Texas Teacher Guide TM Test & ple Lesso m a Teacher Guide n S Mathematics Table of Contents Correlation Charts Sample Lesson uction r t s n I y d a Re with is updated t the lates nce TEA guida
Table of Contents Ready Program Overview................................A5 Ready and Test Ways.to.Use. Ready Books...............................................................A6 Getting.Started.with. Ready Books.............................A7 Testing.with. Ready Test..............................A8 Teaching.with. Ready.............................A10 i-ready Going.Online.with. i-ready................................a12 Ways.to.Use. i-ready.and. Ready Books.....................A1 Getting.Started.with. i-ready.and. Ready Books.................A15 Features of Ready............................A16 Supporting Research......................................A26 Correlation Charts.Correlations.to.the.-Assessed.TEKS.in.Mathematics...................A29. Ready Test.Questions.by.TEKS.Standards...................A33 Ready Test Scoring Guide.........................A39 Lesson Plans (with Answers) Reporting Category 1 Numbers, Operations, and Quantitative Reasoning Lesson.1. Read,.Write,.Compare,.and.Order.Whole.Numbers........1 Lesson.2. Read,.Write,.Compare,.and.Order.Decimals............7 Lesson.3. Equivalent.Fractions.......................13 Lesson.. Compare.and.Order.Fractions.................19 Lesson.5. Fractions.Greater.Than.1....................25 Lesson.6. Decimal.and.Fraction.Relationships...............31 Lesson.7. Add.and.Subtract.Whole.Numbers...............37 Lesson.8. Add.and.Subtract.Decimals...................3 Lesson.9. Arrays.and.Area.Models.....................9 Lesson.10. Model.Multiplication.and.Division................55.1.A.1.B.2.A.2.C.2.B.2.D.3.A.3.B..A..B TEKS
Reporting Category 1 (continued) Lesson.11. Basic.Multiplication.Facts....................61 Lesson.12. Multiply.Whole.Numbers.....................67 Lesson.13. Divide.Whole.Numbers.....................73 Lesson.1. Round.Whole.Numbers.....................79 Lesson.15. Estimation.and.Problem.Solving.................85..C..D..E.5.A.5.B TEKS Reporting Category 2 Patterns, Relationships, and Algebraic Reasoning Lesson.16. Fact.Families..........................91 Lesson.17. Number.Patterns........................97 Lesson.18. Related.Number.Pairs......................103.6.A.6.B.7.A TEKS Reporting Category 3 Geometry and Spatial Reasoning Lesson.19. Angles..............................109 Lesson.20. Lines..............................115 Lesson.21. Geometric.Figures........................121 Lesson.22. Translations,.Reflections,.and.Rotations.............127 Lesson.23. Lines.of.Symmetry........................133 Lesson.2. Locate.and.Name.Points.on.a.Number.Line...........139 TEKS.8.A.8.B.8.C.9.B.9.C.10.A Reporting Category Measurement Lesson.25. Estimate.and.Measure.Using.Customary.and.Metric.Units....15 Lesson.26. Convert.Units.of.Measurement.................151 Lesson.27. Measure.and.Estimate.Volume..................157 Lesson.28. Time.and.Temperature......................163 TEKS.11.A,.11.E.11.B.11.C,.11.D.12.A,.12.B Reporting Category 5 Probability and Statistics Lesson.29. Combinations..........................169 Lesson.30. Bar.Graphs...........................175 TEKS.13.A.13.B
Correlation Charts Correlations to the -Assessed TEKS in Mathematics The chart below correlates each test item in Ready Mathematics Test, Grade to a Reporting Category and TEKS standard. The chart also indicates the corresponding lesson in Ready Mathematics, Grade that provides comprehensive instruction for that TEKS standard. Use this chart to determine which lessons your students need. Reporting Categories and TEKS Standards Ready and Test Test 1 Test Item Numbers Test 2 Test 3 Lesson(s) Reporting Category 1: Numbers, Operations, and Quantitative Reasoning The student will demonstrate an understanding of numbers, operations, and quantitative reasoning..1 Numbers, operations, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. The student is expected to A use place value to read, write, compare, and order whole numbers through 999,999,999. Supporting Standard 11 31 Lesson 1 B use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using [concrete objects and] pictorial models. Readiness Standard 1, 19, 23 1, 3, 5 3, 9, 26 Lesson 2.2 Numbers, operations, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to A use [concrete objects and] pictorial models to generate equivalent fractions. Supporting Standard 35 2 Lesson 3 B model fraction quantities greater than one using [concrete objects and] pictorial models. Supporting Standard 12 36 Lesson 5 C compare and order fractions using [concrete objects and] pictorial models. Supporting Standard 17 2 Lesson D relate decimals to fractions that name tenths and hundredths using [concrete objects and] pictorial models. Readiness Standard 3, 6 8, 21 10, 32 Lesson 6.3 Numbers, operations, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. The student is expected to A use addition and subtraction to solve problems involving whole numbers. Supporting Standard 1 Lesson 7 B add and subtract decimals to the hundredths place using [concrete objects and] pictorial models. Supporting Standard 1 5 Lesson 8. Numbers, operations, and quantitative reasoning. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to A model factors and products using arrays and area models. Supporting Standard 17 Lesson 9 B represent multiplication and division situations in picture, word, and number form. Supporting Standard 28 29 Lesson 10 C recall and apply multiplication facts through 12 3 12. Supporting Standard 18 17 Lesson 11 D use multiplication to solve problems (no more than two digits times two digits without technology). Readiness Standard 3, 27, 39 7, 29, 33, 18, 2 Lesson 12 A29
