PREPARE STUDENTS FOR ALGEBRA - Literacy and Facilitates whole-class and individual interactive...
Transcript of PREPARE STUDENTS FOR ALGEBRA - Literacy and Facilitates whole-class and individual interactive...
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
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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
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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?
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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
PROBLEM-SOLVING 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
PROBLEM-SOLVING 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
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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
TransMath Level 2 Results: 2013–14 and 2014–15
All Level 2(n=2,745)
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
TransMath Level 3 Results: 2013–14 and 2014–15
All Level 3(n=1,442)
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
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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
Comparison Group(n = 28)
13.07
Mea
n Sc
ore
TransMath Group(n = 25)
21.02
0
10
20
30
40
50
60
70
Attitudes Toward Math Survey Gains in Mean Score
Comparison Group(n = 28)
53.35
Mea
n Sc
ore
TransMath Group(n = 25)
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
8 www.voyagersopris.com/transmath
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.
The part-to-whole relationship is a comparison of the part to what we define as the whole.
14
22 Unit 1 • Lesson 3
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
Unit 1 • Lesson 3 9
Name Date
Uni
t 1
Skills MaintenanceMaking Fair Shares
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
22 Unit 1 • Lesson 3
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
Unit 1 • Lesson 3 9
Name Date
Uni
t 1
Skills MaintenanceMaking Fair Shares
Activity 1
Divide the rods into the fair shares indicated.
1. Halves
2. Fourths
3. Thirds
4. Sixths
Lesson 3 Skills Maintenance
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.
The part-to-whole relationship is a comparison of the part to what we define as the whole.
14
9
WATCH FOR questions guide teachers in assessing student understanding.
REINFORCE UNDERSTANDING with interactive online models.
28 Unit 1 • Lesson 3
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.
16 Unit 1 • Lesson 3
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
26 Unit 1 • Lesson 3
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?
Reinforce Understanding Remind students that they can review lesson concepts by accessing the online Unit 1 Lesson 3 Teacher Talk Tutorial.
10 Unit 1 • Lesson 3
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
2. Unit fraction = 15
One part
Whole
3. Unit fraction = 12
One part
Whole
4. Unit fraction = 13
One part
Whole
Lesson 3 Apply Skills
Unit 1 • Lesson 3 11
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
2. Unit fraction: 15
Fraction: 45
3. Unit fraction: 16
Fraction: 36
4. Unit fraction: 110
Fraction: 2
10
2 × 13
6 × 18
4 × 15
3 × 16
2 × 110
Lesson 3 Apply Skills
DISTRIBUTED PRACTICE in every lesson provides continued practice of previously learned skills.
26 Unit 1 • Lesson 3
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?
Reinforce Understanding Remind students that they can review lesson concepts by accessing the online Unit 1 Lesson 3 Teacher Talk Tutorial.
10 Unit 1 • Lesson 3
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
2. Unit fraction = 15
One part
Whole
3. Unit fraction = 12
One part
Whole
4. Unit fraction = 13
One part
Whole
Lesson 3 Apply Skills
Unit 1 • Lesson 3 11
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
2. Unit fraction: 15
Fraction: 45
3. Unit fraction: 16
Fraction: 36
4. Unit fraction: 110
Fraction: 2
10
2 × 13
6 × 18
4 × 15
3 × 16
2 × 110
Lesson 3 Apply Skills
26 Unit 1 • Lesson 3
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?
Reinforce Understanding Remind students that they can review lesson concepts by accessing the online Unit 1 Lesson 3 Teacher Talk Tutorial.
10 Unit 1 • Lesson 3
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
2. Unit fraction = 15
One part
Whole
3. Unit fraction = 12
One part
Whole
4. Unit fraction = 13
One part
Whole
Lesson 3 Apply Skills
Unit 1 • Lesson 3 11
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
2. Unit fraction: 15
Fraction: 45
3. Unit fraction: 16
Fraction: 36
4. Unit fraction: 110
Fraction: 2
10
2 × 13
6 × 18
4 × 15
3 × 16
2 × 110
Lesson 3 Apply Skills
30 Unit 1 • Lesson 3
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.
Unit 1 • Lesson 3 17
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
18 Unit 1 • Lesson 3
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
Activity 4 • Distributed Practice
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
30 Unit 1 • Lesson 3
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.
Unit 1 • Lesson 3 17
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
18 Unit 1 • Lesson 3
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
Activity 4 • Distributed Practice
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.
10 www.voyagersopris.com/transmath
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.
178 Unit 4 • Lesson 5
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.
2. Change 734 into an improper fraction.
3. Change 859 into an improper fraction.
4. Change 378 into an improper fraction.
Lesson 5 Apply Skills
Reinforce Understanding
Use the Unit 4 Lesson 5 Teacher Talk Tutorial to review lesson concepts.
192 Unit 4 • Lesson 9
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.
11
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.
12 www.voyagersopris.com/transmath
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
14 www.voyagersopris.com/transmath
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
15
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