Mathematics – Grade 6
Unit of Study: Ratio, Proportion, and Percent
Second Grading Period – Weeks 1- 4 (17 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleThe students need to develop the ability to work with and between fractions, decimals, and percents. In order to be able to work well with these types of numbers, students need a strong understanding of ratio and proportion which is necessary for Algebra. / Students should understand that:
· proportions and ratios are a type of fractions.
· there are relationships between fractions, decimals and percents that can help them to evaluate correctly what they see in the media.
· percents, decimals and fractions are found in everyday life from shopping trips, income taxes and data analysis.
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(A) compare and order non-negative rational numbers.
6.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to:
6.2(C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates.
6.3 Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to:
6.3(A) use ratios to describe proportional situations.
6.3(B) represent ratios and percents with concrete models, fractions, and decimals.
6.3(C) use ratios to make predictions in proportional situations.
6.4 Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to:
6.4(A) use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area.
6.8 Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to:
6.8(B) select and use appropriate units, tools, or formulas to measure and to solv / ” I CAN” statements highlighted in yellow should be displayed for students.
I can:
· use visual models such as colored water and tiles to represent ratios. (TEKS 6.3B)
· use ratios to find equivalent rates. (TEKS 6.2C)
· use pictorial models and ratios to find proportions. (TEKS 6.3A)
· use multiplication to create scale drawings to find ratios and proportions. (TEKS 6.2C)
· use Cuisenaire rods and graph paper to model equivalent fractions, decimals, and percents. (TEKS 6.3B)
· use a number line to represent percents, fractions, and decimals. (TEKS 6.1A)
· use ratios to make predictions in similar situations. (TEKS 6.3C)
· use a table to describe relationships between the length, width, and perimeter of a rectangle. (TEKS 6.4A)
· use measurement tools in order to create scale drawings. (TEKS 6.8B)
e problems involving length (including perimeter), area, time, temperature, volume, and weight.
6.10 Measurement. The student uses statistical representations to analyze data. The student is expected to:
6.10(D) solve problems by collecting, organizing, displaying, and interpreting data.
Skills / 6.11 Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
6.11(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.
6.11(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.
6.12 Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to:
6.12(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. / I can:
· use a variety of problem solving strategies in order to solve world problems. (TEKS 6.11C)
· create a problem solving plan in order to solve world problems. (TEKS 6.11A)
Evidence of Learning
At least 80% of the time, students will demonstrate on paper or use models to show that they can:
1. convert between fractions, decimals, and percentages in problem solving situations.
2. follow a problem solving strategy in order to solve word problems.
Mathematics – Grade 6
Unit of Study: Ratio, Proportion, and Percent
Second Grading Period CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills· Why is it that percents, fractions, decimals and ratios can look so different but still mean the same thing?
· What types of professions use scale drawings?
· When is it easier to use a fraction? percent? decimal? ratio?
· What type of information can proportional reasoning give me? / Grade 4
· use place value to read, write, compare, and order whole numbers through 999,999,999. (TEKS 4.1A)
· use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete objects and pictorial models. (TEKS 4.1B)
· use multiplication to solve problems (no more than two digits times two digits without technology). (TEKS 4.4D)
· use division to solve problems (no more than one-digit divisors and three-digit dividends without technology). (TEKS 4.4E)
· describe the relationship between two sets of related data such as ordered pairs in a table. (TEKS 4.7A)
· estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary. (TEKS 4.11A)
Grade 5
· use place value to read, write, compare, and order whole numbers through 999,999,999,999. (TEKS 5.1A)
· use place value to read, write, compare, and order decimals through the thousandths place. (TEKS 5.1B)
· use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology). (TEKS 5.3B)
· 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. (TEKS 5.3C)
· describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams. (TEKS 5.5A)
· select and use appropriate units and formulas to measure length, perimeter, area, and volume. (TEKS 5.10C)
The Teaching Plan
Instructional Model & Teacher Directions
The teacher will… / Assessment for Learning
so students can…. / Resources
Days 1 – 15:
· Step 1: Problem Solving: Choose problems that correspond to the TEKS taught during this unit. Use problems from Math Benchmarks website or the Problem Solving questions from McDougal Littell’s Math Course 1, Chapter 8 for problems solving. Follow the 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. / Step 1: Problem Solving
· use math journals to write about their methods of problem solving – what works for them. (TEKS 6.12A)
· use the various problem solving strategies in order to solve problems. (TEKS 6.11C)
· follow the steps in the problem solving checklist in order to solve problems. (TEKS 6.11B) / Step 1: Problem Solving
· McDougal Littell Math Course 1-Chapter 8
· Student math journals – students need either a spiral notebook or a section in their binder for math journal.
· Problem Solving Checklist
· Probing Questions
Days 1&2: Proportional Reasoning Lesson: TAKS Mathematics Preparation Grade 6 (this lesson should take 2 days to complete)
Day 1:
Step 2: Interactive Learning
Engage:
· The teacher will demonstrate ratios by changing the number of drops of food coloring in water. Make sure when discussing ratios and proportions that you mention the different ways of representing them, such as 8/35, 8:35, or 8 to 35.
· The teacher will use the Facilitation Questions on page 76 for discussion.
Explore:
· The teacher is to move about the room and facilitate discussion using the Facilitation Questions on page 77.