Reporting Categories and TEKS Standards Reporting Category 1 (continued) E use division to solve problems (no more than one-digit divisors and three-digit dividends without technology). Readiness Standard Ready and Test Test 1 Test Item Numbers Test 2 Test 3 Lesson(s) 8, 33 15, 22 20, 7 Lesson 13.5 Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to A round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations. 5 26 Lesson 1 Supporting Standard B use strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems. Supporting Standard 37 1 Lesson 15 Reporting Category 2: Patterns, Relationships, and Algebraic Thinking The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning..6 Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. The student is expected to A use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division number 2 31 1 Lesson 16 sentences (fact families) such as 9 3 9 5 81 and 81 9 5 9). Supporting Standard B use patterns to multiply by 10 and 100. Supporting Standard 36 38 3 Lesson 17.7 Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships. The student is expected to A describe the relationship between two sets of related data such as ordered pairs in a table. Readiness Standard 13, 1, 28, 8 6, 12, 1, 6 16, 2, 38, Lesson 18 Reporting Category 3: Geometry and Spatial Reasoning The student will demonstrate an understanding of geometry and spatial reasoning..8 Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to A identify and describe right, acute, and obtuse angles. Supporting Standard 9 13 37 Lesson 19 B identify and describe parallel and intersecting (including perpendicular) lines using [concrete objects and] pictorial 32 30 5 Lesson 20 models. Supporting Standard C use essential attributes to define two- and three-dimensional geometric figures. Readiness Standard 20, 31, 38 5, 9, 23 15, 25, 6 Lesson 21.9 Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to B use translations, reflections, and rotations to verify that two shapes are congruent. Readiness Standard, 15, 29 3, 25, 39 19, 28, 1 Lesson 22 C use reflections to verify that a shape has symmetry. Supporting Standard 21 7 39 Lesson 23.10 Geometry and spatial reasoning. The student recognizes the connection between numbers and their properties and points on a line. The student is expected to A locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths. Readiness Standard 6, 25, 2, 19, 2 6, 11, 23 Lesson 2 A30
Reporting Categories and TEKS Standards Ready and Test Test 1 Test Item Numbers Test 2 Test 3 Lesson(s) Reporting Category : Measurement The student will demonstrate an understanding of the concepts and uses of measurement..11 Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to A estimate and use measurement tools to determine length (including perimeter), area, capacity, and weight/mass using 11, 2, 3 18, 2, 37 7, 27, 35 Lesson 25 standard units SI (metric) and customary. Readiness Standard B perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system. 30 0 Lesson 26 Supporting Standard C use [concrete] models of standard cubic units to measure volume. Supporting Standard 5 20 21 Lesson 27 D estimate volume in cubic units. Supporting Standard 22 36 8 Lesson 27 E explain the difference between weight and mass. Supporting Standard 22 Lesson 25.12 Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to A use a thermometer to measure temperature and changes in temperature. Supporting Standard 10 10 13 Lesson 28 B use tools such as a clock with gears or a stopwatch to solve problems involving elapsed time. Supporting Standard 16 0 Lesson 28 Reporting Category 5: Probability and Statistics The student will demonstrate an understanding of probability and statistics..13 Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The student is expected to A use [concrete objects or] pictures to make generalizations about determining all possible combinations of a given set of data or 35 27 33 Lesson 29 of objects in a problem situation. Supporting Standard B interpret bar graphs. Readiness Standard 7, 26, 0, 7 16, 32, 3, 8 12, 30, 3, 8 Lesson 30 Underlying Processes and Mathematical Tools.1 Underlying processes and mathematical tools. The student applies Grade mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to A identify the mathematics in everyday situations. 8, 11, 1, 3 B solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. C select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. D use tools such as real objects, manipulatives, and technology to solve problems. 7, 18, 2, 26, 27, 30, 33, 39, 0, 7 3, 35, 15, 2, 36, 0, 1, 6 16, 17, 28, 29, 32, 3, 8 6, 7, 12, 1, 27, 31, 33, 38 8, 17, 22, 27, 31, 35, 7, 12, 20, 30, 33, 2, 3, 5 1, 18, 2, 3, 39, 7 10, 16 10, 18, 13, 0 * * * * *The underlying process and mathematical tools skills are addressed throughout the student book. A31
