6th Grade Common Core Math

Tips and Support for Common Core Math Implementation

The Importance of Conceptual Understanding in Math

Why not just teach the steps?

Students take information from the world using all their senses. Why should learning mathematics be much different? Let’s look at how athletes learn to play sports. Imagine taking a child to watch a professional baseball player for 50 minutes a day and then be expected to win a game. It seems ridiculous because in order to play the sport, the player must feel the bat and gloves in their hands. They must run the bases to determine how long it will take. They need to imagine hitting the ball into the outfield. No matter how much you watch the pros, until you get your whole body involved, there is no way to really excel at the sport. This is not much different than a student watching a teacher for 50 minutes and then be expected to successfully complete their math tasks. Truly understanding mathematics involves more than just memorizing steps or formulas. In order to truly comprehend mathematical concepts, our teaching methods should involve the use of moving and placing manipulatives in order for students to feel and see what is really happening in a problem and therefore be able to predict a reasonable outcome.

What do conceptual learning activities look like? 

Conceptual learning activities often incorporate the mathematical practices.

  • Make sense of problems and persevere in solving them
: When a student asks and demonstrates the reasonableness of the answer, they are using this math practice (and arguably others as well). For example:
    •  “What is 7.245 x 6.18?” A student demonstrates conceptual understanding of mathematics when she or he explains that 850.015 cannot be a reasonable product because by estimating the smallest possible response as 7 X 6, and the largest possible response as 8 X 7; therefore making the product between 42 and 56.

    Image Attribution: by Alana Gilliam

  • Model with mathematics: A student demonstrates conceptual understanding of prime numbers when she or he is asked to prove if a number is a prime or composite number, and she/he creates a model to demonstrate it is prime by building only two arrays to show the different multiplication combinations of the number, while a composite number has more than two.

ResourceWhat is Conceptual Understanding?

Performance Tasks demonstrate Conceptual Understanding

Before beginning a new topic, study the performance based assessment. What are the students truly expected to be able to do conceptually? This should be our “GPS.” We need to have a clear understanding of the concept at hand to effectively facilitate learning.

Do you teach the steps, or do you teach the concepts?

How do you allow students to demonstrate their conceptual understanding daily?

I wanted to give a big thank you to Robyn Gonzales, Common Core Coach and Title I Teacher at SMES, for the ideas, resources, and the wording in the top and bottom portions of this post. 

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Tips, Mathematical Practices, and Ideas about Dividing Fractions and Mixed Numbers — Week 2

Topic 9- Dividing Fractions and Mixed Numbers

November 21-December 4 (Dec. 5 posttest/pretest)

Lesson

9-1 Understanding Division of Fractions

CCSS

6.NS.1

AZ Standards

M06-S1C2-04, M06-S1C2-05, M06-S5C1-01

9-2 Dividing a Whole Number by a Fraction 6.NS.1 M06-S1C2-04, M06-S1C2-05, M06-S5C1-01
9-3 Dividing Fractions 6.NS.1 M06-S1C2-04
9-4 Estimating Quotients 6.NS.1 M06-S1C2-04, M06-S1C3-02
9-5 Dividing Mixed Numbers 6.NS.1 M06-S1C2-04
9-6 Solving Equations 6.EE.7 M06-S1C2-04
9-7 Problem Solving: Look for a Pattern 6.NS.6 M06-S3C1-01

Double Dose Recommendations:

  • Kim Sutton math routines.
  • Pre-teach the following: Area, 5 days (#34-38)

Tip of the Week:

Creative Commons License Photo Credit: Adelle & Justin via Compfight

The Performance Assessment has students working with fractions in recipes. Here’s an online activity that complements the performance task:

Feeding Frenzy

In this activity, students will multiply and divide a recipe to feed groups of various sizes. Students will use unit rates or proportions and think critically about real world applications of a baking problem.

Technology Integration Resources:

Videos:

Mathematical Practices:

Model with Mathematics  The CCSS says this about Model with Mathematics, “In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community.”
With the holidays, could you ask the students to Model with Math by asking  questions about how much food your household needs to buy to host a holiday party?
How do students demonstrate their conceptual understanding of mathematics in your classroom? What performance tasks do you have students work on?
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Tips, Mathematical Practices, and Ideas about Dividing Fractions and Mixed Numbers

Topic 9- Dividing Fractions and Mixed Numbers

November 21-December 4 (Dec. 5 posttest/pretest)

Lesson

9-1 Understanding Division of Fractions

CCSS

6.NS.1

AZ Standards

M06-S1C2-04, M06-S1C2-05, M06-S5C1-01

9-2 Dividing a Whole Number by a Fraction 6.NS.1 M06-S1C2-04, M06-S1C2-05, M06-S5C1-01
9-3 Dividing Fractions 6.NS.1 M06-S1C2-04
9-4 Estimating Quotients 6.NS.1 M06-S1C2-04, M06-S1C3-02
9-5 Dividing Mixed Numbers 6.NS.1 M06-S1C2-04
9-6 Solving Equations 6.EE.7 M06-S1C2-04
9-7 Problem Solving: Look for a Pattern 6.NS.6 M06-S3C1-01

Double Dose Recommendations:

  • Kim Sutton math routines.
  • Pre-teach the following: Area, 5 days (#34-38)

Tip of the Week:

Think about incorporating these ideas/resources:

  • The Topic Opener/STEM Project on page 201 not only brings in math in the context of the real world, but it also requires informational text reading and researching. 
  • New York City Department of Education created a performance task, Share My Candy, for dividing fractions by fractions, which includes a rubric.

Technology Integration Resources:

Videos:

Online & interactive practice, that progressively gets more difficult from IXL:

  1. Divide fractions: Divide by fractions – with models
  2. Divide fractions: Reciprocals
  3. Divide fractions: Divide fractions
  4. Divide fractions: Estimate quotients when dividing mixed numbers
  5. Divide fractions: Divide fractions & mixed numbers
  6. Divide fractions: Divide fractions & mixed numbers: word problems

Mathematical Practices:

MP6- Attend to Precision

  • Communicate precisely to others
  • Use clear definitions in discussion with others and in their own reasoning
  • State the meaning of symbols they choose (equal sign)
  • Specific with units of measure, labeling, and quantities
  • Calculate accurately and efficiently

Question/Practice Stems

  • Why do you believe that to be true?
  • How did you reach your conclusion?
  • How does your answer connect to the question?
  • What math vocabulary did you use today?
  • How did you use it?
  • What does that symbol mean?
  • What would happen if your removed the symbol?
  • How would the problem change?
  • Does my work need labeling? If so, what? Why?

Are students applying the math practices daily?  How do you know?  What do the math practices sound like and look like in your classroom? 

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