Connected Mathematics Project 3 : Assessment Support · PDF fileStudents answer questions that draw out their ... that you can give—Check-Ups and Partner Quizzes. ... Connected Mathematics

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Assessment Support

Introduction

Formative and Summative Assessment

Observation

This guide examines Connected Mathematics Project (CMP3) assessment options that help you monitor students’ progress, inform your instruction, and evaluate students’ performance in mathematics.

It also explains how to use both formative and summative assessment tools and resources to target your instructional goals.

Most assessments can serve either formative or summative functions, depending on how you interpret the results.

The assessment is formative if you use the results to inform your instruction. The assessment is summative if you use the results to evaluate students’ understanding of concepts and skills.

Now, examine the varied opportunities for formative and summative assessment in the CMP3 curriculum, and explore how you might use them to inform your instruction and increase students’ learning.

The curriculum provides numerous opportunities to assess students’ understanding by observing students during their group work and class discussions. As students solve problems, they engage in the mathematics and apply their knowledge with their peers. This gives you the opportunity to observe and listen.

Use the Suggested Questions throughout the Launch, Explore, and Summarize phases of each Problem to prompt discussion and elicit students’ thinking and understanding.


Checkpoints

End of Investigation

This type of observation as a form of assessment is important, since some students are better able to show their understanding in verbal situations rather than in formal written assignments.

Some of the assessment tools give you and your students an opportunity to check their understanding at key points in the unit. CMP3 provides checkpoints to help students solidify their understanding, determine the areas that need further attention, and help you make decisions about whether students are ready to move on.

The Applications, Connections, and Extensions (ACE) exercises and the Mathematical Reflections are two CMP3 features that students do at the end of every Investigation. These features assess their understanding of the concepts that they learned throughout the Investigation.

2. A university marching band consists of 60 members. The band director wants to arrange the band into a rectangular array for the halftime activities.

a. In how many ways can she arrange the band? Make a sketch of each arrangement.

b. How many rectangular arrangements are possible if the band adds one member and becomes a 61-member band?

3. The prime factorization of Tamika’s special number is 2 * 2 * 3 * 11 and the prime factorization of Cyrah’s special number is 3 * 3 * 5 * 5.

a. What is the least common multiple of the two special numbers?

b. What is the greatest common factor of the two special numbers?

c. List all the factors of Tamika’s number.

d. Is Tamika’s number even or odd? Is Cyrah’s number even or odd?

e. Is Tamika’s number a square number? Is Cyrah’s number a square number?

4. Shani gave a clue for her secret number.

Clue 1: My number is a factor of 90.

a. Can you determine what Shani’s secret number is?

b. What is the smallest Shani’s number can be? What is the largest Shani’s number can be?

c. Brandon says the secret number must also be a factor of 180. Is he correct?

d. Shani gave a second clue for her secret number.

Clue 2: My number is prime.

Now can you determine what the secret number is?

e. Shani gave a third clue for her secret number.

Clue 3: Twenty-one is a multiple of my secret number.

Now can you determine what the secret number is?

For Exercises 5–7, insert parentheses and addition, subtraction, or multiplication signs on the left side of the equality sign to make a true statement.

5. 3 2 1 = 9

6. 6 4 3 2 = 26

7. 5 7 2 7 = 21

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Looking Back

While working on the Problems in this Unit, you investigated some important properties of whole numbers. Finding factors and multiples of numbers and identifying prime numbers helps in answering questions about clocks and calendars, puzzles and games, and rectangular patterns of tiles. Factoring also focuses attention on the properties of even and odd numbers, square numbers, greatest common factors, and least common multiples.

Use Your Understanding: Number PatternsTest your understanding of multiples, factors, and prime numbers by solving the following problems.

1. The Red Top Taxi Company wants to keep its cars in good operating condition. It has a schedule for regular maintenance checks on each car. Oil is to be changed once every 6 weeks. Brakes are to be inspected and repaired every 10 weeks.

a. After a new cab is put in service, is there ever a week when that cab is scheduled for both an oil change and a brake inspection? If so, what is the first such time?

b. Suppose the oil change time is extended to 8 weeks and the brake inspection to 12 weeks. Is there ever a week when the cab is due for both an oil change and a brake inspection? If so, when will such a incident first occur?

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Mathematical Reflections

In this Investigation, you used common factors and common multiples to solve problems. These questions will help you summarize what you learned.

Think about your answers to these questions. Discuss your ideas with other students and your teacher. Then write a summary in your notebook.

1. How can you decide if finding common multiples or common factors is helpful in solving a problem? Explain.

2. a. Describe how you can find the common factors and the greatest common factor of two numbers.

b. What information does the greatest common factor of two numbers provide in a problem?

3. a. Describe how you can find the common multiples and the least common multiple of two numbers.

b. What information does the least common multiple of two numbers provide in a problem?

