Essential Unit 5 (E05)

MATHEMATICS-9

ESSENTIAL UNIT 5 (E05)

(Factors, Multiples, & Patterns)

(July 2013)

Unit Statement: The student will explore patterns observable in multiplication products with a goal of recognizing and applying proper math concepts and terminology, and developing and applying problem-solving skills in real-life situations.

Essential Outcomes: (must be assessed for mastery)

Problem solving and higher order thinking components are essential for “A” level mastery. Each TSW can contain problem solving and higher order thinking components (as found in suggested text).

1. The Student Will find all the factors of a number by using models. (Go Math4 5.1)*

2. TSW determine whether a number is a factor of a given number. (5.2)

3. TSW apply the “Make-A-List” strategy to solve problems. (5.3)

4. TSW determine if one number is a multiple of another given number. (5.4)

5. TSW explain the relationship between factors and multiples. (5.4)

6. TSW identify numbers as being either: prime, composite, or neither. (5.5)

7. TSW generate a number pattern and describe the features of the pattern. (5.6)

*Suggested Go Math chapter sections to use with TSW’s

Introduced and Practiced Outcomes:

1. The Student Will practice basic facts to improve accuracy or speed.

2. TSW discuss the concepts using the key terms.

Key Terms and Concepts:

Prime factor Composite number Common multiple Pattern Term

Prime number Factor Multiple Divisibility array

Suggested Assessment Tools and Strategies:

Go Math! 4 instruments for assessment

Anecdotal records for formative notes

Original project rubrics

Suggested Resources:

Go Math! 4 adopted student editions, Chapter 5

Go Math! 4 chapter 5 planner matrix located in the Teacher Edition, pp. 191A-191F (hard copy, CD &/or online)

Go Math! 4 EverydayCounts whiteboard lessons (CD or online)

Go Math! 4 eplanner (These are helpful with prepping for, and organizing the manipulatives and other support materials if using the text to teach the lesson.)

School manipulatives collection for 9 year old classes

Additional Resources:

These materials will not be provided automatically, but schools are encouraged to purchase them to support the course.

Everyday Math Counts Kit for Grade 4 to include the teacher manual

Technology Links:

These links.are part of the Go Math! 4 program purchased and should provide support until 2020. Access to the internet versions of the electronic resources suggested above is achieved through these links.

WebPath express (On library computers, if not on classroom desktops)

http://www.hmhelearning.com

http://www-k6.thinkcentral.com

Suggested Activities:

· In math journal, have students explain the process used to get the prime factorization of any number and make connections by giving examples of how that is useful.

· Create “Prime Factor Trees” by gluing numbered circles (ornaments) onto triangular arrangements with green strips connecting these circles. Try to balance the factorization to create the most triangular arrangement on the 2-D paper. (composite factors should be at the top of the tree, just beneath the large composite number being factored)

· Play the games in the centers, online, or private collections to provide opportunities for students to practice verbalizing their thoughts. Ex: Use dice or playing cards to allow players to create factorization exercises. Observe as they determine if numbers are P or C and if C, what is the P-factorization.

· Page 191C, GM Chapter 5 TE, plus digital path info

· Mad math sheets

Suggested Cross-curricular Activities:

Art forms can be assembled from multiple, folded, bilaterally symmetrical evergreen tree patterns which students glue together in a stack of 4 to 16 (or more). Use yarn to connect the higher composite-numbered circles or spheres to their factor-numbered circles or spheres. This “decorates” a Christian holiday Christmas Tree. The starting number can be written on a star at the top of the 3-D form.

Research and report on the largest prime number known and find out when it was first identified.

Do an analysis of everyone’s age to see how many “Prime” birthdays they have had, or expect to have. Were they born on a PRIME day? What other historical events occurred on “prime” days?

How many ribs are in your body and which ones are the “Prime” ribs? (Humor—ar..ar. . !)

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE………………..

QSI MATHEMATICS-9 E05

What I need to do…..E05 –FACTORS, MULTIIPLES, AND PATTERNS

Task
TSW / ‘A’ LEVEL / ‘B’ LEVEL / P
Teacher comments
find all the factors of a number by using models. / I can find all the factors of a number by using models.
determine whether a number is a factor of a given number. / I can tell if a number is a factor of a given number.
apply the “Make-A-List” strategy for problem solving. / I choose to use this strategy to solve unfamiliar problems. / I know what the “Make-A-List” strategy is and I can use it to solve a problem.
determine if one number is a multiple of another given number. / I can tell if one number is a multiple of another given number.
explain the relationship between factors and multiples. / I can create new examples to help explain how factors are connected to multiples. / I can explain the relationship between factors and multiples in a given problem.
identify numbers as being either: prime, composite, or neither. / I can identify numbers as prime, composite, or neither.
generate a number pattern and describe the features of the pattern. / I can make new sequences that have complicated rules not used in class, and I can tell what a rule is for harder new patterns. / I can make a pattern that follows the same rule as one discussed in class, and tell what the rule is.

My E05 Rubric

In order to receive a ‘B’, I must have all ‘B’ level boxes checked.

In order to receive an ‘A’, I must have all boxes checked.

Student Name: Date:

QSI MATHEMATICS-9 E05