each, explaining how the coordinate plane is used and why it is important to that job. Share with the class.
2. Use string and stakes to create a coordinate plane in the yard. Take turns with friends and family tossing a beanbag, or a similar object, onto the grid. Give the coordinates of the location where the object lands. If correct, the person earns a point. The winner is the person with the most points.
1 Plot a point that lies on AB, and label it Q.
2 What are the coordinates for point Q?
3 List the ordered pairs for each labeled point that lies in Quadrant II.
4 List one ordered pair that lies on the circle and inside the rectangle.
5 List one ordered pair that lies inside the circle and that is located in Quadrant IV.
6 Plot a point that could be used to complete a rectangle that is twice the area of triangle MNP. Label the point R. What are the coordinates for point R?
7 Plot point (x, y) where x < 0 and x · y > 0. Label the point S. Explain how you determined where to plot point S.
___________________________________
___________________________________
8 In which quadrant does point S lie?
9 In which quadrant does point J lie? Explain. ___________________________________
___________________________________
Connections
Use the coordinate grid to answer questions 1–9.
y
x
A
B
F C
E D
J
M
N P
4
3
2
1
–1
–2
–3
–4
–4 –3 –2 –1 1 2 3 4
Name __________________________________________
Standards 4.5(C), 4.5(D) – Readiness
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Unit 25 Homework
✁
1. Use small square crackers (saltines, graham crackers) to create a rectangle. Work with your child to identify the perimeter of the cracker rectangle. Have your child draw the rectangle on paper and record the perimeter and area. Then challenge your child to make and record as many rectangles as possible with the same perimeter but different areas. Repeat the activity and find rectangles with the same area but different perimeters.
2. Have your child use a measuring tape to find the lengths and widths of rectangular rooms in the house to the nearest whole foot. Use the dimensions to find the perimeter of each floor by adding the lengths. Use the dimensions to find the area of each floor by multiplying the length and width.
Parent Activities
1 Carmen plans to put plastic edging around a rectangular flower bed. The width of the flower bed is 12 feet, and the length is twice the width. What is the perimeter of Carmen’s flower bed?
Answer: ______________
Carmen decides to spread fertilizer over the top of the flower bed. She purchases a bag of fertilizer.
FERTILIZER
Will Carmen have enough fertilizer for the flower bed?
Answer: ______________
Explain your answer.
_______________________________
_______________________________
_______________________________
2 Several Olympic sports are played on indoor courts. The table shows three Olympic sports and the dimensions, in feet, of the rectangular courts on which they are played. Find the areas and perimeters of the courts.
Sport l w P A
Basketball 28 15
Volleyball 18 9
Badminton 13 6
3 Liam’s dad built a deck in the backyard. The rest of the yard is planted with grass. A diagram of the backyard is shown.
