PREPARE STUDENTS FOR ALGEBRA - …€¦ · 3 TransMath simultaneously teaches foundational...

TransMath Third Edition Overview Grades 5–10

PREPARE STUDENTS FOR ALGEBRA WITH NUMBER SENSE AND PROBLEM SOLVING

PROVEN SOLUTION

2 www.voyagersopris.com/transmath

WHAT IS TRANSMATH?

TransMath® is a comprehensive math intervention curriculum that targets middle and high school students who lack the foundational skills necessary for entry into algebra. Typical TransMath students are two or more years below grade level and respond to the unique approach of TransMath.

Using a dual topic approach, TransMath emphasizes fewer topics in greater depth while accelerating students to more advanced math, from number sense to rational numbers to understanding algebra.

TransMath:

• Deepens conceptual understanding and builds problem-solving proficiency through the use of explicit instruction and multisensory strategies

• Embeds lesson-by-lesson models to support teacher preparation and strengthen teachers’ content knowledge

• Facilitates whole-class and individual interactive learning accessing digital tools to increase opportunities for mathematical discourse and peer learning

• Provides students and teachers with eBook access to support learning and foster more meaningful interaction

3

TransMath simultaneously teaches foundational computation skills while providing the rich, grade-level problem-solving experiences necessary for high-stakes assessments.

The National Mathematics Advisory Panel says ...

To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills.

• Place Value

• Whole Numbers

• Operations

• Factors

• Multiples

• Estimation

• Fractions

• Multistep Problems

• Mean, Median, Range

• Measurement

LEVEL 1Developing Number Sense • Fractions

• Decimal Numbers

• Percentages

• Exponents

• Negative Numbers

• Estimation

• Data and Statistics

• Two-Dimensional Geometry

• Probability

LEVEL 2Making Sense of Rational Numbers • Properties

• Simple Algebraic Expressions

• Inequalities

• Functions

• Square Roots

• Irrational Numbers

• Estimation

• Ratio and Proportion

• Coordinate Graphs

• Slope

• Three-Dimensional Geometry

LEVEL 3Algebra: Expressions, Equations, and Functions

Successful entry into algebra

Having a program like TransMath that breaks [math] down is amazing ... When my students say ‘I can’t do fractions,’ and then by the end of the lesson they’re getting 95 percent and saying ‘Yes, I can,” it’s really great to see.

—Sarah Sherman, Teacher

Kennedy Middle School, Albuquerque, NM


Level 1 Level 3Level 2

Taught to Mastery in:

WHO IS TRANSMATH FOR ?TransMath benefits students who require immediate support:

• Students lacking foundational skills necessary for successful entry into algebra

• Students scoring two or more years below grade level on state standardized tests

Can your students solve this equation:10(x + 5) = 2x + 56?

10(x + 5) = 2x + 56 Recognize that the equation is balanced Recognize that unlike terms cannot be combined Recognize that 2 is a coeffi cient Be able to use the Distributive Property to rewrite without parentheses Know basic multiplication

10x + 50 = 2x + 56 Recognize that unlike terms cannot be combined

10x + 50 + –50 = 2x + 56 + –50 Understand the need to maintain a balanced equation Know the Property of Opposites (i.e., 50 and –50)

10x + 50 – 50 = 2x + 56 + –50 Know how to add integers Know basic subtraction

10x + 0 = 2x + 6 Recognize that the equation is balanced

10x + –2x = 2x + 6 + –2x Understand the need to maintain a balanced equation Know the Property of Opposites (i.e., 2x and –2x)

–2x + 10x = 2x + –2x + 6 Be able to use the Commutative Property to combine like terms Know how to add integers

8x = 0 + 6 Recognize that the equation is balanced Know basic addition

1818 · 8x =

1818 · 6 Be able to use reciprocals

Know how to multiply fractions

88x = 68 Know that 1x = x (the “invisible coeffi cient”)

Know about fractions equal to one (i.e., = 1) Know basic multiplication

x = 34 Know how to simplify fractions Know about greatest common factors

88

Prerequisite skills for Algebra profi ciency

graphic.indd 1 6/8/15 12:40 PM

WHO BENEFITS FROM TRANSMATH?

5

DUAL TOPICS

TRANSMATH THIRD EDITION: REDESIGNED TO INTEGRATE THE CONCEPTS AND SKILLS OF TODAY’S STANDARDSEach TransMath lesson is delivered in dual concepts: topic 1 provides a conceptual skill; topic 2 provides a problem-solving skill. These two topics are often not related to avoid cognitive overload and provide students a greater opportunity to not only master foundational skills but also move toward grade-level proficiency through problem-solving activities.

