Pearson Integrated High School Mathematics : Program Overview · The Pearson Integrated High School...
7
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved. 1 Program Overview Introduction Integrated Pathway This guide explores the Pearson Integrated High School Mathematics program. It discovers how to use the blended print and digital curriculum to teach the five-part lesson structure. This guide also examines how the program is built to address the Common Core State Standards (CCSS). Pearson’s Integrated High School Mathematics program follows the Common Core’s integrated pathway of Mathematics I, Mathematics II, and Mathematics III. The program combines standards from all of the mathematical content strands. Each year, students learn concepts from all six conceptual categories. Pearson Integrated High School Mathematics helps students make connections within mathematics from one conceptual category to another. The program also ensures that students make explicit connections between the Standards for Mathematical Content and the Standards for Mathematical Practice. This helps further build their mathematical understanding and problem-solving strategies. In addition, the problems more closely resemble real-world situations that are more likely to require math skills from a variety of content strands. The visually rich problems facilitate understanding of the problem situations so students can connect to mathematical models more easily. In the Pull It All Together activities, student are often expected to apply a mathematical model to the situations presented. 4 80 in. 480 in. Problem 4 Using a Scale Factor to Find Capacity Containers A bottle that is 10 in. high holds 34 oz of milk. e sandwich shop shown at the right is shaped like a milk bottle. To the nearest thousand ounces how much milk could the building hold? e scale factor of the bottles is 1 i48. e ratio of their volumes, and hence the ratio of their capacities, is 13i483, or 1 i110,592. 1 110,592 5 34 x Let x 5 the capacity of the milk-bottle building. x 5 34 ? 110,592 Use the Cross Products Property. x 5 3,760,128 Simplify. e milk-bottle building could hold about 3,760,000 oz. STEM Standards for Mathematical Practice 15
Transcript of Pearson Integrated High School Mathematics : Program Overview · The Pearson Integrated High School...
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.1
Program Overview
Introduction
Integrated Pathway
This guide explores the Pearson Integrated High School Mathematics program. It discovers how to use the blended print and digital curriculum to teach the five-part lesson structure. This guide also examines how the program is built to address the Common Core State Standards (CCSS).
Pearson’s Integrated High School Mathematics program follows the Common Core’s integrated pathway of Mathematics I, Mathematics II, and Mathematics III. The program combines standards from all of the mathematical content strands. Each year, students learn concepts from all six conceptual categories.
Pearson Integrated High School Mathematics helps students make connections within mathematics from one conceptual category to another. The program also ensures that students make explicit connections between the Standards for Mathematical Content and the Standards for Mathematical Practice. This helps further build their mathematical understanding and problem-solving strategies. In addition, the problems more closely resemble real-world situations that are more likely to require math skills from a variety of content strands.
The visually rich problems facilitate understanding of the problem situations so students can connect to mathematical models more easily.
In the Pull It All Together activities, student are often expected to apply a mathematical model to the situations presented.
RA
CTI
CES
MAT
HEM
ATIC
AL
PRA
CTI
CES
MAT
HEM
ATIC
AL
PRA
CTI
CES
MAT
HEM
ATIC
AL
PRA
CTI
CES
MAT
HEM
AT
480 in.480 in.
Problem 4
Got It?
Lesson 11-7 Areas and Volumes of Similar Solids 745
Using a Scale Factor to Find Capacity
Containers A bottle that is 10 in. high holds 34 oz of milk. The sandwich shop shown at the right is shaped like a milk bottle. To the nearest thousand ounces how much milk could the building hold?
The scale factor of the bottles is 1 i 48.
The ratio of their volumes, and hence the ratio of their capacities, is 13 i 483, or 1 i 110,592.
1110,592 5
34x
Let x 5 the capacity of the milk-bottle building.
x 5 34 ? 110,592 Use the Cross Products Property.
x 5 3,760,128 Simplify.
The milk-bottle building could hold about 3,760,000 oz.
4. A marble paperweight shaped like a pyramid weighs 0.15 lb. How much does a similarly shaped marble paperweight weigh if each dimension is three times as large?
Lesson CheckDo you know HOW? 1. Which two of the following cones are similar? What is
their scale factor?
2. The volumes of two similar containers are 115 in.3 and 67 in.3. The surface area of the smaller container is 108 in2. What is the surface area of the larger container?
Do you UNDERSTAND? 3. Vocabulary How are similar solids different from
similar polygons? Explain.
