Mathematics – Grade 7
Unit of Study: TEKS Spiraling/Testing Weeks 1-4, Numbers, Operation, and Quantitative Reasoning
Fourth Grading Period – Weeks 1-7 (24 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleNumbers follow patterns, such as place value, ratios or multiples. / Students should understand that:
· they can use scientific notation to make their numbers easier to read and understand.
· that the square root is the length of one side of a square.
· slope factors, and multiples are relationships between numbers
TEKS / TEKS Specificity - Intended Outcome
Concepts / 6.1 Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to:
6.1(D) write prime factorizations using exponents.
6.1(E) identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers.
6.1(F) identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers. / ” I CAN” statements highlighted in yellow should be displayed for students.
I can:
· write numbers using scientific notation. (TEKS 8.1D))
· use factors and multiples to find relationships between numbers (TEKS 6.1E,F)
· find the square root of numbers pictorially and through computation (TEKS 8.1C)
· slope is the related to multiples and ratios. (TEKS 8.2D)
7.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to:
7.1(C) represent squares and square roots using geometric models.
7.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to:
7.2(D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio. / 8.1 Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:
8.1(C) approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as , , ).
8.1(D) express numbers in scientific notation, including negative exponents, in appropriate problem situations.
8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:
8.2(D) use multiplication by a constant factor (unit rate) to represent proportional relationships.
Skills / 7.13 Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
7.13(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematics topics.
7.13(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.
7.13(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
7.13(B) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
7.14 Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to:
7.14(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.
7.14(B) evaluate the effectiveness of different representations to communicate ideas.
7.15 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:
7.15(A) make conjectures from patterns or sets of examples and nonexamples.
7.15(B) validate his/her conclusions using mathematical properties and relationships. / I can:
· use a variety of problem solving strategies in order to solve world problems. (TEKS 7.13C)
· create a problem solving plan in order to solve world problems. (TEKS 7.13A)
Evidence of Learning
80% of the time, students will demonstrate on paper or use models to show that they can:
· write a set of numbers using scientific notation.
· find the square root of a set of numbers using computation or pictures.
· find the slope of a line given a set of points.
CURRICULUM GUIDE
Why do you think they call it slope or square root? / Grade 5
5.3(B): Use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology).
5.3(C): use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context.
5.3(D): identify common factors of a set of whole numbers.
Grade 6
6.1(D) write prime factorizations using exponents.
6.1(E) identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers.
6.1(F) identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers.
6.2(C): use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates.
Grade 7
7.1(C) represent squares and square roots using geometric models.
7.2(D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio.
The Teaching Plan
Instructional Model & Teacher Directions
The teacher will… / Assessment for Learning
so students can…. / Resources
April 6-23: Campuses are to use these days to choose their own lessons to spiral TEKS that are shown to be of greatest need according to campus data from FMA’s and benchmark assessments. District weaknesses according to the benchmark exam are 7.1D, 7.2A,C,D, 7.3B, 7.5B, 7.14A,B,C, 7.16A,B. Resources can be found by accessing the following link:
Middle School Region 4 Publications
April 27-May 1: These days are set aside for TAKS testing.
Note: The purpose of the following lessons is to preview or provide students with a step up to 8th grade content.
Note: For Step 1 Problem Solving:
· Use Problem Solving Checklist and the strategies that were studied in the Lane County Mathematics Project. Since only 10 minutes are allotted each day for problem solving, it will take more than one day to complete the checklist, therefore, one problem can be used over a period of several days.
Note: The follow lessons begin with a review of sixth grade TEKS dealing with prime factorization, greatest common factor and least common multiple.
Days 1&2
Day 1
Step 1: Problem Solving: : Follow steps 1-4 of the Problem Solving Checklist using Math Benchmarks 6.1D / · use math journals to write about their methods of problem solving – what works for them. (7.14A)
· use the various problem solving strategies in order to solve problems. (7.13C)
· follow the steps in the problem solving checklist in order to solve problems. (7.13C) / · Student math journals – students need either a spiral notebook or a section in their binder for math journal.
· Problem Solving Checklist
· Probing Questions
· Math Benchmarks 6.1D
Step 2: Interactive Learning:
Teacher begins with the activity on page 165. Discuss vocabulary: prime number, composite number, prime factorization, and factor tree. Assign students to complete Vocabulary in Mathematics in their spirals for prime numbers and composite numbers. / Students will take make a list of prime numbers in their journal and then complete Vocabulary in Mathematics in their journals for prime numbers and composite numbers. (6.1E) (Marzano) / McDougal Littell Math Course 2, Chapter 4.1, p. 165
Vocabulary in Mathematics
Step 3: Visual Learning and Practice:
Teacher will model Examples 1 and 2 and use factor trees to find the prime factorization, which will be written using exponents. Students will work with a partner to complete Guided Practice problems 2-6 on page 166. / Students will find the prime factorization of a number using number trees and write it using exponents. (6.1D,E) They will work with a partner. (Marzano) / McDougal Littell Math Course 2, Chapter 4.1, p. 166
Day 2
Step 1: Problem Solving: : Follow steps 1-4 of the Problem Solving Checklist using Math Benchmarks 6.1D / · use math journals to write about their methods of problem solving – what works for them. (7.14A)
· use the various problem solving strategies in order to solve problems. (7.13C)
· follow the steps in the problem solving checklist in order to solve problems. (7.13C) / · Student math journals – students need either a spiral notebook or a section in their binder for math journal.