CONCEPTUAL SKILL

PROBLEM-SOLVING SKILL

Whole Number Operations

Factors, Primes, Composites

Common Factors

Compositions

Fraction Concepts

Adding and Subtracting

Fractions

Working with Data

Problem Solving with Data

Measuring Two-Dimensional

Objects

Area and Perimeter

Properties and Shapes

Transformations and Symmetry

Statistics

Units of Measurement

CONCEPTUAL SKILL


Fractions: Fair Shares and Part/

Whole

Fractions: Magnitude, Equivalence,

and Operations

Mixed Numbers

Decimals and Operations

Percent

Probability

Integers and Integer Operations

Fraction Problem Solving

Tools for Measurement

Tessellations

Geometry

Measurement

Probability and Percent Problem

Solving

Graphing

Coordinate Graphs

CONCEPTUAL SKILL


Fractions and Decimals

Variables

Inequalities

Algebraic Patterns

Algebraic Expressions

Algebraic Rules and Properties

Intro to Functions

Square Roots

Irrational Numbers

Statistics

Ratios, Proportions,

Percents

Surface Area of 3D Shapes

Volume of 3D Shapes

Geometry Construction

& Angle Measurement

Lines and Angles

Working with Coordinate

Graphs

Non-Linear Functions

Level 1: Developing Number Sense Level 2: Making Sense of Rational Numbers

Level 3: Algebra: Expressions, Equations, and Functions

Download samples at www.voyagersopris.com/transmath


TRANSMATH MOVES STUDENTS TOWARD ALGEBRA READINESSThe Measure: Progress Assessment of Quantile Growth

The Progress Assessment yields a Quantile® (Q) score based on the Quantile Framework for Mathematics from MetaMetrics®. Used to indicate students’ optimal learning range and monitor progress toward grade-level goals, the Quantile scores indicate what math content students are ready to learn and what they already understand.

Quantile Growth Overall Quantile Gain for All Students, Students with Disabilities (SWD), and English Language Learners (ELL)

TransMath Level 1 Results: 2013–14 and 2014–15

All Level 1(n=3,751)

SWD(n=406)

ELL(n=164)

Qua

ntile

Initial PA Final PA

0

100

200

300

400

500

600

402.93

500.37

368.09

474.10

344.94

483.08



SWD(n=296)

ELL(n=147)

Qua

ntile

Initial PA Final PA

0

100

200

300

400

500

600

700

800

900

476.54

803.70

413.68

762.50

414.83

758.33



SWD(n=239)

ELL(n=59)

Qua

ntile

Initial PA Final PA

0

100

200

300

400

500

600

700

800

900

676.28761.02

645.29730.86

630.59

858.31

RESULTS

Group # of Students

Initial PA

Final PA

Quantile Gain

Effect Size

All Level 1 3,751 402.93 500.37 97.44 0.51

SWD 406 368.09 474.10 106.01 0.60

ELL 164 344.94 483.08 138.14 0.80

Group # of Students

Initial PA

Final PA

Quantile Gain

Effect Size

All Level 2 2,745 476.54 803.70 327.16 1.84

SWD 296 413.68 762.50 348.82 2.35

ELL 147 414.83 758.33 343.50 2.31

Group # of Students

Initial PA

Final PA

Quantile Gain

Effect Size

All Level 3 1,442 676.28 761.02 84.74 0.53

SWD 239 645.29 730.86 85.57 0.57

ELL 59 630.59 858.31 227.72 1.38

7

68

69

70

71

72

73

74

75

76

77

78Total Test (n = 21)

Applications (n = 22)

Operations (n = 21)

Basic Concepts (n = 22)

2 standard deviations below national average70

Year 1 PretestBefore TransMath

Year 1 PosttestAfter 1 year of TransMath

Year 2 PosttestAfter 2 years of TransMath

n = number of students

Stan

dar

d S

core

73

71

75

72

76

74

77 KeyMath3 results for students with special needs with TransMath instruction over two school years: Fall 2008 to Spring 2010.

Intervention programs targeting students struggling in math often take more than one year of implementation to effect positive change, which makes the results in Year 2 of particular interest. In Year 1 of the TransMath implementation, the TransMath students showed no significant gains in FCAT developmental scale score. In Year 2, by contrast, the TransMath students made statistically significant growth, gaining, on average, 158 DSS points.

On average, TransMath students who had scored nearly two standard deviations below the national average at pretest were able to improve their standard score by nearly four points or nearly one-third of a standard deviation; that is, the TransMath group brought its performance closer to the national average.

