CGI –Nuts and Bolts Day 2

CGI –Nuts and BoltsDay 2

Carrie [email protected]

Homework Review

Discuss in your table groups your three AH-HAs from Chapter 2.

Multiplication (Grouping)

Multiplication is all about putting items together in groups. Sometimes those groups are units of their own such as inches or cents. Other times you compare an items by grouping in comparison (3 times as big as).

A bee has 6 legs. How many legs do 5 bees have?

Multiplication—Related Problem Types

•Grouping—finding the total number of objects •Rate –quantities that children can represent with counters.•Price --a special kind of rate problem in which the rate is price per item.•Multiplicative Comparison—involve a comparison of two quantities in which one is described as a multiple of the other

Examples: Children’s Mathematics page 46

There was an ant parade walking across a table. They walked 7

inches, stopped and then continued walking. They did this 4 times.

How far did the ant parade walk?

Leo bought 6 gumballs. Each gumball costs 12 cents. How much money did Leo spend on gumballs?

Mary is saving up money to go on a trip. This month, she saved three times as much money as she saved last month. Last month, she saved $24.00. How much money did Mary save this month?

Division— Two Problem Types

•Measurement Division—Children construct a given number of sets each containing a specified number of objects. They then count how many sets they made.(Baking cakes with each cake needing a specific amount)

•Partitive Division– Find the number of objects in the group rather than the number of groups. Deal the object into the correct number of groups one at a time.(Passing out candy one at a time)

Kathy has 24 cookies. She puts 6 on each plate. How many plates

will she need?

Mr. Gomez has 12 cupcakes. He wants to put the cupcakes into 4

boxes so there’s the same number in each box. How many cupcakes

can go in each box?

Division—Related Problem Types

•Grouping—finding the total number of objects •Rate –quantities that children can represent with counters.•Price --a special kind of rate problem in which the rate is price per item.•Multiplicative Comparison—involve a comparison of two quantities in which one is described as a multiple of the other

Examples: Children’s Mathematics page 46

Kelly had 53 cents. Pencils cost 9 cents each. How many pencils can

Kelly buy?

The turtle at the zoo was 45 pounds. It is five times heavier than the baby turtle. How much

does the baby turtle weigh?

Sort the problem types by categories.Discuss with your table group how you were able to recognize each problem type.

Problem Type Sort

Strategy Types

•Direct Modeling•Counting Strategies (Most students get stuck here)•Derived Facts/Number Facts

Direct Modeling

Direct Modeling follows the story problem.Direct Modeling uses manipulatives or drawings.

Direct ModelingExample: Robin had 4 toy cars. Her friends gave her 7 more toy cars for her birthday. How many toy cars did she have then?

Student makes a set of 4 cubes and a set of 7 cubes. She pushes them together and then counts them, “1,2,3,4,5,6,7,8,9,10,11,” pointing to a cube with each count. Karla then responds, “She had 11 cars.”

Counting StrategiesCounting strategies show that a student can hold some portion of the problem in their head. There still may be manipulatives and drawings used for part of the problem.

The student will usually use a simultaneous double counting which is used to keep track of counts rather than to represent objects in the problem.

Counting StrategiesExample: Robin had 4 toy cars. Her friends gave her 7 more toy cars for her birthday. How many toy cars did she have then?

Jamie counts, “4 [pause], 5,6,7,8,9,10,11. She has 11 cars. As Jamie counts, he extends a finger with each count. When he has extended seven fingers, he stops counting and gives the answer.

Derived Facts/Number Facts

Students show knowledge of number facts during problem solving. Does not have to be the fact that is in the problem.

Derived Facts/Number FactsExample: 6 frogs were sitting on lily pads. 8 more frogs joined them. How many frogs were there then?

Rudy, Denise, Theo, and Sandra each answer “14,” almost immediately.Teacher: How do you know there were 14?Rudy: Because 6 and 6 is 12, and 2 more is 14.Denise: 8 and 8 is 16. But this is 8 and 6. That is 2 less, so it’s 14.Theo: Well, I took one for the 8 and gave it to the 6. That made 7 and 7, and that’s 14.Sandra: 8 and 2 more is 10, and 4 more is 14.

Using the Strategies

Identify the following problem type:

Abubu had 12 stickers. He lost 4 of them. How many does he have now?

Use as many different strategies as you can to solve this problem. Label them as Direct Modeling, Counting, or Derived Facts.

Using the Strategies

Identify the following problem type:

Keisha has 6 beads. How many more does she need to collect to have 13 beads altogether?

Use as many different strategies as you can to solve this problem. Label each strategy as Direct Modeling, Counting, or Derived Fact.

Parts of a Student Interview

Counting Skills•Shows place value knowledge•Numbers they know—allows you to modify if necessary

Problem Solving•Not about correct answers•Allows you to see and hear student strategies

Conducting a Student Interview

•With a partner•Don’t allow the student to get frustrated•Prompt rather than give answers•Change number choices if necessary•Change vocabulary if necessary•All about the experience•No wrong questions from the teacher

Reflecting on the Student Interview

•Complete Student Interviews Debrief Page with your partner.•Discuss the pros and cons of the interview.

What to do NextConnecting to the Common

Core StandardsKindergarten (CC.K.CC.1) Know number names and the count sequence.Example: I would like to eat 7 jelly beans. Count out 7 jelly beans for me to eat.

First (CC.1.NBT.1) Extend the counting sequence. Count to 120, starting at any number less than 120.Example: Evan had 10 marbles. His dad gave him some more. Now Evan has 16 marble. How many more marbles did Evan’s dad give him?


Core StandardsSecond (CC.2.NBT.2) Understand place value. Count within 1000; skip count by 5’s, 10’s, and 100’s.Example: Mom bought be 3 packs of gum. Each pack of gum had 10 pieces of gum in it. How many pieces of gum did Mom buy me?

Third (CC.3.OA.9) Identify arithmetic patterns and explain them using properties of operations.Example: Juan’s dad paid him $7 each day for cleaning his room. Make a chart showing how much money, he earned each day for a week.


Core StandardsFourth (CC.4.NBT.2) Read and write multi-digit whole numbers using base ten numerals, number names, and expanded form. Example: Ryan bought 4 packs of baseball cards. The first pack only had 7 cards in it. The second pack had 20 cards in it. The third pack had 300 cards in it. The fourth pack had 2,000 card in it. How many card did Ryan just buy?


Core StandardsFifth (CC.5.NBT.5) Fluently multiply multi-digit whole numbers using the standard algorithm.Example: The cattle at the Marion Farm are fed 428 bales of hay each day. The horses are fed 12 times as much as the cattle. How many bales of hay are the horses fed each day?


Core StandardsACTIVITY:

Use your Common Core Guide to make word problems for the first nine weeks of your grade level.

Don’t concentrate too much on number choice, just the problem type and the solution strategies.

Homework

•Read Counting Collections Article•Try a counting activity in your classroom (whole or small group)•Send a reflection of your experience with the counting collections lesson activity by email or comment to the wiki•Pose the questions with your class.•Bring the student work the next time we meet•Continue to grow with us on wiki http://nlrsdcgi.wikispaces.com/

Documents

CGI –Nuts and Bolts Day 2