Reporting Categories and TEKS Standards Underlying Processes and Mathematical Tools (continued) Ready and Test Test 1 Test Item Numbers Test 2 Test 3.15 Underlying processes and mathematical tools. The student communicates about Grade mathematics using informal language. The student is expected to A explain and record observations using objects, words, pictures, numbers, and technology., 6, 9, 12, 13, 15, 17, 19, 20, 25, 29, 31, 32, 3, 38, 2, 5, 6 2, 3,, 8, 9, 13, 19, 20, 21, 25, 30, 35, 39, 2, 5, 7 2, 5, 6, 10, 11, 15, 19, 21, 23, 25, 26, 28, 29, 32, 36, 37, 1, 6, 8 Lesson(s) B relate informal language to mathematical language and symbols. 1, 23 1, 11, 23, 3 3, 9 *.16 Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to A make generalizations from patterns or sets of examples and nonexamples. B justify why an answer is reasonable and explain the solution process. 2, 1, 21, 28, 36, 8 5, 22 16, 38, * 5, 22, 37 26, 37 1 * * *The underlying process and mathematical tools skills are addressed throughout the student book. A32
Lesson 5 Fractions Greater Than 1 (Student Book pages 25 30) TEKS.2.B Model fraction quantities greater than one using [concrete objects and] pictorial models. GeTTinG STarTed PREREquiSiTES In order to complete this lesson, the student is expected to: Write fractions to represent a model Name the fraction the model represents. 3 5 8 understand the concept of equivalent fractions (See Lesson 3, Student Book pages 13 18) Write a fraction that is equivalent to 1 2. [Answers will vary.] Write a fraction that is equivalent to 3. [Answers will vary.] use knowledge of multiplication and division to generate equivalent fractions How many tenths are equivalent to 5? 3 8 10 How many twelfths are equivalent to 1 3? 3 12 Review prerequisite skills as needed. Use the problems provided to check for readiness. TAP STudEnTS PRioR KnoWlEdgE Briefly review with students the concept of using models to represent decimals greater than 1. Remind students that the decimal point is read as and. using Models to Represent decimals Draw two 10 3 10 grids horizontally aligned on the board. Completely shade the grid on the left. Shade 25 squares, 2 of the left-most columns and the bottom five squares of the 3rd column from the left of the grid on the right, to illustrate the decimal 1.25. Have students read the decimal illustrated by the grids. Review the procedure. Tell them to name the number of whole grids, and then name the decimal part of the partially shaded grid. Display blank decimal grids. Name a decimal and have volunteers instruct you on how to illustrate the decimal on the grid. Read decimals Write 2.5 on the board and have a volunteer read the decimal. [two and five tenths] Provide additional examples, gradually increasing the complexity of the decimal by including hundreds and thousandths and a greater whole number part. Include some nondecimals so students can hear the difference between a decimal and a nondecimal. 25
Introduction AT A glance Read and discuss the introduction on page 25 with the class to help students understand the concept of modeling fractions greater than one. Lesson 5 Fractions Greater Than 1 TEKS.2.B Model fraction quantities greater than one using [concrete objects and] pictorial models. instructional SuPPoRT Use the following to explain the introduction in greater depth. Writing Mixed numbers and improper Fractions On the board, draw the diagram that represents 1 1. Explain that a mixed number consists of a 2 whole number and a fraction. Identify the part of the model that represents the whole number and the part that represents the fractional part. Emphasize the use of the word and to separate the whole-number part from the fractional part. Ask students how they would change the diagram to model 2 1. [Add another circle with both halves 2 shaded.] Introduction This lesson will show you how to write fractions greater than 1. Fractions are used to show part of a whole. They can also show numbers that are larger than one whole. When a fraction is written as an improper fraction, its numerator is greater than or equal to its denominator. A mixed number has a whole-number part and a fraction part. An example of a mixed number is 1 1 2. improper fraction: 3 2 mixed number: 1 1 2 Like decimals, you say the word and between the whole-number and the fraction part of a mixed number. So 1 1 is read one and one-half. 2 Write a fraction that shows the shaded part of the model: Write the denominator. Each whole is divided into 3 equal parts. The denominator is 3. Write the numerator. Count the total number of shaded parts. There are 7 shaded parts. Write the fraction. number of shaded parts in model number of equal parts in each whole 5 7 3 The fraction that represents the shaded model is 7 3. 