Mathematics – Grade 6
Unit of Study: Whole Numbers and Decimals
First Grading Period – Weeks 1-3 (11 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleThe students should develop an ability to use a multi-step process in order to solve word problems. The students will explore the value of decimals and be able to order them. In addition, students will use skills in rounding and estimation in order to add and subtract decimals. These skills will help students to solve problems using decimals, such as with money and measurement, in and outside of the mathematics classroom. / Students should understand that:
· in order to effectively and efficiently solve problems, students need to be able to implement a process that includes understanding the problem, creating a plan, working it out and checking for reasonableness..
· in order to budget their money effectively, students need a strong understanding of decimals.
· a strong knowledge of decimals is necessary when dealing with household projects such as landscaping, construction, cooking or sewing.
· there are different strategies for solving problems.
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.
6.1(B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals.
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(B) use addition and subtraction to solve problems involving fractions and decimals.
6.2(C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates.
6.2(D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required. / ” I CAN” statements highlighted in yellow and italicized should be displayed for students.
I can:
· use hundreds charts, place value mats or number lines to round whole numbers and decimals and solve addition and subtraction problems. (TEKS 6.2B,D)
· use hundreds charts, place value mats or number lines to round whole numbers and solve multiplication and division problems. (TEKS 6.2C,D)
· use rulers, number lines and place value charts to compare and order decimals. (TEKS 6.1A,B)
· round decimals using number lines and place value charts. (TEKS 6.2D)
· use a graph to organize my data. (TEKS 6.10A)
Process 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.
6.11(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques
such as mental math, estimation, and number sense to solve problems..
6.12(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. / I can:
· create a plan in order to solve word problems. (TEKS 6.11B,C)
· use manipulatives like rulers and number lines to round decimals. (TEKS 6.11C,D)
· use manipulatives like base ten blocks to add and subtract decimals. (TEKS 6.11C,D)
· explain verbally and in writing how I solve my math problems. (TEKS 6.12A)
Evidence of Learning
80% of the time, students will demonstrate on paper or use models to show that they can:
1. compare and order a set of decimals.
2. round a set of decimals in order to solve word problems.
3. add and subtract decimals.
Mathematics – Grade 6
Unit of Study: Whole Numbers and Decimals
First Grading Period – Weeks 1-3 (11 days) CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills· How can metric rulers and number lines help us compare, order and round decimals?
· How does round decimals compare to rounding whole numbers?
· When is it necessary to round a decimal?
· What are some important things we need to remember when adding and subtracting decimals? / · Use place value to read, write, compare, and order decimals through the thousandths place (TEKS 5.1B).
· 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 models to relate decimals to fractions that name tenths, hundredths, and thousandths (TEKS 5.2D).
· Relate decimals to fractions that name tenths and hundredths using concrete objects and pictorial models. (TEKS 4.2D).
· Use addition and subtraction solve problems involving whole numbers and decimals (TEKS 5.3A).
· Add and subtract decimals to the hundredths place using concrete objects and pictorial models (TEKS 4.3B)
· Use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology) (TEKS 5.3B).
· Use multiplication to solve problems (no more than two digits times two digits without technology) (TEKS 4.4D).
· 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).
· Use division to solve problems (no more than one-digit divisors and three-digit dividends without technology) (TEKS 4.4E).
· Use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems (TEKS 5.4).
· Round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations (TEKS 4.5A).
· Use strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems (TEKS 4.5B).
· Use tables of related number pairs to make line graphs (TEKS 5.13A).
The Teaching and Learning Plan
Instructional Model & Teacher Directions
The teacher will… / So students can…
Days1-9:
Step 1: Problem Solving: Begin each day with problem solving. for 10 minutes.
Use the following experiences from the Lane County Mathematics Project. The identified problems will be teacher directed for the purposes of building a background in problem solving strategies.
Problem Solving Strategy:
· Day 1: Guess and Check: Week 1-Day 1
· Day 2: Guess and Check: Week 1-Day 2
· Day 3: Guess and Check: Week 1-Day 3
· Day 4: Guess and Check: Week 1-Day 4
· Day 5: Guess and Check: Week 1-Day 5 / Step 1: Problem Solving
· Students can use the strategy of guessing and checking in order to solve problems.(TEKS 6.11C)
· Students can use the strategy of looking for a pattern in order to solve problems.(TEKS 6.11C)
· Day 6: Look for a Pattern: Week 2-Day 1
· Day 7: Look for a Pattern: Week 2-Day 2
· Day 8: Look for a Pattern: Week 2-Day 3
· Day 9: Look for a Pattern: Week 2-Day 4 / Step 3: Visual Learning and Practice
Practice:
· In their journals, the pairs will elaborate on the strategies that they used to reach their targets.(TEKS 6.2D)
Step 4: Differentiate/Assessment
Draw Conclusions:
· Individually, the students will apply estimation to play “Target Difference” and “Target Quotient.”(TEKS 6.2D)
Day 1: Investigation 1.2-Hitting the Target, pp. 9-10.
Step 2: Interactive Learning, pp. 9-10:
Explore:
· Model games, Forming a Sum Close to 100 and Forming a Product Close to 200. Have a student volunteer assist you at the overhead and use overhead dice so that the students can see how the game is played. Stress that the focus is on using estimation to reach their target. Give the students about 10 minutes to play each game in pairs.
