Glencoe. Math Triumphs: Foundations for Algebra 1 (Teacher Handbook)

383 Pages·34.377 MB·English

Contents in Brief
Chapter 1 Numbers and Operations
Chapter 2 Decimals
Chapter 3 Fractions and Mixed Numbers
Chapter 4 Real Numbers
Chapter 5 Measurement and Geometry
Chapter 6 Probability and Statistics
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Table of Contents
Vertical Alignment
Welcome to Math Connects . . . . . . . . . . . . . . . . . . . . . . . . . . T4
An overview of the vertical alignment of Macmillan/McGraw-Hill’s
and Glencoe’s PreK–12 mathematics programs
Implementing Intensive Intervention . . . . . . . . . . . . . . . . . . . . . T6
Program Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T7
Balanced approach of concepts, skills, and problem solving
Assessment
Comprehensive Assessment System . . . . . . . . . . . . . . . . . . . . . T10
Diagnostic, Formative, and Summative assessments linked to
Data-Driven Decision Making
Table of Contents T3
W elcome to
M a t h Connec
t
s
Concepts • Skills • Problem Solving
The only true vertically aligned PreK–12 Mathematics Curriculum
Math Connects offers three dimensions of vertical alignment.
1 Content Design 2 Instructional Design 3 Visual Design
Vertical content alignment is a process Our strong vertical alignment in The student pages of Math Connects
that ensures you and your students instructional approach from have a consistent visual design from
experience an articulated, coherent PreKindergarten through Algebra 2 grade to grade. This aids students’
sequence of content from grade level to provides a smooth transition for students transition from elementary school to
grade level. This provides you with the from elementary to middle school to middle school and from middle school
assurance that content is introduced, high school. Our common vocabulary, to Algebra 1. Students are more likely to
reinforced, and assessed at appropriate technology, manipulatives, lesson planning, succeed when they are already familiar
times in the series, eliminating gaps and and Data-Driven Decision Making reduce with how to navigate student pages.
unnecessary duplication. You are able to the confusion students often encounter
target your instruction to student needs when transitioning between grade levels
because you are not teaching content without this built-in articulation.
intended to be covered later or that
students have previously mastered.
TTIIEERR Intensive
3
Intervention
PreK-2 3–5
TTIIEERR
1 Daily Intervention
TTIIEERR
2 Strategic Intervention
T4 Teacher Handbook
5 Keys to Success
1 Backmapping 3 Ongoing Assessment
According to College Board research, about 80% of students Math Connects includes diagnostic, formative, and summative
who successfully complete Algebra 1 and Geometry by 10th assessment; data-driven instruction; intervention options; and
grade attend and succeed in college. (Changing the Odds: performance tracking, as well as remediation, acceleration, and
Factors Increasing Access to College, 1990) Math Connects enrichment tools throughout the program.
was conceived and developed by backmapping with the final
result in mind—student success in Algebra 1 and beyond.
4 Intervention and Differentiated Instruction
2 Balanced, In-Depth Content A three-tiered Response To Intervention (RTI) is provided.
Math Connects was developed to specifically target the skills
TTIIEERR
and topics that give students the most difficulty, such as 1 Daily Intervention Reteach masters and
Problem Solving, in each grade span. Alternative Strategy suggestions address concepts from
a different modality or learning style.
Grades K–2 Grades 3–5
TTIIEERR
2 Strategic Intervention Teachers can use the
1. Problem Solving 1. Problem Solving
myriad of intervention tips and ancillary materials, such
2. Money 2. Fractions
3. Time 3. Measurement as the Strategic Intervention Guide (1–5) and Study
4. Measurement 4. Decimals Guide and Intervention (6–8).
5. Fractions 5. Time
6. Computation 6. Algebra
TTIIEERR
3 Intensive Intervention For students who are
Grades 6–8 Grades 9–12
two or more years below grade level, Math Triumphs
1. Fractions 1. Problem Solving provides step-by-step instruction, vocabulary support, and
2. Problem Solving 2. Fractions data-driven decision making to help students succeed.
3. Measurement 3. Algebra
4. Algebra 4. Geometry
5. Computation 5. Computation
6. Probability
5 Professional Development
— K–12 Math Market Analysis Survey, Open Book Publishing, 2006
Math Connects includes many opportunities for teacher
professional development. Additional learning opportunities in
various formats—video, online, and on-site instruction—are fully
aligned and articulated from Kindergarten through Algebra 2.
6–8 Pre-Algebra and Algebra 1 Geometry and Algebra 2
Welcome T5
Implementing
Intensive Intervention
TTIIEERR
Data-Driven Intensive Intervention
3
Ongoing assessment aids the teacher in student placement, progress monitoring, and exit.
Instructional Design Classroom Implementation
1 Diagnose and Prescribe
• Diagnostic and Placement
Test Teacher prepares individual or
• Online Readiness Quiz group intervention plan(s).
• Chapter Preview
• Assessment Masters:
Chapter Pretest
2 Teach and Practice
• Student Study Guide
Teacher modifies instruction based on
• Teacher Edition strategies
results of formative assessments.
• Manipulatives
3 Advance and Exit
Test success indicates that a student can
• Progress Check
progress to another Math Triumphs chapter
• Assessment Masters:
(if needed) or exit the intervention program.
Chapter Test
Foundational Skills for Algebra 1
Number and Operations
Geometry and Measurement
Data Analysis
T6 Teacher Handbook
Program Organization
Program Organization
Provide Personalized Instruction
Consumable student study guides and minimal preparation requirements allow for flexibility and
personalized instruction in any setting.
• After school • Summer school
• Before school • Intersession
• Tutoring • Pull-out/Resource room
L3es-so8n Add Fractions
VOCABULARY
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Fully worked-out Examples enable students and 4. Circle