Unit ProjectDon’t forget to write about your favorite number!

What new concepts have you learned about your number?

WHAT’S

NEX

T

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The ACE exercises are homework questions that help students uncover math relationships and build stronger problem-solving strategies and skills. Students’ performance on the ACE exercises provides a summative assessment of learning.

Mathematical Reflections can either serve as a summative or formative assessment, depending on how you apply this feature during instruction. Students answer questions that draw out their understanding of the summative content of the Investigation.

Mathematical Reflections include teacher support that focuses on how possible students’ responses might inform your instruction.

Applications Connections Extensions

Connections 60. The Spartan Bike Shop keeps a record of their business transactions.

They start their account at zero dollars. Write a number sentence to represent each transaction. Then find the new balance.

BIKE SHOP

For Exercises 61 and 62, write a number sentence for each situation. Then answer the question.

61. The air temperature drops from 94°F to 72°F in 15 minutes. What is the change in temperature?

62. The Teacher’s Pets team has 50 points in Math Fever. They miss a question worth 200 points. What is their new score?

63. Find four different numbers, in order from least to greatest, that lie between the two given numbers.

a. -4.5 and -3.5

b. -0.5 and 0.5

49Investigation 2 Adding and Subtracting Rational Numbers

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ExtensionsConnectionsApplications

Extensions 41. Jocelyn and Moesha decide to play the Factor Game on a 100-board.

A 100-board includes the whole numbers from 1 to 100.

a. What will Jocelyn score if Moesha chooses 100 as her first move?

b. What will Jocelyn score if Moesha chooses 99 as her first move?

c. What is the best first move on a 100-board?

42. What number am I?

Clue 1 When you divide me by 5, the remainder is 4.

Clue 2 I have two digits. Both digits are odd.

Clue 3 The sum of my digits is 10.

43. The sum of the proper factors of a number may be greater than, less than, or equal to the number. Mathematicians use this idea to classify numbers as abundant, deficient, or perfect. Each whole number greater than 1 falls into one of these three categories.

a. Draw and label three circles as shown below. The numbers 12, 15, and 6 have been placed in the appropriate circles.

Abundant Deficient Perfect

12 15 6

Use your factor list to determine what each label means. Then, write each whole number from 2 to 30 in the correct circle.

b. Are the labels appropriate? Why or why not?

c. In which circle does 36 belong?

d. In which circle does 55 belong?

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Before a Unit Every unit in CMP3 has a Unit Readiness check that students can access through Dash or MathXL® for School. The Unit Readiness consists of ten quick skill questions that provide diagnostic information about your students’ level of readiness to learn the mathematics in the unit.

Use the Unit Readiness Report to indicate which objectives students are proficient in and which you need to reteach.


During a Unit

Looking Back

During the unit, there are two formative, hand-graded assessments that you can give—Check-Ups and Partner Quizzes.

Check-Ups are short, individual assessment instruments. The questions tend to be less complex and more skill-oriented than questions on quizzes and unit tests. Check-Ups are intended to provide insight into students’ understanding of the baseline mathematical concepts and skills of the unit.

The Partner Quiz questions are richer and more challenging than the Check-Up questions. These questions provide insight into how students apply ideas from the unit to new situations.

Both assessments provide useful diagnostic information on how students understand and grasp the unit concepts.

Looking Back is a summative assessment that includes questions that check students’ understanding of the unit’s content. You will also find questions that require students to explain their reasoning about the key concepts of the unit.

Teacher support is provided throughout the unit to help you maximize learning opportunities that the assessments provide.


End of Unit

Unit Tests

Performance-based assessment is an important assessment tool in the next-generation assessments for the Common Core State Standards. The Unit Project is a performance-based, open-ended task that allows students to engage in independent work and demonstrate a broad understanding of the ideas in the unit.

Teacher support includes scoring rubrics and Sample Student Work.

In addition, there are hand-graded Unit Tests at the end of every CMP3 unit. These tests assess a summative mastery of concepts and skills for a collection of Investigations.

The Unit Test is an individual assessment intended to inform you about a student’s ability to apply, refine, modify, and possibly extend the mathematical knowledge and skills that he or she acquires in the unit.


If your school uses MathXL® for School for extra skills practice, you have access to additional assessments. Assess your students’ knowledge at the beginning of the year, and check their mastery mid-year and at the end of the year.

The assessments are comprehensive, and because they are auto-graded, you receive immediate results and insight as to how your students progress and perform over the course of the entire year.

This guide explored CMP3 assessment options that help you monitor students’ progress, inform your instruction, and evaluate students’ performance in mathematics.

It also discussed how to use both formative and summative assessment tools and resources to target your instructional goals.

MathXL® for School

Review

Documents

Connected Mathematics Project 3 : Assessment Support · PDF fileStudents answer questions that draw out their ... that you can give—Check-Ups and Partner Quizzes. ... Connected Mathematics