Step 3: Visual Learning and Practice, pp. 9-10:
Practice:
· At the end of the 10 minutes, have them answer the practice questions for each game in their journal. During the entire practice, make sure to circulate around the classroom to make sure the students are on task. Follow-up with a whole group debriefing session.
Step 4: Differentiate/Assessment, pp. 9-10:
Draw Conclusions:
· Have the students answer questions 5-7 under Draw Conclusions. Value questions 5 and 6 at 30 points each and 7 at 40 points. Assess for 80% mastery.
· Teacher will monitor students and or work with small groups to provide interventions for students who are struggling. / Step 2: Interactive Learning
Explore:
· In pairs the students will use estimation to reach their target sum and product.(TEKS 6.2D)
Day 2: Unit 1.2-Whole Number Estimation, pp. 11-14.
Step 2: Interactive Learning:
Example 1, p. 11:
· Skip this example.
Example 2, p. 12:
· Display 2a and 2b. Ask the students, “How do you know where to round these numbers? What happens when you have a single digit numeral? What is the purpose of rounding while multiplying?
Example 3, p. 12:
· Display the word problem for the students. Have them work with a partner or independently to solve the problem. Circulate around the room to ensure the students are on task.
· Extension Questions: How do you know your answer is correct? How did you choose where to round? Why didn’t you round to the hundreds? Explain the concept of compatible numbers?
Step 3: Visual Learning and Practice, pp.11-12:
· Skip the guided practice on pages 11 and 12. Instead at the end of Example 3, use #39 Guided Problem Solving, p. 13 for practice.
· Extension Questions: How do you know your answer is correct? How did you choose where to round?
Step 4: Differentiate/Assessment, pp. 13-14:
· Skip the skill practice and move onto the problem solving section. Choose several problems of your choice (maybe 4) and assess for 80% mastery.
· Teacher will monitor students and or work with small groups to provide interventions for students who are struggling. / Step 2: Interactive Learning
Example 2:
· Students will use hundreds charts, place value mats or number lines to round numbers in order to solve multiplication problems. (TEKS 6.2C, 6.11D)
Example 3:
· Students will use hundreds charts, place value mats or number lines in order to round whole numbers and solve division problems.(TEKS 6.2D, 6.11D)
· Students will work in small groups to devise their problem solving plan.(TEKS 6.11B, C)
Step 3: Visual Learning and Practice
· Students will use hundreds charts, place value mats or number lines in order to round whole numbers and solve division problems.(TEKS 6.2D, 6.11D)
· Students will work in small groups to devise their problem solving plan and share it with the class.(TEKS 6.11B, C)
Step 4: Differentiate/Assessment
· Students will work independently to round numbers in order to solve word problems.(TEKS 6.2C,D, 6.11B, C, D)
Day 3: Unit 3.6-Technology Activity-Adding and Subtracting Decimals, p. 155
Step 2: Interactive Learning
Example, p. 155:
· Give the students the scenario. Ask them to use the calculators to solve the problem and record their keystrokes in their journals. Look for different approaches. Ask the students, “Do you need to input the 0 in 0.932? What is the purpose of the zero? Then have them round the numbers to come up with an estimate of the distance. Is the estimate less than or greater than the actual amount? Why?”
Step 3: Visual Learning and Practice
Practice, p. 155:
· Choose several practice problems from this section, both skill and problem solving. Save Problems 12 and 13 for the assessment. Have the students solve the problems using their calculators and recording their keystrokes in their journal. Then have the students estimate the answers and compare the two solutions. Ask the students, “How does estimating the answer help you determine if your answer is reasonable?”
Step 4: Differentiate/Assessment
Practice, p. 155
· In their journals the students will solve problems 12 and 13. They will begin by estimating the answer to the problem. Then they will solve the problem and show a pictorial representation, number sentence and a written explanation of their process and justification. After the problem is solved the students need to record their keystrokes on the calculators.
· Teacher will monitor students and or work with small groups to provide interventions for students who are struggling. / Step 2: Interactive Learning: Example
Step 3: Visual Learning and Practice
AND
Step 4: Differentiate/Assessment
· The students will use calculators to solve mathematics problems and record their keystrokes.(TEKS 6.2B, 6.11D)
· The students will estimate the answers to problems involving decimals in order to determine reasonableness. (TEKS 6.2D)
Day 4: Unit 3.1-Decimals and Place Value, pp. 119-123
Step 2: Interactive Learning:
Examples 1-3, p. 119-120:
· Use base-10 pieces to review the different place values in the activity. Follow up by modeling the following using the decimals 3.12, 28.6.
· Expressing a Number in Different Ways: Express the number in word form, decimal form and expanded form. Use place value grids on the overhead and look at the different ways to break apart a number as seen in Example 1 on page 119. Also use the steps listed under the Key Concept on page 120 (including place value chart).
Step 3: Visual Learning and Practice, p.122:
· Skip the Skills Practice. In partners, have the students complete problem 51 from the Problem Solving section, locate on page 122.
Step 4: Differentiate/Assessment, pp. 122-123:
· Choose several problems of your choice (maybe 4) from the Problem Solving and Mixed Review for TAKS and assess for 80% mastery.
· Teacher will monitor students and or work with small groups to provide interventions for students who are struggling. / Step 2: Interactive Learning
Examples 1-3:
· Students will represent decimals using words, place value blocks and place value charts.(TEKS 6.1B, 6.12A)
Step 3: Visual Learning and Practice
· Students will choose place value blocks, place value charts, words, or numbers to represent decimals and help them solve word problems.(6.1B, 6.12A)