Content Area: Math
Unit Title: Multiply and Divide Decimals Unit:1
Target Course/Grade Level: Sixth Grade Timeline:4weeks
Unit Summary:Students estimate, model, multiply, and divide decimals. They begin with multiplying and dividing decimals by whole numbers, and then multiply and divide decimals by decimals. Students use estimation to understand these operations, focus on place value, and verify that their final answers are correct. The emphasis is for students to become competent in their ability to multiply and divide decimals in real-world situations.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
6.MP.1 Make sense of problems and persevere in solving them.
6.MP.2 Reason abstractly and quantitatively.
6.MP.3 Construct viable arguments and critique the reasoning of others.
6.MP.4 Model with mathematics.
6.MP.6 Attend to precision.
6.MP.7 Look for and make use of structure.
6.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: The Number System
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples
Standard # / Standards
6.NS.2 / Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 / Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.EE.1 / Write and evaluate numerical expressions involving whole number exponents.
6.EE.2b / Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both as single entity and a sum of two terms.
9.1.8.A.1 / Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving skills.
9.1.8.A.2 / Implement problem-solving strategies to solve a problem in school or the community.
9.1.8.B.2 / Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, generational, etc.) and determine how the data can best be used to design the multiple solutions.
9.1.8.C.1 / Determine an individual’s responsibility for personal actions and contributions to group activities.
9.1.8.C.2 / Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, assignments and projects.
9.1.8.C.3 / Model leadership skills during classroom and extracurricular activities.
Unit Essential Questions
- What kind of result do you expect when you multiply or divide a whole number by a decimal?
- How is multiplying a decimal by a decimal different than multiplying a decimal by a whole number? How is it similar?
- How is dividing decimals similar to and different from dividing whole numbers?
- How is the placement of the decimal point determined when multiplying and dividing by powers of ten?
- When multiplying a decimal by a decimal or a whole number, multiply as with whole numbers. To place the decimal in the product, find the sum of the number of decimals in each factor. The product has this number of decimal places.
- To divide decimals, change the divisor into a whole number by multiplying it by some power of 10. Then multiply the quotient by the same power of 10. Divide as with whole numbers.
- To estimate the product of decimals, round all decimals to the nearest whole numbers before multiplying. To estimate quotients, use compatible numbers; numbers that divide easily.
- When multiplying by a power of ten move the decimal to the right, when dividing do the opposite.
Unit Learning Targets
Students will ...
- Multiply and divide decimals by whole numbers and decimals
- Represent numbers using exponents
Evidence of Learning
Summative Assessment
- Estimate products and quotients of decimals
- Multiply and divide with decimals
- Solve real-world problems involving multiplication and division of decimals
Equipment needed: base 10 models, number lines, centimeter rulers, grid paper, 10x10 grids, play money, centimeter cubes, Smart Board, white boards, calculators, Elmo
Teacher Instructional Resources: Textbook (To be determined)
Study Island
Khan Academy Videos
Formative Assessments
- Skill sheets
- Quizzes/Tests
- Student workbook
- Homework
- Math games
- Study Island
Integration of Technology:
- Smart Board to play online games, utilize online resources, generate models with Smart Software.
- Kahn Academy Videos
- Elmo – for demonstration
- Study Island
Technology Resources:
– Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice modules for additional practice/remediation.
- Web-based instruction, practice, assessment and reporting built from NJ standards.
- IXL 6th grade online interactive activities for the students to complete
- AAA math 6th grade – online interactive activities and problems for the student to complete.
– Grade level material for practice, lessons, games, etc.
Opportunities for Differentiation:
Decelerate: Provide students with decimal models.
Use grid paper to align numbers.
Identify patterns in division for correct decimal placement.
Accelerated: Students will multiply decimals to the thousandths.
Write powers of 10 using exponents and multiply without expanding.
Teacher Notes:
It is important that student write numbers with the same place value beneath each other.