Grades 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

 12/8, 36/8, 60/8

 Ratio work

 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.

 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

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

 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.

 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?

 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?

 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.

 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?

 4 th grade-  5 th grade-  6 th grade-

 4 th grade- ◦ Brownies, cakes, square pizzas that focus on the costs of ingredients and the area of shapes  5 th grade- ◦ Making lemonade, juice, punch, etc.

 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

 Pick a topic that belongs to your grade level…  What would it look like for students to demonstrate proficiency?

 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?

 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?

 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?

 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?

 Let’s look at the tasks embedded in the article  Which is the “easiest”? Why?  Which is the “most difficult”? Why?

 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?

 Questions?