-50

0

50

100

150

200

DSS

Cha

nge

All TransMathStudents(n = 79)

Free/ReducedLunch

(n = 51)

Nonwhite(n = 32)

Limited/Low English

Pro�cient(n = 8)

ExceptionalStudent

Education(n = 13)

n = number of students

158 164

5

-3

144

61

30

186

-21

160

Year 1 Year 2

4

6

8

10

12

14

16

18

20

Student Growth on CTB TerraNova Test

Comparison Group(n = 28)

13.36

Mea

n Sc

ore

TransMath Group(n = 25)

15.11

12.36

17.88Fall 2004 Spring 2005

0

5

10

15

20

25

30

Core Concepts Test ScoresAfter Instruction—June 2005


13.07

Mea

n Sc

ore


21.02

0

10

20

30

40

50

60

70

Attitudes Toward Math Survey Gains in Mean Score


53.35

Mea

n Sc

ore


51.86 50.92

65.36Fall 2004 Spring 2005

Higher Academic Outcomes for TransMath Students in Two Bremerton, Washington, Schools

Students Improve Standard Score by Nearly Four Points in a Georgia School District

Two-Year Gain on the State Assessment for Lee County Public Schools, Florida


WHAT MAKES TRANSMATH WORK ?

Unit 1 • Lesson 3 25

14 Unit 1 • Lesson 3

Lesson 3

Rods with different lengths can represent the same part-to-whole relationship. It’s all about the relationship of the part to its whole. Example 2 shows this.

Example 2

What is the part-to-whole relationship shown with the two rods below?

One part

The whole

Again, three parts are needed to make the whole.

Three parts

The whole

So the unit fraction is 13.

Numerator

Denominator Whole

Part13

Even though the part and whole rods in Example 2 are shorter than the corresponding rods in Example 1, the part-to-whole relationship is still 13.

Apply SkillsTurn to Interactive Text, page 10.

Reinforce UnderstandingUse the Unit 1 Lesson 3 Teacher Talk Tutorial to review lesson concepts.

The part-to-whole relationship is a comparison of the part to what we define as the whole.

Check for UnderstandingEngagement Strategy: Think, Think

Draw two purple rods on the board. Label one rod as “the whole.” Label the other rod as “1

2.” Ask students the questions listed below. Allow think time after each question and encourage them to use the rods to help them answer the questions. Then call on one student to answer.

Ask:

Can you give an example of a comparison where the purple rod is the whole? (When compared to the white rod, the purple rod represents one whole and the white rod represents 1

4.)

Can you give an example of a comparison where the purple rod is 12? (When compared to the brown rod, the purple rod represents 1

2 and the brown rod represents one whole.)

What is a part-to-whole relationship? (continued)

Demonstrate• Have students look at Example 2 at the top

of page 14 of the Student Text. This example shows one part and the whole. Point out to students that three of the parts are needed to make the whole. It is the same part-to-whole relationship as in Example 1. The Cuisenaire rods are a different size, but the relationship between them remains the same. The one part is one-third of the whole.

• Review key vocabulary at the end of the example. Ask students, “What is the numerator and what does it represent? What is the denominator and what does it represent? What is a unit fraction and why is it important?” Be sure students understand these terms and their importance.

• Summarize the concept students should take away from today’s concept building. When working with a part-to-whole relationship, the focus is on how the part compares to the whole. It is that relationship that gives the fraction meaning.

Discuss

Call students’ attention to the Power Concept.

Reinforce Understanding Remind students that they can review lesson concepts by accessing the online Unit 1 Lesson 3 Teacher Talk Tutorial.


14


Skills MaintenanceMaking Fair Shares(Interactive Text, page 9)

Activity 1

Students divide rectangles into fair share segments. Notice the rectangles are called rods in preparation for today’s lesson where students are introduced to a new math tool called Cuisenaire rods.

Vocabulary Developmentunit fraction Cuisenaire rods

Skills MaintenanceMaking Fair Shares

Building Number Concepts: Part-to-Whole Relationships

In this lesson, students learn about the importance of the part-to-whole relationship represented by a fraction. They learn that this relationship begins with recognizing the “whole” and then comparing part(s) to the whole. Students are introduced to the unit fraction, which is at the foundation of the conceptual understanding of fractions.

ObjectiveStudents will understand fractions as part-to-whole relationships.

Problem Solving: Representing Fractions with Cuisenaire Rods

Students are introduced to a new tool for understanding fractions, Cuisenaire rods. These are the Cuisenaire rods that young students use to learn place value. They are a helpful tool for understanding fractions as well. Like the number line, they are linear models.

ObjectiveStudents will use a linear model (Cuisenaire rods) to examine part-to-whole relationships.

