Unit+6+Investigation+1+2010

Day 1
Learning Targets for the week:
 * I can solve a story problem using tens and ones.
 * I can try out new strategies for solving double-digit addition and subtraction problems.
 * I can automatically add or subtract tens to / from a number.
 * I can solve a story problem using the number line.

Introduction

 * Go over learning targets. Have students self-assess where they are.
 * Assign partners. Make pairs slightly heterogeneous (ie. strong with strong or middle; middle with struggling)
 * Explain procedure for rotating. Remind them of the importance of reading directions, and that teachers will NOT help until they see evidence that they have carefully read the directions and discussed with their partner.
 * Remind them that partners MUST take turns recording.
 * Remind them they must clean up their center before rotating.
 * Explain where to find extra work if they finish too quickly.
 * Everyone will go to most centers this week, but not today.

Possible Centers

 * Huge hundreds chart (adding, subtracting by jumping tens) -- moving toward mental math __//With a teacher; classrooms alternate days//__
 * Script for teacher
 * Number line for story problems about distance (footsteps) -- taking jumps on the number line __//Can be independent or with a teacher//__
 * Materials for the center:
 * Story problems: (pairs can decide which problem they start with. The problems start easier and get harder.) [|distance addition1.doc]
 * the large number line from the curriculum box
 * Gummi Worms problems (lend themselves to tens and ones) __//Can be independent or with a teacher//__
 * Materials for the center:
 * Story problems: (pairs can decide which problem they start with. The problems start easier and get harder.) [|Gummi worms1.doc]
 * Digi blocks
 * Base ten blocks
 * Collect 50 cents __//independent//__
 * Boom with basic facts __//independent//__
 * Rectangle Riddles //__independent__//


 * EXTRA WORK**:
 * Challenge problem for pairs who finish before others: [|gummi worms challenge.doc]
 * Also you may put out rectangle riddles from last week.


 * Sharing / Reflection** last ten minutes
 * Think, Pair, Share: Find a new partner. Silently think about one new thing you learned or got better at today. Tell your partner. Have a few share with the entire class.
 * Celebrate learning / independent work.

Mini-lesson

 * Start with the challenge: we are going to see how many ways we can find to solve double-digit addition / subtraction problems. We are going to find strategies and list them on charts.
 * Have 2 pairs from yesterday share. Have their work already displayed on a chart. They explain what they did.
 * After the first pair shares, students turn-and-talk. One student explains the strategy to his / her partner. If your partner needs help understanding it, help him / her.
 * After the second pair shares, the second partner explains the new strategy.

Sharing
last 10 - 15 minutes of class
 * Tell a new partner a new strategy you tried or something you learned today.
 * Chart one more strategy.

Day 3
Follow similar procedure to Day 2. When solving problems, students MUST try a new strategy. This is their learning target for the day.

Day 4 (Monday)
__//Small group, still struggling with tens and ones//__

Learning Target:
 * I can solve a story problem using tens and ones.
 * I can say how many tens and ones there are in a number.

Begin with review practice of tens and ones. Use digis and base ten blocks (let students choose? or alternate)
 * Mini-lesson**
 * 1) I have 3 tens and 4 ones. How many digis do I have? and other similar questions
 * 2) I have 45 digis. How many groups of ten do I have? How many extras? and other similar questions

Then have them solve an addition problem from the worksheet.
 * Work time / sharing**

[|race cars easier.doc]

Use digis or base ten blocks for the problem. Show work on paper or white boards. Use Session 1.1 as a guide. Share strategies. Be sure students have some practice writing the problem like this: 20 + 3 + 20 + 6.

Model how to solve it on a number line, using a large one on the floor or the one that comes with the curriculum.

__//Large group//__

Learning Target:
 * I can add and subtract ten to or from a number efficiently.
 * I can solve story problems using tens and ones.
 * I can solve story problems by taking big jumps on the number line.
 * I can solve a story problem in the most efficient way possible.


 * Mini-lesson**

Practice adding ten to a number quickly in the group. Check that everyone can do it. (Do some oral problems on the rug where you are adding ten or multiples of ten. If they seem ready, take away ten or multiples of ten. Have students draw it on the board, or on white boards. Also make a big number line on the rug so they can count steps on it. This is also a good routine to do during transitions throughout the day.)

A good activity for the beginning of class or for small groups:

Connecting jumping on the number line to tens
Solve problems, with some mixing of addition and subtraction, and some adding and subtracting groups of tens with zero ones.
 * Work time**

race car problems: [|race cars1.doc]

Have a few pairs show their work on bigger paper or on the white board. Have the class watch and talk about which strategies are efficient. Students choose a new strategy they would like to try tomorrow.
 * Sharing**

Alternatively, have a gallery walk of work from today. Students look at it and then say what they noticed.

Day 5 (Tuesday)
__Small group__

Learning Target:
 * I can solve a story problem using tens and ones.
 * I can visualize a story problem so I know what I need to do to solve it.
 * I can automatically add and subtract 10 from a number.

1. Quick review of tens and ones in numbers (see above) 2. Give them a problem to solve together: Kamiya has 22 stickers. She gets 10 more. How many does she have now? Talk about what happens when you add ten to a number. Use hundreds charts and little frogs to hop ten. Give students a hundreds chart and let them practice adding ten and see where they end up. Let them try the same problems using base tens, digis, hundreds chart, number line, so they see it in many ways. 3. More story problems. Focus on what happens when you add 10s to a number.

//__Large Group__//

Learning Target:
 * I can add ten to a number efficiently and subtract ten from a number efficiently.
 * I can visualize a story problem so I know what I need to do to solve it.
 * I can solve story problems using tens and ones.
 * I can solve story problems by taking big jumps on the number line.

