enVision Mathematics Topics 2-6
5th Grade; September – November (10 weeks); 1st/2nd Trimester
Embedded Files
Topic Title(s):
Use Models and Strategies to Add and Subtract Decimals (Topic 2)
Fluently Multiply Multi-Digit Whole Numbers (Topic 3)
Use Models and Strategies to Multiply Decimals (Topic 4)
Use Models and Strategies to Divide Whole Numbers (Topic 5)
Use Models and Strategies to Divide Decimals (Topic 6)
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
5.NBT.B. Number & Operations in Base Ten: Perform operations with multi-digit whole numbers and with decimals to hundredths.
Fluently multiply multi-digit whole numbers using the standard algorithm. (CCSS: 5.NBT.B.5)
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.* (CCSS: 5.NBT.B.6)
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.** (CCSS: 5.NBT.B.7)
Defend calculations with explanations based on properties of operations, equations, drawings, arrays, and other models. (MP3)
Use models and drawings to represent and compute with whole numbers and decimals, illustrating an understanding of place value. (MP5)
Use the structure of place value to organize computation with whole numbers and decimals. (MP7)
Inquiry Questions
We sometimes use arrays and area models to model multiplication and division of whole numbers. Do these models work for decimal fractions, too? Why or why not?
How is computation with decimal fractions similar to and different from computation with whole numbers?
Coherence Connections
This expectation represents major work of the grade.
In Grade 4, students use place value understanding and properties of operations to perform multi-digit arithmetic.
This expectation connects with other ideas in Grade 5: (a) understanding the place value system for decimals, (b) using equivalent fractions as a strategy, (c) applying and extending previous understandings of multiplication and division, and (d) converting like measurement units within a given measurement system.
In Grade 6, students compute fluently with multi-digit numbers and find common factors and multiples.
Academic Vocabulary & Language Expectations:
Compatible numbers, Associative Property of Addition, Commutative Property of Addition, compensation, underestimate, overestimate, partial products, variable
Assessments:
Topic 2 Assessment (PDF), Topic 3 Assessment (PDF), Topic 4 Assessment (PDF), Topic 5 Assessment (PDF), Topic 6 Assessment (PDF)
Instructional Resources & Notes:
enVision Mathematics Topics 2-6
Additional enVision Mathematics Resources
Let's Investigate! Buying Lunch (TE) (supports Lessons 2-3, 2-4, 2-5)
Let's Investigate! Growing Areas (TE) (supports Lessons 3-4, 3-5, 3-6)
Let's Investigate! Big Growing Areas (TE) (supports Lessons 4-6, 4-7)
Let's Investigate! Group Hike (TE) (supports Lessons 5-5, 5-6)
Let's Investigate! Lenca Cloth (TE) (supports Lessons 6-4)
3-Act Math Recording Sheets (Topic 3, Topic 5)
Supplemental Lesson Resources: Topic 2, Topic 3, Topic 4, Topic 5, Topic 6
Additional Math Games: Multi-Digit Multiplication & Division (additional materials and preparation may be required)
Additional Math Games: Operations with Decimals (additional materials and preparation may be required)
Notes:
*Focus on conceptual strategies for division in Topic 5, specifically using an area model or “partial quotients” to divide whole numbers. Students do not need to know or use the standard algorithm. (Students do not need to know or use the standard algorithm for dividing whole numbers until 6th Grade.)
**Focus on conceptual strategies for division in Topic 6, specifically using models, “partial quotients,” and/or place value strategies to divide decimals. Students do not need to know or use the standard algorithm. (Students do not need to know or use the standard algorithms for adding, subtracting, multiplying, and dividing decimals until 6th Grade.)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 2: Add Decimals, Subtract Decimals
Tier 1 Intervention Topic 3: Multiply Multi-Digit Numbers
Tier 1 Intervention Topic 4: Multiply a Decimal by a Whole Number, Multiply Decimals
Tier 1 Intervention Topic 5: Divide Multi-Digit Numbers
Tier 1 Intervention Topic 6: Divide Decimals
Coherence Map/Concept Progressions: 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7
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