Secondary Math Academy - Grade 6
Units 05 - 06
- Explore engaging activities to support learning standards for Grade 6 Units 5 - 6
- Complete SIM Lesson Plan Blueprint for Grade 6 Units 5 - 6.
- Collaborate with peers to brainstorm differentiated activities for students above grade-level, on grade-level, or in need of Tier I intervention.
Hays CISD Professional Learning Norms
- Be present by listening and participating actively.
- Take care of yourself and those around you.
- Stay on schedule; honor everyone’s time.
- Silence your device; use technology for learning.
- After the learning event, provide constructive feedback to presenter(s) via electronic survey.
- Share what you learn; spread best practices across the district.
Must use Hays CISD Google account (email@example.com) to access content and documents.
During this unit, students are formally introduced to proportional reasoning with the building blocks of ratios, rates, and proportions.
Ratios - 3 types & 3 ways
- Part-Whole (fractions)
Every ratio has a dual.
Fractions are a special type of ratio.
Rates are a comparison of two quantities or a description of the way quantities change over time.
Ratios and rates are ordered pairs.
- a to b
Discussions of Ratio Situations Should Focus on These Questions
- In addition to the explicit facts, what else do I know about this situation?
- Does it make sense to simplify this ratio? Can this ratio be extended?
- If I extend or simplify this ratio, what information is gained or lost?
- If I choose a smaller or larger sample, will the ratio apply?
- What is the meaning of a divided ratio
- Unit rate - relationship between one quantity and 1 unit of another quantity
- Almost every rate will require some discussion over the nuances in meaning
- Rates can be constant or varying
- Some rates are reported as single numbers
6.3E Represent ratios and percents with concrete models, fractions, and decimals.
Is it possible to fix the mix up?
Let's find out here.
Conversions Within a Measurement System
- What's an answer you know is too high?
- What's an answer you know is too low?
Don't forget the rulers...
(Site within the Hays CISD Teacher Content Resources website)
Students interpret the acronym in the order the letters are presented, leading them to multiply before dividing and add before subtracting.
E - Exponents (the exponent tells how many times the base is multiplied by itself)
M - Multiply/Divide...whichever comes first!
S - Subtract/Add...whichever comes first!
Numeric and Algebraic Expressions
6.7A - The student is expected to generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.
Generate equivalent numerical expressions” is synonymous to “simplify.” For example, |2 - 5| + 3 = 3 + 3. Students are expected to understand that each step in the simplifying process generates an equivalent expression. Exponents may only be whole numbers. Bases, however, have no limitation
6.7D - The student is expected to generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
For this SE, expressions may be entirely numeric or a mixture of numbers and one variable.
Expressions versus Equations
One-Variable One-Step Equations
- Start with integer values using algebra tiles
- Progress to rational number constants (this includes negative fractions and decimals)
- Remember that coefficients in Grade 6 are limited to positive rational numbers or integers (negative fractions and decimals are not expected)
If you have not explicitly used algebra tiles with integer operations in Unit 4, you will most likely need to spend time reviewing how algebra tiles are used.
Watch Your Words! (Equations)
Words to use and avoid when teaching students to solve equations.
Use this Padlet link to add content.
Nix: Switch the Side and Switch the Sign
This ditty hides the actual operation being used. Students who memorize a rhyme have no idea what they are doing. This leads to misapplication and the inability to generalize appropriately.
Fix: Talk about Inverse Operations
Talk about inverse operations or getting to zero (in the case of addition) or one (in the
case of multiplication) instead. The big idea is to maintain the equality by doing the same operation to both quantities.
Writing Equations from Verbal Descriptions and Vice Versa
...including geometric concepts.
- Sum of the angles in a triangle, complementary angles, supplementary angles, sum of angles in a quadrilateral, etc.
Grade 4 introduced geometric concepts such as geometric attributes, parallel and perpendicular lines, and angle measures including complementary and supplementary angles.