With white boards, practice breaking some numbers into tens and ones and writing equations for them: 65 = 10 + 10 + 10 + 10 + 10 + 10 + 5 Then pose a problem: 54 + 23 and see if they can start at 54 and then add on 23. 54 + 10 = 64 64 + 10 = 74 74 + 3 = 77
 * Mini-lesson**

Large group should work on challenge problems from last week, or more easy problems if they need extra practice. Small group should do easier tens problems.
 * Work Time**

Gallery walk of work from today: students put a sticky dot by a problem that gives them a new idea? Or have 2 pairs share together -- each pair shares what they did, the other pair watches, asks questions, gives praise, then they trade.
 * Sharing**

Day 6 (Wednesday)
//Whole class together//

Learning Target:
 * I can add ten to a number efficiently and subtract ten from a number efficiently.
 * I can visualize a story problem so I know what I need to do to solve it.
 * I can solve story problems using tens and ones.
 * I can solve story problems by taking big jumps on the number line.

Teach Sage 'n Scribe problem-solving routine:
 * Mini-lesson**
 * 1) Each pair gets story problems and a sheet of paper folded in half lengthwise.
 * 2) For the first round, Partner A is the Sage and Partner B is the scribe. The Sage tells the Scribe how to do the first problem. The Scribe writes it down in the first column.
 * 3) When finished, the Scribe provides any help necessary and then praises the Sage for his/her good work.
 * 4) Reverse roles for the next problem.

Students may choose to work alone if they prefer. Problems: [|double digit strategies sage n scribe.doc]

Try the Sage 'n Scribe
 * Work time**

Use the lesson in the book for an overview of sharing solutions (page 38).
 * Sharing**

Debrief how they liked Sage 'n Scribe.

Day 7 (Thursday)
Do a "Smart Talk" routine about the Sage n' Scribe and how they like it, what they like best about it, what is hard.

Review the rules of Sage 'n Scribe: who can hold the pencil? What is hard? What can you say if it's hard to understand your partner?
 * Mini-lesson:**

Work time:
Sage n' Scribe again.

[|sage n scribe double digit strategies 2.doc]

Pull small groups to do number line work on the rug (groups of 4)


 * Sharing**

Share subtraction problem on the rug (have a pair show their work on the board?)

Day 8 (Monday)
Learning targets:
 * I can choose the best strategy to solve a story problem.
 * I can evaluate strategies to see which are most efficient.

Start with a few mental math problems that involve double-digit addition and lend themselves to adding multiples of tens. Ask students to put a thumb up when they have the answer, and come whisper it to you. After most students have it, list answers on the board, then get some explanations of how students solved the problems in their heads.
 * Mini-lesson:**

Introduce a day of reflection on the problem-solving strategies we have been using (the tools in our toolbox)

Look at the learning targets. Explain that good mathematicians have different strategies for solving different problems, and they choose the one that fits the problem they are facing.


 * Work time: //poster project//** **//reflection//**


 * Have the story problems from last week written up large on chart paper that are ready to be turned into posters. Have the key for the gallery walk written up large in a few places.
 * Students work in 2s to show a strategy they used last week on the Sage 'n Scribe. They use a piece of blank white paper and markers, so their work is visible on a poster. Tell them their work will be on display, and they will not be able to talk about it, so they have to be very clear in how they solved it.
 * Ask specific students to show specific strategies that you choose from their work last week.
 * Put together posters with the students' work, as they finish. Group different strategies together; for example, for one problem you might have 4-6 different strategies for solving it on a poster.
 * If pairs finish their problems for the poster, they can continue work on Sage 'n Scribe problems from last week.

//Galley walk//


 * When the posters are finished, hang them up so students can walk around and look at them. Introduce the gallery walk by saying that when you choose a strategy, you have to think about what is efficient, but also which strategy works best for you, or you feel most comfortable with.
 * Model how to walk silently in the gallery, and to look at each problem and think to yourself if you can understand it. Then model (using a think-aloud) how to choose one that makes the most sense to you and the one that seems the most efficient.
 * On each poster, they should indicate which strategy makes the most sense to them, and which one seems most efficient. (use colored markers) They can put question marks by ones they don't understand.
 * Key:
 * ? = I don't understand
 * check mark = most comfortable with this one
 * e = most efficient strategy
 * They should draw on a post-it or an index card one new strategy they would like to try out.


 * Sharing**

Reflect on one or two of the posters.
 * What can we tell about our class as mathematicians from this poster?
 * Which strategies did we think were most efficient? Which did we think made the most sense to us?
 * Which strategies do people want to try for themselves?
 * What did you learn? What was hard? What can you tell about how to make your work clear for an audience?

Other stuff
Start with some sharing of solving 23 + 37 on the number line on the rug. Model how to show it on the number line and with tens and ones.

Problems for big group: [|Unit6Session5harder.doc]

Problems for lower students: [|Unit6Session5easier.doc]

End with sharing 64-23 on number line and with tens and ones.

Share some subtraction strategies.

Ask everyone to show subtraction on a number line, or at least to try it.

Show how to break a number into its jumps of 10. For example, 43= 10 + 10 + 10 + 3, then you take the jumps.

Make sure they are writing +10 or -10 above their jumps, and the total on the number line where they land.

Continue to demonstrate problems on number line and with digi blocks and with hundreds chart.

Finish story problems.

At the end, play Guess My Number on the hundreds chart. (p.56)

Extra problems for today: [|Unit6Session6.doc]