Secondary Math Academy - Grade 6

Units 05 - 06

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Learning Goals

  • 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.

Hays CISD Teacher Content Resources

Must use Hays CISD Google account ( to access content and documents.

So...How did it go?

  • Which activities did you use from last time?
  • How did students respond?
  • Are there any changes you would make for next time?
  • Thoughts? Comments? Reflections?
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Find a reason why each one does not belong.

During this unit, students are formally introduced to proportional reasoning with the building blocks of ratios, rates, and proportions.

Ratios versus Rates

"All rates are ratios, but not all ratios are rates."

Ratios - 3 types & 3 ways


  • Part-Part
  • Part-Whole (fractions)
  • Whole-Part

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:b
  • a to b
  • a/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
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6.3E Represent ratios and percents with concrete models, fractions, and decimals.

Strip Diagrams

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Ratio Tables

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Nana's Paint Mixup

Is it possible to fix the mix up?

Show students how to find equivalent ratios to 5 red / 1 white. We can't do 5 red to 1 white because we already have 5 white in the pan. Is there another equivalent ratio we CAN do?

Let's find out here.

Bubble Wrap

How long will it take to pop the other squares?

Link to complete lesson here.

Act 1 — Bubble Wrap

Conversions Within a Measurement System

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Faclon Radar

Staked Conversions within Rates
Falcon Radar - Act 1
What should the speedometer read? What will its fastest speed be? Its slowest speed?

  • What's an answer you know is too high?
  • What's an answer you know is too low?
Falcon Radar - Act 3
Link to complete task here.

Don't forget the rulers...

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Hays CISD SPED Curriculum and Instruction

(Site within the Hays CISD Teacher Content Resources website)

Accomodation Central

Presented by Shea Howard and Melissa Corona

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Assessment Resources

These resources are from various states. Items should be vetted for alignment to the TEKS and intent of the unit of instruction.


MCAS Question Search

Virginia DOE - SOL

National Assessment of Educational Progress

Partnership Resource Center

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Students interpret the acronym in the order the letters are presented, leading them to multiply before dividing and add before subtracting.


G - Grouping Symbols (parentheses, brackets, braces) -> ( ) [ ] { }
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!

Order of Operations Foldable – GEMS

Link to foldbale can be found here.

NCTM - Rules that Expire Articles

Are There Other Rules That Expire?

Join us as we continue this conversation on MTMS’s blog at

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

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One-Variable One-Step Equations

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  • 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.
Padlet Overview

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.

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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.

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Link to the complete post here.

Writing Equations from Verbal Descriptions and Vice Versa

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...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.
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