25 Give students 2 paper circles. Have them fold each paper circle in half. Ask students to unfold the circles and to color one whole circle and one-half of the other circle. Point out that they have colored 2 of one circle and of the other. Ask 2 1 2 students how many halves they have colored in all. 3 3 2 using a Model to Write improper Fractions Emphasize that the denominator in an improper fraction is the number of parts each whole is divided into, not the total number of parts. The numerator is the total number of shaded parts. It will always be a number that is the same as or larger than the denominator. Real-World Connection Ask students to think of recent situations where they have used mixed numbers in their conversations. Have them give examples. Examples: describing amounts of food eaten; Students may say that they ate 1 sandwiches for 1 2 lunch or had 2 apples as a snack. 1 2 26
Modeled Modeled EXAMPLE 1 What improper fraction represents the shaded part of the model? EXAMPLE 2 look at the model below. What mixed number represents the shaded part of the model? Follow these steps to solve the problem. Step 1 Step 2 Try It! Write the denominator. Each whole is divided into 6 equal parts. So the denominator is 6. Write the numerator. Count the total number of shaded parts. There are 28 shaded sixths in the entire model. Step 3 Write the improper fraction. numerator denominator 5 number of shaded parts in model number of equal parts in each whole 5 6 28 SOLUTION: The improper fraction that represents the shaded model is 28 6. Use what you know to solve this problem. 1 What improper fraction represents the shaded part of 13 the model? 5 Follow these steps to solve the problem. Step 1 Step 2 Step 3 Try It! Write the whole-number part of the mixed number. There are 6 triangles completely shaded. This represents 6 wholes. The whole-number part is 6. Write the fraction part. Each triangle in the model is divided into equal parts. In the last triangle, 1 of the parts are shaded. So, the fraction is 1. Write the mixed number. A mixed number has a part that is a whole number and a part that is a fraction. The model shows 6 wholes and of another triangle. 1 SOLUTION: The mixed number that represents the shaded model is 6 1. Use what you know to solve this problem. 1 What mixed number represents the shaded part of the model? 3 3 26 27 AT A glance Read and discuss each Example problem on pages 26 and 27 with the class. Model the steps used to solve each example. Then have students solve the Try it! problems that follow the example. STEP By STEP Walk the class through each Example problem. Read aloud each question and discuss how to solve the problem. To ensure understanding, demonstrate each step beneath the problem. The steps model the thinking designed to lead students to a correct solution. After discussing each example, direct students to solve the related Try it! problems. Read each question with students. Then have students, individually or in pairs, answer the problem and write the solution. After students have completed the problems, discuss their solutions as a class. 3 Page 26: 1 5 13. Page 27: 1 3 3. TEAChER TiPS Use the following to discuss the example problems in more detail. improper Fractions (Example 1, page 26) Point out that the improper fraction is read twentyeight sixths, that is, twenty-eight divided by six. Remind students that the denominator is the number of equal parts in each whole while the numerator is the total number of shaded parts. Mixed numbers (Example 2, page 27) An alternate method of describing the model is 1 1 1 1 1 1. 1 Because equals 1, this can be rewritten as 1 1 1 1 1 1 1 1 1 1 1 1 or 6 1. 1 1 27
Guided AT A glance Guide students through the multiple-choice problem on page 28. STEP By STEP First, have students read the problem and the Think About it. Then have them solve the problem independently. Tell students to validate their answer choice by reading the detailed explanation of the correct answer [B] that follows the four choices. Then discuss the explanation with the class to help guide students thinking. This section concludes with an investigation into the reasons why three of the four answer choices are not correct. Discuss these analyses with students to help them understand precisely why one answer choice is feasible and the three other choices cannot be justified or supported. TEAChER TiPS Use these tips to discuss the explanation of the correct answer. Finding improper Fractions Review the properties of improper fractions. The numerator will always be the same as or larger than the denominator. The denominator is the number of parts each model is divided into. Working Backwards Guided Think about it This problem asks you to find the improper fraction that represents the shaded area of the model. Which answer choices are written as improper fractions? Read the Think About It to understand the problem. Then solve the problem. Circle the correct answer. The shaded area represents the amount of the pies eaten at a picnic. Which fraction shows the amount of pie eaten? A 8 B 31 8 C 1 8 d 31 EXPLANATION: The denominator is 8 because each pie has 8 equal parts. There are 31 shaded parts, or 31 pieces of pie eaten. The numerator is 31. Write the numerator over the denominator. The fraction is 8 31. CORRECT ANSWER: Answer choice B is correct. INCORRECT ANSWERS: Read why the other answer choices are not correct. A The numerator of does not show the shaded parts. 8 C is not correct because it represents the amount of pie that 1 8 is left, not the amount that was eaten. d The denominator of 31 is not the 8 equal parts in each whole. 28 Students can consider each answer choice in succession. For example, students would determine that 31 has the correct numerator, but the denominator shows the number of pies, not the number of parts in each pie. 28