HomeworkStudents fill in missing fractions on a number line, divide rectangles into fair shares, and tell the unit fraction represented by rods. In Distributed Practice, students practice basic computational skills with whole numbers.

Lesson Planner

Part-to-Whole RelationshipsProblem Solving: Representing Fractions with Cuisenaire Rods

Lesson 3


Name Date

Uni

t 1


Activity 1

Divide the rods into the fair shares indicated.

1. Halves

2. Fourths

3. Thirds

4. Sixths

Lesson 3 Skills Maintenance

DUAL TOPICS avoid cognitive overload.

VOCABULARY DEVELOPMENT builds student understanding.

VISUAL MODELS illustrate difficult concepts.

ASK questions help teachers guide discussions that assess understanding.

POWER CONCEPTS focus instruction.

DIGITAL MANIPULATIVES provide opportunities for students to interact.

TAKE A CLOSER LOOK


Skills MaintenanceMaking Fair Shares(Interactive Text, page 9)

Activity 1

Students divide rectangles into fair share segments. Notice the rectangles are called rods in preparation for today’s lesson where students are introduced to a new math tool called Cuisenaire rods.

Vocabulary Developmentunit fraction Cuisenaire rods


Building Number Concepts: Part-to-Whole Relationships

In this lesson, students learn about the importance of the part-to-whole relationship represented by a fraction. They learn that this relationship begins with recognizing the “whole” and then comparing part(s) to the whole. Students are introduced to the unit fraction, which is at the foundation of the conceptual understanding of fractions.

ObjectiveStudents will understand fractions as part-to-whole relationships.

Problem Solving: Representing Fractions with Cuisenaire Rods

Students are introduced to a new tool for understanding fractions, Cuisenaire rods. These are the Cuisenaire rods that young students use to learn place value. They are a helpful tool for understanding fractions as well. Like the number line, they are linear models.

ObjectiveStudents will use a linear model (Cuisenaire rods) to examine part-to-whole relationships.

HomeworkStudents fill in missing fractions on a number line, divide rectangles into fair shares, and tell the unit fraction represented by rods. In Distributed Practice, students practice basic computational skills with whole numbers.

Lesson Planner

Part-to-Whole RelationshipsProblem Solving: Representing Fractions with Cuisenaire Rods

Lesson 3


Name Date

Uni

t 1


Activity 1

Divide the rods into the fair shares indicated.

1. Halves

2. Fourths

3. Thirds

4. Sixths

Lesson 3 Skills Maintenance



Lesson 3

Rods with different lengths can represent the same part-to-whole relationship. It’s all about the relationship of the part to its whole. Example 2 shows this.

Example 2

What is the part-to-whole relationship shown with the two rods below?

One part

The whole

Again, three parts are needed to make the whole.

Three parts

The whole

So the unit fraction is 13.

Numerator

Denominator Whole

Part13

Even though the part and whole rods in Example 2 are shorter than the corresponding rods in Example 1, the part-to-whole relationship is still 13.

Apply SkillsTurn to Interactive Text, page 10.

Reinforce UnderstandingUse the Unit 1 Lesson 3 Teacher Talk Tutorial to review lesson concepts.


Check for UnderstandingEngagement Strategy: Think, Think

Draw two purple rods on the board. Label one rod as “the whole.” Label the other rod as “1

2.” Ask students the questions listed below. Allow think time after each question and encourage them to use the rods to help them answer the questions. Then call on one student to answer.

Ask:

Can you give an example of a comparison where the purple rod is the whole? (When compared to the white rod, the purple rod represents one whole and the white rod represents 1

4.)

Can you give an example of a comparison where the purple rod is 12? (When compared to the brown rod, the purple rod represents 1

2 and the brown rod represents one whole.)

What is a part-to-whole relationship? (continued)

Demonstrate• Have students look at Example 2 at the top

of page 14 of the Student Text. This example shows one part and the whole. Point out to students that three of the parts are needed to make the whole. It is the same part-to-whole relationship as in Example 1. The Cuisenaire rods are a different size, but the relationship between them remains the same. The one part is one-third of the whole.

• Review key vocabulary at the end of the example. Ask students, “What is the numerator and what does it represent? What is the denominator and what does it represent? What is a unit fraction and why is it important?” Be sure students understand these terms and their importance.

• Summarize the concept students should take away from today’s concept building. When working with a part-to-whole relationship, the focus is on how the part compares to the whole. It is that relationship that gives the fraction meaning.

Discuss

Call students’ attention to the Power Concept.



14

9

WATCH FOR questions guide teachers in assessing student understanding.

REINFORCE UNDERSTANDING with interactive online models.