· Problem Solving Checklist
· Probing Questions
· Math Benchmarks 6.1D
Day 2
Step 4: Differentiate/Assessment:
Assign students to complete problems 9-11, with partners and 12 independently, from page 166. Teacher will monitor students and/or reteach TEKS 6.1D,E with small groups for students who are struggling.
Reteach Suggestions: Reteach TEKS (6.1D,E) using the TAKS formatted questions for 6.1D,E in McDougal Littell Course 2 Problem Solving Practice from pages 168-169.
Recommended Homework: McDougal-Littell section 4.1, page 167, problems 1,2,6,7,16-21. (Marzano) / Students will find the prime factorization of a number using number trees and write it using exponents. (6.1D,E) / McDougal Littell Math Course 2, Chapter 4.1, p. 166-169
Day 3:
Step 1: Students will follow step 5 of the Problem Solving Checklist and
write a new problem, like this problem, for others to solve. / · of problem solving – what works for them. (7.14A)
· use the various problem solving strategies in order to solve problems. (7.13C)
· follow the steps in the problem solving checklist in order to solve problems. (7.13C) / · Student math journals – students need either a spiral notebook or a section in their binder for math journal.
· Problem Solving Checklist
· Probing Questions
· Math Benchmarks 6.1D
Step 2: Interactive Learning:
Activity 4.2 Greatest Common Factor:
See the teacher notes for activity preparation and materials management. Prepare index cards with the following numbers: 8,12,16,18,20,24,28,32,36,40,42,48,64,80,100,120,144,180. Numbers can be repeated so that each person receives a card. / Students will work individually with their number card and write the factors of their number.(6.1E) / McDougal Littell Math Course 2, Activity Generator Disc, Activity 4.2.
Index cards
Strips of paper
Step 3: Visual Learning and Practice:
From step 2 of the Activity Generator Disc, copy the table from Step 2 for each student and provide them with a thin strip of paper.
From step 3 of the Activity Generator Disc, pair students up with a partner who has a different number. / Individually, each student will record their information in their table.
With their partner, students will record their information in their table.
Students will complete the last column. Then, they will mingle with other students who have different numbers and record data in the table in order to find the greatest common factor. (6.1E) (Marzano) / McDougal Littell Math Course 2, Activity Generator Disc, Activity 4.2.
Step 4: Differentiate/Assessment:
Facilitate a class discussion to draw conclusions. Assign the students to complete Draw Conclusions questions 1-3 to demonstrate they can find the greatest common factor. Teacher will monitor students and/or reteach TEKS 6.1D,E with small groups for students who are struggling.
Reteach Suggestions: Reteach TEKS 6.1D,E using the TAKS formatted questions for 6.1D,E in McDougal Littell Course 2 problem solving questions from pages 173-174.
Recommended Homework: McDougal-Littell practice work book, section 4.2, page 172, problems 3-5, 16, 45, 47. (Marzano) / Students participate in a class discuss regarding their findings and complete Questions 1-3 to describe how to find the greatest common factor. (6.1E) / McDougal Littell Math Course 2, Activity Generator Disc, Activity 4.2.
McDougal Littell Math Course 2, Chapter 4.2, pp. 172-174
Day 4:
Step 1: Have students exchange one of their problems with a partner and solve each others problems. / · of problem solving – what works for them. (7.14A)
· use the various problem solving strategies in order to solve problems. (7.13C)
· follow the steps in the problem solving checklist in order to solve problems. (7.13C) / · Student math journals – students need either a spiral notebook or a section in their binder for math journal.
· Problem Solving Checklist
· Probing Questions
· Math Benchmarks 6.1D
Step 2: Interactive Learning:
Activity 4.4 Investigating the Least Common Multiple from the Activity Generator Disc.
Provide students with the recording sheet. Pair students and assign them to follow steps 1-4 to find the least common multiple of two numbers. / Students will work in pairs to find the least common multiple of 3 sets of numbers. (6.1F) (Marzano) / McDougal Littell Math Course 2, Activity Generator Disc, Activity 4.4.
Step 3: Visual Learning and Practice:
Assign students to complete Draw Conclusions questions 1-5 with their partner using their observations of least common multiple. Then assign students to complete Explore 2. / Students will use their observations of least common multiples to answer the Draw Conclusions questions 1-5. Then have the students use prime factorization to find the least common multiple and complete Explore 2. (6.1F) (Marzano) / McDougal Littell Math Course 2, Activity Generator Disc, Activity 4.4
Step 4: Differentiate/Assessment:
Assign students to complete the Draw Conclusions 6-12 from the Activity Generator Disc as a class to demonstrate their knowledge of least common multiple. Teacher will monitor students and/or reteach TEKS 6.1F with small groups for students who are struggling.
Reteach Suggestions: Reteach TEKS (6.1F) using the TAKS formatted questions for 6.1F in McDougal Littell Course 2 pages 186.