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GO ON
Lesson 1-1 Number Groups 5
Program Organization T7
Guided Practice
Guided Practice U1se 2>.5,4 < , or 2=.4 5to compare each pair of numbers.
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progress and guide your instruction. In which place values are the digits the same?
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GO ON
Lesson 2-2 Compare and Order Decimals 57
StepbyStepProblem-Solving Practice
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he quit?
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Check o fUf nedaecrhs tsatenpd.: I underlined key words. .
Plan: To solve the problem, I will .
Solve: The answer is .
Check: I checked my answer by Step-by-Step Problem-Solving Practice walks the student
through a four-step problem-solving strategy (Understand,
Plan, Solve, Check) that is relevant to the word problem. Aids
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T8 Teacher Handbook
Program Organization
Balance
McGraw-Hill’s Math Triumphs is designed to provide students a balanced approach to
mathematics learning by offering them the opportunity to:
• investigate concepts and build their conceptual understanding;
• review, learn, and practice basic computational and procedural skills; and
• apply mathematics to problem solving in real-world situations.
F7ind theS vkoillulms,e Cof oenacche fpigtusre,. and Problem Solving
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Independent Practice V = 99 ccmm 66..55 ccmm 11..55 mm
Skill, Concepts, and Problem Solving V = VV == V = 11 mm
provide homework opportunities and 10 triangular prism V =
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GO ON
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140 Chapter 4 Real Numbers
Program Organization T9
Comprehensive
Assessment System
Data-Driven Decision Making
Math Triumphs offers frequent and meaningful assessment of student progress
within the curriculum structure and teacher support materials.
ss m e n t a n d 11Intervention S
e y
Ass ste
Diagnostic m
33
Summative
22
Formative
11
Diagnostic
STEP 1 Chapter Pretest Are you ready for Chapter 1?
Take the Chapter 1 Pretest to find out.
STEP 2 Preview Get ready for Chapter 1. Review these skills and compare
them with what you will learn in this chapter.
Initial Assessment Assess students’ knowledge What You Know What You Will Learn
You know how to add. Lesson 1-3
at the beginning of the year with the Example: 5 + 4 = 9 You can use a number line to add
Diagnostic and Placement Tests. TRY IT! integers.
1 2 + 5 = 2 3 + 5 = -3 + -2 = -5
3 4 + 7 = 4 6 + 6 =
Entry–Level Assessment Assess students’ prior -6-5-4-3-2-1 0 1 2
knowledge at the beginning of a chapter You know how to subtract. Lesson 1-4
Example: 12 - 4 = 8 You can use algebra tiles to subtract
with one of the following options. TRY IT! integers.
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3
T10 Teacher Handbook