enVision Mathematics Topic 1
6th Grade; August – September (4 weeks); 1st Quarter
Embedded Files
Topic Title(s):
Use Positive Rational Numbers
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP6. Attend to precision.
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):
6.NS.A. The Number System: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for 2/3 ÷ 3/4 and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that 2/3 ÷ 3/4 = 8/9 because 3/4 of 8/9 is 2/3. (In general, a/b ÷ c/d = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? (CCSS: 6.NS.A.1)
6.NS.B. The Number System: Compute fluently with multi-digit numbers and find common factors and multiples.
Fluently divide multi-digit numbers using the standard algorithm. (CCSS: 6.NS.B.2)
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (CCSS: 6.NS.B.3)
Create and solve word problems using division of fractions, understanding the relationship of the arithmetic to the problem being solved. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Reason about the contextualized meaning of numbers in word problems involving division of fractions, and decontextualize those numbers to perform efficient calculations. (MP2)
Model real-world situations involving scaling by non-whole numbers using multiplication and division by fractions. (MP4)
Accurately add, subtract, multiply, and divide with decimals. (MP6)
Inquiry Questions
When dividing, is the quotient always going to be a smaller number than the dividend? Why or why not?
What kinds of real-world situations require the division of fractions?
How can the division of fractions be modeled visually?
How do operations with decimals compare and contrast to operations with whole numbers?
Coherence Connections
This expectation (6.NS.A) represents major work of the grade.
This expectation (6.NS.B) is in addition to the major work of the grade.
In Grade 5, students apply and extend previous understandings of multiplication and division to divide whole numbers by unit fractions and unit fractions by whole numbers.
In Grade 5, students divide whole numbers with two-digit divisors and perform operations with decimals.
In Grade 6, this expectation connects with solving one-step, one-variable equations and inequalities.
In Grade 7, students apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Academic Vocabulary & Language Expectations:
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 1
Let's Investigate! Tasks
Let's Investigate! Play-ing with Decimals (TE) (relates to Lesson 1-1)
Let's Investigate! Cuanto Queso (TE) (relates to Lesson 1-4)
5th-to-6th Grade Warm-Ups for Activating Prior Knowledge (Geoff Krall)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Understand Division with Fractions, Divide Fractions, Divide Multi-Digit Whole Numbers, Multiply Multi-Digit Decimals, Divide Multi-Digit Decimals
Coherence Map/Concept Progressions: 6.NS.A.1, 6.NS.B.2, 6.NS.B.3
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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