4. Error Analysis Two cubes have surface areas 49 cm2 and 64 cm2. Your classmate tried to find the scale factor of the larger cube to the smaller cube. Explain and correct your classmate’s error.
hsm11gmse_1107_t10073.ai
The scale factor of thelarger cube to the smallercube is 7 : 8.
20 m 25 m 30 mCone 1 Cone 2 Cone 3
45 m35 m30 m
hsm11gmse_1107_t10067.ai
How does capacity relate to volume?Since the capacities of similar objects are proportional to their volumes, the ratio of their capacities is equal to the ratio of their volumes.
MATHEMATICAL PRACTICES
STEM
GEOM12_SE_CCS_C011L07.indd 745 2/2/11 4:32:52 PM
Standards for Mathematical Practice 15
HSIM14_ANC_NA_OIG_01-27.indd Page 15 22/05/13 2:55 AM s-059 /129/PE00739_ANC/HSIM14_ANCILLARIES/ANCILLARY/HSIM14/Math_01/XXXXXXXXXX/Layout/In ...
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.2
Implementing the Common Core State Standards
Standards for Mathematical Content
Standards for Mathematical Practice
First, take a look at the implementation guide—Implementing the Common Core State Standards. You will find an overview of the Standards for Mathematical Content and the Standards for Mathematical Practice—the two sets of standards that make up the Common Core State Standards for Mathematics (CCSSM).
The high school Standards for Mathematical Content consist of six conceptual categories that define what students should understand and be able to do.
These conceptual categories are Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability.
The Standards for Mathematical Practice describe eight processes, practices, and dispositions of mathematically proficient students. They draw from problem-solving skills, reasoning skills, and the mathematical ways of thinking.
Your Implementing the Common Core State Standards guide has explicit information on how the program teaches and assesses these standards. It provides tools and resources to support your instruction.
The Observation Protocol is one example. Use this tool to monitor your students’ progress toward developing proficiency with the Standards for Mathematical Practice.
The Observation Protocol provides a list of characteristics for each math practice. Note the characteristics that your students exhibit as you observe them solving problems. You can reproduce or download the protocol from PearsonSuccessNet.com. You will find it within the Teacher Resources link. Use the Observation Protocol for daily formative assessment during your instruction.
Standards for Mathematical PracticeObservational Protocol
Name of Student
Suggested rating: P = shows proficiency; D= developing; E = emerging; 0 = No evidence
1. Make sense of problems and persevere in solving them.
a. identifies main task of the problem
b. relates to other problems
c. explains relationships among numbers or quantities
d. identifies solution plan
e. checks reasonableness of solution
f. checks solution plans
g. uses a different method to check solution
h. compares/contrasts solution plan
NOTES
2. Reason abstractly and quantitatively
a. explains relationships among numbers
b. writes an equation or expression for a problem
c. explains referents and meaning of numbers
d. explains meaning of quantities
NOTES
3. Construct viable arguments and critique the reasoning of others.
a. asks appropriate questions
b. compares and contrasts various solutions
c. explains solution and justifies conclusions
d. recognizes flaws in logic/thinking
NOTES
4. Model with mathematics.
a. represents a problem situation
b. identifies the key quantities
c. represents relationships among quantities graphically
d. analyses relationships of quantities
e. explains relationships among quantities
f. asks whether the solution is reasonable
NOTES
Dates of Observations
58 Observation Protocol
HSIM14_ANC_NA_OIG_52-79.indd Page 58 23/05/13 1:31 AM s-059 /129/PE00739_ANC/HSIM14_ANCILLARIES/ANCILLARY/HSIM14/Math_01/XXXXXXXXXX/Layout/In ...
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.3
Program Components
The Pearson Integrated High School Mathematics program is a blended print and digital program. The digital and print components aid in teaching and student learning and engagement.
The Pearson Integrated High School Mathematics program contains the print write-in student worktext and the Teacher’s Guide.
The write-in student worktext is a personal learning journal and resource text. Direct students to the worktext to record their work, take notes, and complete additional practice with the More Practice and Problem Solving features. Note the Quick Response (QR) codes on the first page of each lesson. Prompt students to scan these codes to view math videos developed by Virtual Nerd.
The Teacher’s Guide is a comprehensive resource that you can use to plan and teach your lessons. The guide contains images from the student worktext and the Interactive Digital Path. In addition, you will find math background information, facilitating questions, teaching notes, answers to problems, formative assessment suggestions, and suggestions for differentiation.
The student worktext and the Teacher’s Guide contain Activity Labs, Technology Labs, and Lesson Labs. These labs are hands-on activities designed to build students’ understanding and prepare them for later concepts.