Lesson 3

Check for UnderstandingEngagement Strategy: Look About

Have students model the fraction 35 at their desks. Tell them to look about the classroom and get help from other students if they are having any difficulties. Circulate around the room and be sure students have used three red rods and one orange rod to model 35.

Reinforce Understanding Remind students that they can review lesson concepts by accessing the online Unit 1 Lesson 3 Problem Solving Teacher Talk Tutorial.

How do we select Cuisenaire rods to model a fraction? (continued)

Demonstrate

• Have students look at Example 2 on page 16 of the Student Text. In this example, students are shown how to model the fraction 25.

• Have students look at the denominator of 25 first. Explain that this helps to determine which rods to use. The denominator is the same as the denominator in Example 1. In Example 1, we modeled the unit fraction 15 with a red rod. Use the red rod to represent the unit fraction and the orange rod for the whole.

• Ask students to look at the fraction to be modeled. The fraction 25, NOT 15, is being modeled. Ask students to name how many more red rods are needed to model 25. Because two unit fractions are needed, the fraction can be written as 2 × 15, or 25.

• Have students look at the next picture in Example 2. The picture shows a representation for 25. Two of the red rods and one orange rod represent the fraction 25. Have students model 25 at their desk. Be sure they have two red rods and one orange rod to model the fraction 25.

• Review the vocabulary at the end of the example. These key terms are critical to conceptual understanding of part-to-whole relationships.


Lesson 3

What if we are given a fraction that is not a unit fraction? Let’s look at an example.

Example 2

Select Cuisenaire rods to show 25.

First, repeat the process in Example 1 to find the unit fraction. These rods show 15.

One part

The whole

Because the numerator of 25 is 2, we need two unit fractions.

Two parts

The whole

The fraction can be written as

2 × 15, or 25.

Numerator

Denominator Whole

Part25

Notice how important the unit fraction is when we work with part-to-whole relationships.

Problem-Solving ActivityTurn to Interactive Text, page 12.

Reinforce UnderstandingUse the Unit 1 Lesson 3 Problem Solving Teacher Talk Tutorial to review lesson concepts.

16


Lesson 3

Apply Skills(Interactive Text, pages 10–11)

Have students turn to pages 10 and 11 in the Interactive Text, which provides students an opportunity to practice identifying part-to-whole relationships represented by rods.

Activity 1

Students are given two rods representing a unit fraction and the whole and are to name the unit fraction. Remind them to divide up the whole if they cannot see the relationship without the lines.

Activity 2

Students are shown the unit fraction and a second fraction made up of multiple unit fractions. Students complete the multiplication that shows the number of unit fractions in the second fraction and then name the second fraction. A model is provided to help students understand what is expected of them.

Monitor students’ work as they complete these activities.

Watch for:

• Can students name a fraction given a model of the unit fraction and the whole?

• Do students understand that there are other fractions using the same whole that are multiples of the unit fraction?

• Can students use a unit fraction to name other fractions that use the same whole?



Name Date

Apply SkillsUsing Rectangles to See Part-to-Whole Relationships

Activity 1

Name the unit fraction represented by each pair of rods. Partition the whole if needed to find how many unit fractions make up the whole.

1. Unit fraction = 12

One part

Whole


One part

Whole


One part

Whole


One part

Whole

Lesson 3 Apply Skills


Name Date

Uni

t 1

Activity 2

The unit fraction is shown. Use it to describe the fraction shown.

Model

Unit fraction: 13

Fraction: 23

1. Unit fraction: 18

Fraction: 68


Fraction: 45


Fraction: 36


Fraction: 2

10

2 × 13

6 × 18

4 × 15

3 × 16

2 × 110


DISTRIBUTED PRACTICE in every lesson provides continued practice of previously learned skills.


Lesson 3



Activity 1


Activity 2



Watch for:






Name Date


Activity 1



One part

Whole


One part

Whole


One part

Whole


One part

Whole



Name Date

Uni

t 1

Activity 2


Model

Unit fraction: 13

Fraction: 23


Fraction: 68


Fraction: 45


Fraction: 36


Fraction: 2

10

2 × 13

6 × 18

4 × 15

3 × 16

2 × 110



Lesson 3



Activity 1


Activity 2



Watch for:






Name Date


Activity 1



One part

Whole


One part

Whole


One part

Whole


One part

Whole



Name Date

Uni

t 1

Activity 2


Model

Unit fraction: 13

Fraction: 23


Fraction: 68


Fraction: 45


Fraction: 36


Fraction: 2

10

2 × 13

6 × 18

4 × 15

3 × 16

2 × 110



Lesson 3

Homework

Go over the instructions on pages 17–18 of the Student Text for each part of the homework.