Guided AT A glance Have each student complete short-answer problems 1 3 on page 29. STEP By STEP Before students complete short-answer problems 1 3, tell students that the hints provide clues for solving the problems. Make sure students understand that they must write a solution and an explanation for each problem. Have pairs of students share and discuss solutions and explanations. Follow up the Pair/Share activity with a whole-class discussion of their work. SoluTionS And SAMPlE ExPlAnATionS FoR discussion 1 Solution: 1 6 Explanation: I counted the number of whole figures,. Then I added the number of shaded parts out of the 6 equal sections in the partially shaded hexagon. 2 Solution: 27 10 Explanation: Each circle is divided into tenths. This is the denominator. The total number of shaded sections, 27, is the numerator. 3 Solution: 1 9 Explanation: The numerator is the number of shaded parts in the model, 1. The denominator is the number of equal parts in each whole, 9. Hints Guided A mixed number has a whole number part and a fraction part. In a mixed number, the denominator stands for the number of equal sections in each whole. When the model shows more than one whole but the question asks for a fraction, it means the answer will be an improper fraction. Solve each problem. Use the Hints to help you. Then explain how you found your solution. 1 What mixed number represents the shaded part of the model? 1 Solution: 6 Explanation: Responses will vary. 2 The model below is 2 7 10 shaded. What improper fraction matches the shaded model? 27 Solution: 10 Explanation: Responses will vary. 3 What fraction represents the shaded part of the model? 1 Solution: 9 Explanation: Responses will vary. PAIR SHARE With your partner, share and discuss each of your solutions and explanations. 29 Mini-lesson This mini-lesson will show students how to use number lines to write a mixed number. 1. On the board, draw a number line that is divided into 9 equal sections. Place the following fractions in sequential order at each tick mark:,,,,, 0 1 2 3 1, 1, 1, 1 1 2 3 Below 0 write 0, below write 1, and below 1 write 2. using a number line to Write Mixed numbers 2. Have students guide you in labeling the number line to show fourths from 0 to 2. 3. Point out the whole numbers written below the fractions.. To help students get a sense of the size of mixed numbers, ask, Is 1 1 between 0 and 1? [no] 5. Draw a point on the number line. Have students write the mixed number that names the point on the number line. 29
AT A glance Have each student solve problems 1 on page 30. STEP By STEP First, explain to students that multiple-choice problems 1 are similar to those they will encounter on the. Then have students read the directions and answer the questions independently. Remind students to fill in the correct answer choices on the answer form at the bottom of the second column. 1 Which fraction does the shaded part of the model represent? A B C D 21 }} 8 3 } 8 21 }} 2 21 }} 3 3 Which mixed number does the shaded part of the model represent? A 1 } 3 B 3 } C 1 } D 5 1 } After students have completed the problems, review and discuss correct answers. Have students record the number of correct answers in the box provided. AnSWERS And ExPlAnATionS FoR discussion Answer Form 1 B C D 2 F H J 3 A B D F G J 2 Serena is painting vases. Each vase is a different color. The graph shows how many vases of each color she has painted so far. Color Red Key: Green Yellow Number Painted stands for 1 vase. Which color has she painted 8 } 2 vases? F Red G Green H Yellow J Not here 30 Which fraction of the model is shaded? F 3 G 3 1 } 3 H 3 2 } 3 J Answer Form 1 A B C D 2 F G H J 3 A B C D F G H J Number Correct 1 Write the total number of shaded parts for the numerator, 21. Write the number of equal parts each shape is divided into for the denominator, 8. 2 In the graph, find the color that has 8 half vases, which is whole vases. 3 The whole number,, is the number of completely shaded figures; the fraction is the number of shaded parts, 1, over the number of parts each figure is divided into. There are 3 parts completely shaded in each of the first two figures. These are the wholes. There are 2 parts of the last figure shaded. This is the numerator, written over the number of parts each figure is divided into, or the denominator. 30
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