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.4
Digital Components
You can access digital courseware for the program through the Interactive Digital Path at PearsonSuccessNet.com or through the Digital Lesson DVD. Access interactive problem situations that build students’ understanding of the mathematical concepts and increase their engagement. Use the Interactive Digital Path to present problems and guide students through problem solving. Use the tools to aid in their exploration of complex mathematical situations. The Interactive Learning and the Guided Instruction portions of the lesson offer probing questions and suggestions to help students think through the problem.
The Interactive Digital Path contains math tools and activities that you can use to further enhance students’ learning.
You will also find a variety of teacher and student resources, such as lesson enrichments, assessments, Virtual Nerd tutorial videos, and lesson planners.
The Student worktext and the Teacher’s Guide are also available as online eTexts. Point out to students the animated videos that are linked at point of use.
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.5
Lesson Structure
Interactive Learning
The five-part lesson structure is designed to help students develop conceptual understanding, build skill fluency, and build reasoning and problem-solving abilities through an application to real-world contexts.
Each lesson opens with a problem-based interactive situation called Solve It! Present this activity from the Interactive Digital Path as a warm-up to the lesson. Note the space in the write-in student worktext where students can work out their solution plans for the Solve It! problem.
Also notice the format of the Teacher’s Guide for facilitating the Solve It! problem.
The right column has the image from the Interactive Digital Path, while the left column contains probing questions to facilitate this Interactive Learning portion of the lesson.
Patterns and Nonlinear Functions
2-3
Objective To identify and represent patterns that describe nonlinear functions
Solve It! Write your solution to the Solve It in the space below.
The relationship in the Solve It is an example of a nonlinear function. A nonlinear function is a function whose graph is not a line or part of a line.
Essential Understanding Just like linear functions, nonlinear functions can be represented using words, tables, equations, sets of ordered pairs, and graphs.
SOLVE IT!
Concept Summary Linear and Nonlinear Functions
Linear Function
A linear function is a function whose graph is a nonvertical line or part of a nonvertical line.
x
y
O x
y
O Ox
y
Nonlinear Function
A nonlinear function is a function whose graph is not a line or part of a line. O x
y
O x
y
xO
y
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features . . . Also A.CED.2
Chapter 2 An Introduction to Functions110
HSIM14_SE_M1V1_C0203.indd Page 110 29/03/13 8:54 AM s-059 /143/PE00739/INTEGRATED_HSIM14/SE/Math_01/0133234614_G8_9_V1/Layout/Interior_File ...
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.6
Guided Instruction
Lesson Check
Practice
Following the Interactive Learning portion is the heart of the lesson—Guided Instruction. Note the same two-column format. All of the support that you need to facilitate this step is on the left; all of the answers and images from both the Interactive Digital Path and write-in student worktext are on the right.
Use the Interactive Digital Path to guide students through various problems. Notice that the Guided Instruction problems in the Interactive Digital Path are not in the write-in student worktext. This helps students learn better because they focus on understanding the mathematics instead of taking notes. Formatively assess yours students with the Got It? exercises. These problems offer your students a chance to apply what they learned and to create worked-out examples for homework and study reference. Find more formative assessment after each Got It? exercise with the Practice exercises.
Take Note boxes provide definitions or explanations of mathematical concepts, and the Think, Plan and Know-Need-Plan boxes incorporate reasoning in the mathematical discussions.
The Do You Know HOW? and Do You UNDERSTAND? features help you measure students’ understanding of the lesson content. These problems uniquely assess both students’ procedural fluency and conceptual understanding of the concepts.
Provide students with an opportunity to solidify their understanding with More Practice and Problem-Solving Exercises. Direct students to their worktexts or to the Interactive Digital Path to access the problems. Exercises fall into three categories—practice, application, and challenge problems.
Copyright © 2013 Pearson, Inc. or its affiliates. All rights reserved.7
Each lesson ends with a Lesson Quiz. Use the quiz results to provide differentiated instructional support as suggested in the Teacher’s Guide.
Assign the Lesson Quiz through Pearson SuccessNet®’s Success Tracker™, which will automatically score the quiz and assign the appropriate intervention for each student.
Or, print the editable document as a paper and pencil option.
This guide examined the Pearson Integrated High School Mathematics program. It discovered how to use the blended print and digital curriculum to teach the five-part lesson structure. This guide also explored how the program is built to address the CCSS.
Assess and Remediate
Review