Activity 1

Students fill in missing fractions on number lines.

Activity 2

Students divide rectangles into equal parts as instructed. Remind them these fractional parts must be fair shares.

Activity 3

Students tell the unit fraction represented by two rods.

Activity 4 • Distributed Practice

Students practice basic computational skills. Tell students that they practice these skills so they do not forget the algorithms and they continue to get better at them.


Lesson 3

Homework

Activity 1

Find the fractions for the letters on the number line.

1.(h)

0 (a) (b) (c) (d) 118

28

38

48

58

68

78

88

(e) (f) (g)

2.(n)

0 (j) (k) (l) (m) 115

25

35

45

55

3.(r)

0 (p) (q) 113

23

33

Activity 2

Divide the rectangles into the fair shares indicated.

1. Fifths

2. Tenths

3. Fourths

4. Eighths

5. Halves

6. Thirds


Lesson 3

Activity 3

Name the unit fraction represented by each pair of rods.

1. One part

The whole

13

2. One part

The whole

12

3. One part

The whole

14

4. One part

The whole

13


Solve.

1. 277+ 4,234

4,511

2. 4,001– 2,001

2,000

3. 3q633

4. 903+ 1,209

2,112

5. 75× 75

5,625

6. 5q1,520

7. 4,001+ 701

4,702

8. 808× 25

20,200

9. 8q280

211

304

35

Homework

17

18


Lesson 3

Homework

Go over the instructions on pages 17–18 of the Student Text for each part of the homework.

Activity 1

Students fill in missing fractions on number lines.

Activity 2

Students divide rectangles into equal parts as instructed. Remind them these fractional parts must be fair shares.

Activity 3

Students tell the unit fraction represented by two rods.


Students practice basic computational skills. Tell students that they practice these skills so they do not forget the algorithms and they continue to get better at them.


Lesson 3

Homework

Activity 1

Find the fractions for the letters on the number line.

1.(h)

0 (a) (b) (c) (d) 118

28

38

48

58

68

78

88

(e) (f) (g)

2.(n)

0 (j) (k) (l) (m) 115

25

35

45

55

3.(r)

0 (p) (q) 113

23

33

Activity 2

Divide the rectangles into the fair shares indicated.

1. Fifths

2. Tenths

3. Fourths

4. Eighths

5. Halves

6. Thirds


Lesson 3

Activity 3

Name the unit fraction represented by each pair of rods.

1. One part

The whole

13

2. One part

The whole

12

3. One part

The whole

14

4. One part

The whole

13


Solve.

1. 277+ 4,234

4,511

2. 4,001– 2,001

2,000

3. 3q633

4. 903+ 1,209

2,112

5. 75× 75

5,625

6. 5q1,520

7. 4,001+ 701

4,702

8. 808× 25

20,200

9. 8q280

211

304

35

Homework

17

18

ENGAGEMENT STRATEGIES provide ongoing, informal assessment in every lesson.

SKILL APPLICATION provides immediate opportunity for students to practice what they learned.


PLACEMENTTransMath placement is based on students’ skill levels, not grade levels. Students may place into one of these three entry points:

BALANCED ASSESSMENT

Developing Number Sense: For students showing the need for foundational number sense skills

Making Sense of Rational Numbers: For students showing proficiency in basic number sense skills but lacking the foundational skills for rational numbers

Algebra: Expressions, Equations, and Functions: For students showing proficiency with rational numbers but lacking the foundational skills for prealgebra

Entry Point 1 Entry Point 2 Entry Point 3

ONGOING ASSESSMENTInformal Assessment

TransMath provides teachers with numerous opportunities to assess student knowledge as concepts and skills are being developed.

Check for Understanding Informally assesses student learning and prescribes solutions for

immediate support. Embedded engagement strategies provide varied opportunities for student communication, engaging all. Check for Understanding occurs after the modeling of each major lesson concept.

Apply Skills These activities allow students to apply the skills they

learned in the Building Number Concepts section of each lesson.

Problem-Solving Activity Activities allow students to apply knowledge of the concepts from

the Problem Solving section of each lesson.


Name Date

Apply SkillsConverting Mixed Numbers Into Improper Fractions

Activity 1

Convert the mixed numbers into improper fractions.

1. Change 925 into an improper fraction.





Reinforce Understanding

Use the Unit 4 Lesson 5 Teacher Talk Tutorial to review lesson concepts.


Name Date

Problem-Solving ActivityApproximating Answers to Word Problems with Mixed NumbersThe Scatter Plots are having more problems with the house. Help the band by approximating the answers to the measurement problems. 1. The roof on the house leaks everywhere. The entire roof needs to be replaced. What is a good approximation of the area of the roof on the front side of the house?

