Unpacking the Common Core

StandardsGrades 4-6

October 16, 2013

Fraction work…

Whole numbers… Simplify to fourths Simplify to fourths or halves Simplify to halves Don’t simplify at all

Counting Around the class

12/8, 36/8, 60/8

Ratio work

Counting Around the class

You are making bracelets for a school fundraiser. You have purchased:◦ 3 types of glass beads, 3 types of spacer beads (go

between sections of glass beads), and Beading wire Design a bracelet using at least 2 types of glass

beads and one type of spacer bead.◦ Use between 8 and 12 glass beads◦ Use at least 6 spacer beads◦ No more than 25 total beads

Use letters (A, B, C, D, E, F) to represent beads and make a list of your necklace- remember you can only have 25 beads.

Bracelet Making

Write 5 ratios that can be used to mathematically describe your bracelet…

What do we mean?

Options- ◦ Relationship between one type of glass bead used and another

type of glass bead◦ Relationship between one type of glass bead used and total

number of beads◦ Relationship between one type of glass bead and a type of

spacer bead◦ Relationship between one type of spacer bead used and total

number of beads ◦ Relationship between all glass beads and all spacer beads

Bracelet Making- Ratio

Relationship between: one type of glass bead used and another type of glass bead

one type of glass bead used and total number of beads

one type of glass bead and a type of spacer bead

one type of spacer bead used and total number of beads

all glass beads and all spacer beads

Bracelet Making- Ratio

Use the information sheet to determine how many bracelets you can make before you run out of beads? You can only have 1 bag of each type of bead that you need.

Draw a picture and write an equation to explain how you found your answer.

Bracelet Making- when will we run out?

One clasp and beading wire costs 25 cents. Use the information sheet and your bracelet from Part A to determine the cost of 1 bracelet. Write an equation to show your work.

How much will it cost to make all the bracelets that you can?

Bracelet Making- costs

Your bracelet was 8 inches. Your Principal wants matching 24-inch

necklaces (using the same pattern of beads).

If the cost of the clasp and wire is $0.30, what is the cost of making 1 necklace?

How much of each type of bead will you need to make a 24-inch necklace?

Making our bracelet into a necklace…

Your Principal wants you to make a profit that is 60% of the cost to make each piece of jewelry. How much should each bracelet and necklace cost?

You decide to offer a “special” so that when customers buy 3 bracelets, you only make 40% profit.

Predicting Profits

Where would students get hung up or stuck?

How do you battle fatigue?

What would you/could you assess or grade? How much would you focus on grading the various parts of the task?

Debriefing Jewelry Task

4th grade-

5th grade-

6th grade-

Contexts…

4th grade-◦ Brownies, cakes, square pizzas that focus on the

costs of ingredients and the area of shapes

5th grade- ◦ Making lemonade, juice, punch, etc.

Contexts…

A) Understand the concept of unit rate B) Make tables of ratios C) Convert measurement units within a system D) convert measurement units by multiplying or

dividing quantities E) distinguish multiplication comparison from additive

comparison F) Generate a number pattern G) Generate a number pattern with 2 given rules H) Express larger measurement units in smaller

measurement units in the same system I) use ratio reasoning to convert measurement units

Proportions… grade levels?

Pick a topic that belongs to your grade level…

What would it look like for students to demonstrate proficiency?

Proportions…

There are 24 cookies. 3 cookies in each bag and are given to students. If each student eats one of their cookies, how many cookies were eaten?

There were 24 cookies divided among 3 people. 1 person ate all their cookies. The other 2 people saved all of theirs. How many cookies were eaten?

Proportions.. How to teach it?

There are 24 cookies. 3 cookies in each bag and are given to students. If each student eats one of their cookies, how many cookies were eaten?

There were 24 cookies divided among 3 people. 1 person ate all their cookies. The other 2 people saved all of theirs. How many cookies were eaten?

1/3 of 24… ◦ 24 objects in rows of 3… for every group of 3,

shade 1object◦ 24 objects in 3 groups, shade 1 entire group◦ How are they different?

Proportions.. How to teach it?

I am able to drive 30 miles per every gallon of gas in my car….

How many miles can I drive if I have 10 gallons? 20 gallons? 5 gallons?

How many miles can I drive if I have 3.25 gallons? I have 4/5 of a gallon. How far can I go? I have enough gas left to drive 130 miles. How

many gallons do I have? I have 12 and 1/2 gallons left when I start my trip.

How far can I go if I only use 2 and ½ gallons before my first stop? What if I use 3 and ¾ gallons?

Proportions… gas mileage

Professional Reading◦ As you read….What are the essential characteristics of good mathematical tasks?

How can a task dictate or influence how a lesson goes?

Mathematical Tasks

Let’s look at the tasks embedded in the article

Which is the “easiest”? Why? Which is the “most difficult”? Why?

Mathematical Tasks Reading

Where in your classroom does each task type fit?

What type(s) do you most naturally use?

Examples in the back….

What levels should we aim for when we plan most of our instructional tasks?

Mathematical Tasks Reading

Questions?

Wrapping Up our time together