Explain:
· The teacher will facilitate discussion of the lesson from the previous day using the Facilitation Questions from page 78. / Step 2: Interactive Learning
Engage:
· Students will describe ratios by observing what happens to the color of water as the number of drops of food coloring increases. (TEKS 6.3A)
· This will be a whole group activity.
Explore:
· Working in groups of 2-4 students, the class will explore the ratios of the different measurements of a rectangle using color tiles and complete the Perimeter of a Rectangle worksheet. (TEKS 6.3B, C)
Explain:
· Students will participate in a whole group discussion regarding the ratios and relationships they discovered completing the Perimeter of a Rectangle worksheet. (TEKS 6.3A, 6.10D) / Step 2: Interactive Learning
· TAKS Mathematics Preparation Grade 6– pp. 75-81
· Perimeter of a Rectangle, pp. 87-89
Other materials needed:
· color tiles
Day 2:
Step 3: Visual Learning and Practice
Elaborate:
· The teacher is to provide the students with color tiles. You will circulate around the room to monitor instruction and use the Facilitation Questions on page 82 to assist students in the problem solving process. / Step 3: Visual Learning and Practice
Elaborate:
· Working in groups of 2-4 students, the class will explore the ratios of the different measurements of a rectangle using color tiles and complete the More Perimeters of a Rectangle worksheet. (TEKS 6.3B, C, 6.10D)) / Step 3: Visual Learning and Practice
· TAKS Mathematics Preparation Grade 6– pp. 78-86
· More Perimeters of a Rectangle, pp. 90-92
Other materials needed:
· color tiles
Step 4: Differentiate/Assessment
Evaluate:
· The teacher will provide the students with the evaluation question and the goal is to assess the student with at least a 3 from the Mathematics Performance Assessment Rubric on page 269.
· Teacher will monitor students and/or work with small groups to provide interventions for students who are struggling.
· Suggested Homework: Assign Selected Response problems, pp. 99-103, questions 1, 2, 4, 5, 6. Differentiate homework according to student needs and abilities. / Step 4: Differentiate/Assessment
Evaluate:
· Students will work independently to complete the evaluation question following the Problem Solving Checklist (TEKS 6.3A) / Step 4: Differentiate/Assessment
· TAKS Mathematics Preparation Grade 6– page 86
· Evaluation question, p. 93
· Mathematics Performance Assessment Rubric, p. 269
· Problem Solving Checklist
· Probing Questions
Day 3: Rates: McDougal Littell Unit 8.2
Step 2: Interactive learning:
· Pose the Space scenario from Example 1 on page 407 to the class. Ask them to find the equivalent rate and unit rate in small groups. As the students work on the problem, circulate around the classroom and facilitate learning by asking questions such as, What is an equivalent rate?, What does equivalent mean? What is a unit rate? What does unit mean?
· Skip Examples 2 and 3. / Step 2: Interactive Learning
· Student will work in groups of 2-3 to find equivalent and unit rates. One or two groups will then share their answers with the class. (TEKS 6.2C, 6.3C) / Step 2 Interactive Learning
· McDougal Littell Math Course 1, Chapter 8, p. 407
Step 3: Visual Learning and Practice:
Explore:
· The teacher will guide the students through Example 5 on page 409. The students will then complete Question 6 independently. / Step 3: Visual Learning and Practice:
· Students will work along with the teacher in their journals on Example 5. They will then solve Question 6 independently. (TEKS 6.2C, 6.3C) / Step 3 Visual Learning and Practice
· McDougal Littell Math Course 1, Chapter 8, p. 409
Other materials needed:
· journals
Step 4: Differentiate/Assessment:
· Assign Problem Solving Questions 32-35 and assess for 80% accuracy.
Teacher will monitor students and or work with small groups to provide interventions for students who are struggling.
Suggested Homework: Problem Solving p. 411, 36-42. Differentiate homework according to student needs and abilities. / Step 4: Differentiate/Assessment
· Students will use ratios and rates to solve problems and write about the steps involved in their journals. (TEKS 6.2C, 6.3C) / Step 4 Differentiate/Assessment
· McDougal Littell Math Course 1, Chapter 8, pp. 410-411
Other materials needed:
· journals
Day 4: Solving Proportions: McDougal Littell Unit 8.3
Step 2: Interactive learning
· Draw the dot pictures from the beginning of unit 8.3 on the board. Label them as shown. Ask the class, What is a proportion? Have the students respond in their math journals. / Step 2: Interactive learning
· Students will communicate mathematically by responding in math journals to questions regarding proportions. (TEKS 6.3C) / Step 2: Interactive Learning
· McDougal Littell Math Course 1, Chapter 8, p. 412
Step 3: Visual Learning and Practice
· Skip to Example 3. Use Animated Math to demonstrate how the model proportions.
· Students will then continue on to solve the Guided Practice questions 1-7.
· Teacher will monitor students and/or work with small groups to provide interventions for students who are struggling. / Step 3: Visual Learning and Practice
· Students will participate by solving the problems at their desk in their journals and then sharing with the rest of the class. (TEKS 6.3C) / Step 3: Visual Learning and Practice
· McDougal Littell Math Course 1, Chapter 8, p. 413
· Animated Math
Other materials needed:
· journals
Step 4: Differentiate/Assessment:
· Assign Problem Solving Questions 44-47, pp. 415-416 and assess for 80% accuracy.
· Teacher will monitor students and or work with small groups to provide interventions for students who are struggling.