2. The back side of the house has an extra roof over the porch. What is an estimation of the area of the roof and porch roof on the back side of the house?

3. The gas pipe to the stove is broken and it needs to be replaced. It comes in under the house and up into the kitchen. About how many feet of pipe does the band need?

4. The band wants to set up a place to practice in the basement, but there are not enough electrical outlets. The wire will have to be run from the first floor to the basement. The length of wire to the first new outlet in the basement is 2058 feet. The length of wire needed for the second outlet in the basement is 323

4 feet. What is the approximate difference between the lengths of the two wires?

518 yards

1134 yards

418 feet

1513 feet

Lesson 9 Problem-Solving Activity

315 yards

1134 yards

1178 yards

518 yards

Reinforce UnderstandingUse the Unit 4 Lesson 9 Problem Solving Teacher Talk Tutorial to review lesson concepts.

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PROGRESS ASSESSMENT POWERED BY THE QUANTILE FRAMEWORK BY METAMETRICS

FORMAL ASSESSMENTEach unit of TransMath contains multiple methods to assess students’ reasoning and ability to communicate ideas. Each type of assessment serves a different purpose.

StudentsAssess Differentiate

Day 1 Day 2

All Quiz X Form A

Review Quiz

Scored 80% or Above

Extension

Scored Below 80%

Reinforcement

Day 1: Students take Quiz during the second half of the lesson.

Day 2: Students work on differentiation activities based on their performance on the Quiz.

End-of-Unit Assessment The End-of-Unit Assessment measures student mastery of skills taught in the unit. Targeted support is then provided on differentiation days to reinforce difficult skills to help students achieve mastery.

Performance Assessment The Performance Assessment measures each student’s ability to reason and communicate. Students practice applying unit concepts in the context of a high-stakes test.

Quiz Quizzes occur every five lessons to give teachers important feedback on student progress. Results inform instruction for differentiation days and subsequent lessons.

StudentsAssess Differentiate Assess

Day 1 Day 2 Day 3 Day 4

AllEnd-of-Unit Assessment

Review Test Performance Assessment

Begin new unit

Scored 80% or Above

Extension Extension

Scored Below 80%

Retest

End-of-Unit Assessment

Day 1: Students take End-of-Unit Assessment to determine differentiation needs.

Day 2: Students work on differentiation activities based on their performance on the assessment.

Day 3: Students continue with differentiation activities or retest.

Day 4: Students take Performance Assessments.


DIFFERENTIATION INFORMED BY DATATransMath offers tools and time to assess, reinforce, and differentiate instruction. Key tools include:

Teacher Differentiation Support

Teachers have access to all of the Teacher and Student materials in eBook format. In addition, teachers have access to:

• Math Toolbox provides a variety of digital manipulatives to use with TransMath lessons

• TeacherTalk Tutorials reinforce lesson concepts using narrated, animated visual models that make the concept concrete for the student

• Interactive Click-Thru slideshow presentations use visual models to concretely develop concepts

• On Track! Extension Activities multistep word problems designed for small groups to prepare students for high-stakes tests

• Form B Retests for Quizzes and End-of-Unit Assessments are available for download

Student Differentiation Support

All of the TransMath resources are available to students in eBook format. Additionally, students have access to the the TeacherTalk Tutorials to reinforce difficult concepts. The Math Toolbox is also available to students in their student eBook as well as through the TransMath Student Center.

VmathLive® provides meaningful online math practice anytime, anywhere. With activities directly aligned with TransMath content, VmathLive provides:

• Extra practice in essential math concepts, skills, and problem-solving strategies

• Playful origami avatars and virtual tutors that encourage continued student participation

• Combination of “learn” and “play” activities

• Embedded multimedia hints to assist students in solving problems—including online conceptual models and videos in English and Spanish

DIFFERENTIATION

VmathLive provides engaging online practice aligned with TransMath content.

13

BUILT-IN TIME FOR DIFFERENTIATIONUnits are either 10 lessons or 15 lessons. TransMath is designed for 50- to 60-minute blocks per day and designates time for differentiation.

10-Lesson Unit

15-Lesson Unit

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Unit Review

Quiz End-of-Unit Assessment Performance Assessment Time for DifferentiationD

Lessons 6–10D DLessons 1–5

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Unit Review

Quiz End-of-Unit Assessment Performance Assessment Time for DifferentiationD

Lessons 11–15D DLessons 6–10DLessons 1–5

PACING GUIDE AT THE LESSON LEVELEvery lesson has a predictable structure. Although TransMath is designed for 50- to 60-minute lesson blocks per day, adjustments can be made to fit multiple scheduling needs.

LESSON STRUCTURE APPROXIMATE TIME FOR A 50- TO 60-MINUTE LESSON

Skills Maintenance Starts each lesson with distributed practice warm-ups 4–5 minutes

Building Number Concepts Develops conceptual understanding of number, operation, and prealgebra topics through:

• Teacher Modeling• Engagement Strategies• Extensive Use of Visual Models• Apply Skills Activities

20–25 minutes

Problem Solving Develops conceptual understanding of geometry, measurement, data, and probability through:

• Teacher Modeling• Engagement Strategies• Extensive Use of Visual Models• Rich, Grade-Level Problem-Solving Activities

20–25 minutes

Homework Provides daily, independent practice with lesson concepts and skills as well as earlier learned skills for continued distributed practice. Assignments take 15–20 minutes outside class.

5 minutes—Assign Homework


STREAMLINED TEACHER MATERIALS

ENGAGING STUDENT MATERIALS

Online Assessment SystemEmbedded within the Teacher Center, a comprehensive

data-management system guides instruction and monitors change.

Teacher Guides—3 Levels,Two-Volume Set at each level

Provides Unit Openers, Lesson Planners, step-by-step instruction, assessment and differentiation supports, and images of related student materials. Print and digital options.

Student Texts and Interactive Texts—3 Levels

Student Texts provide Unit Openers, detailed examples, real-world connections, and homework for each lesson.

Print and digital options.

Interactive texts provide the in-class activities for application of skills.

Teacher Center Provides access to the resources needed to support an

effective TransMath implementation—eBooks, Data Management Resources, VmathLive, TeacherTalk Tutorials

and Click Thrus as well as the Math Toolbox.

Student CenterProvides access to eBooks, VmathLive, Math Toolbox, and animated tutorials

Level 1: 9 units Level 2: 9 units Level 3: 10 units

MATERIALS

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IMPLEMENTATION AND ONGOING SUPPORT

AMOUNT OFINSTRUCTION

USE OFASSESSMENTS

QUALITY OFINSTRUCTION

DIFFERENTIATION

CLASSROOMMANAGEMENT

FIVE KEYS TO SUCCESS

OUR GOAL: PROVIDE THE HIGHEST LEVEL OF EDUCATOR SUPPORT TO INCREASE STUDENT ACHIEVEMENTThe Support Services team is committed to serving teachers and school leaders to achieve results. Our team specializes in partnering with schools and districts to build custom implementation support plans—including planning, training, and ongoing support—to ensure all stakeholders are prepared to implement and sustain Voyager Sopris Learning instructional programs.

These comprehensive services support districts in providing comprehensive, data-focused professional development that aligns with the curriculum and develops the capacity of all teachers. Our services enable districts to have a common framework for evaluating both teacher effectiveness and student achievement.

Our team specializes in partnering with schools and districts to build custom TransMath implementation support plans—including planning, training, and ongoing support—to ensure all stakeholders are prepared to implement and sustain TransMath implementation. Key stages of TransMath implementation include:

PRE-IMPLEMENTATION PLANNING ONGOING

DATA REVIEWLAUNCH

Visit www.voyagersopris.com/transmath to review training options and a comprehensive menu of services.

The professional development

was incredible because the

leaders engaged me in all ways.

They wanted my feedback;

I felt appreciated for my

work. I found all TransMath

professional development

engaging, thought-provoking,

and motivating.

—Angel Roman Hayes Middle School

Albuquerque Public Schools, New Mexico

GET RESULTS. ACCELERATE MATH GROWTH WITH A PROVEN MATH CURRICULUM.

Visit www.voyagersopris.com/transmath for:• Complimentary samples• Comprehensive research and results overview• Highlights of new Third Edition

Visit www.voyagersopris.com/transmath

www.voyagersopris.com / 800.547.6747

Proven to Dramatically Increase Quantile Gains and Performance on Standardized Assessments

Implement digitally, with print components, or with a combination of print and digital.

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We’ve been implementing now for almost three years, and this

last semester, we had 23 percent overall growth in our students

who were in TransMath Level 3. That was looking at all six of

our traditional high schools.

—April Brantley Exceptional Children Program Specialist, Middle and Secondary

Alamance-Burlington School System, North Carolina

PREPARE STUDENTS FOR ALGEBRA - …€¦ · 3 TransMath simultaneously teaches foundational...

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Transcript of PREPARE STUDENTS FOR ALGEBRA - …€¦ · 3 TransMath simultaneously teaches foundational...