Number+6,+Investigation+2

Day 1 (Tuesday)
Learning Targets:
 * I can figure out a mystery number by asking questions and getting clues about about the number.
 * I can use strategies to figure out the mystery number in as few questions as possible.

Begin with a few mental math problems that lend themselves to making jumps of 10. Student put their thumbs up when they know the answer; then they whisper it to you. List answers on the board and share a few mental strategies.
 * Mini lesson:**

In 3 groups, introduce Guess My Number on the 100s chart. Use Lesson 2.1, p. 56. As you write down the questions they ask and what it tells you, make a big deal of questions that eliminate many numbers. Push them to guess the number in as few guesses as possible.
 * Work time:**

Really model your thinking process using a "think aloud" as you choose a number and figure out which numbers to cross out. Ask them to help you figure it out after each question they ask. Which numbers can I cross off?

After using a hundreds chart to model it once or twice, continue to play and have students use hundreds charts and white board markers to cross off numbers it can't be. You can continue to model it on a hundreds chart in front for those who need the modeling, or have students take turns coming up to cross off on the whole-group hundreds chart.

As you go on, you may want to ask if a student wants to come up and help you choose a number, then help answer questions about the number.

They also may need modeling of the kinds of questions to ask: not just more than or less than questions, but also is it odd or even?

//Modifications: one high group may be ready to play independently after a few times through.// //One group should be lower students, and they should use only 1-20 to play. You can fold hundreds charts for them.//

Share at the end in pairs: What kinds of questions helped you cross out a lot of numbers? Start an anchor chart of strategies for guessing the number in as few guesses as possible.
 * Sharing**

Day 2 (Wednesday)
Learning Targets:
 * I can automatically figure out how far a number is from a landmark number. That means I can say how far a number is from a multiple of ten.

Introduce the term "landmark number" as a number it is easy to figure out how to get to. Use a number line / hundreds chart to illustrate. If I am on 7, what is a nearby number that is easy to get to -- that I automatically know how many steps it is to get to it? (They may say 6 or 8 at first, and tell them that is true, but a landmark number is usually a multiple of ten -- 10, 20, 30, 40, 50 because you can really easily jump by tens or from one ten to another in your head.)

Teach Roll - a- Square as outlined in Lesson 2.2.

Introduce the steps as outlined on the small cards that tell them how to play:
 * 1) Say the total.
 * 2) What's the nearest landmark number?
 * 3) How far are you from the nearest landmark number? How many steps?
 * 4) Are there any words under the last cube?

Steps: [|Rollasquaredirections.doc] Recording sheet: [|rollasquarerecordingsheet.doc] (optional -- decide if this makes sense or not, or it may make sense for some students but not for others)

Connect the game to jumping on the number line. Remind them that when they take jumps on the number line, they often jump to a 10, so they need to know automatically how far they are from a 10.

//Modifications: Small, struggling group practices more addition / subtraction of double digit numbers, using strategies from the gallery walk.//

Students play in pairs.
 * Work time**

Do sharing at the end in two groups, the large group and the smaller group.
 * Sharing**

Sharing: How did you figure out how far you were from a landmark number? What if you have 25 cubes? What is the next landmark / friendly number? (30) How do you know how far you are from 30? (They should connect it to the combinations of 10 they know, in this case 5+5.)

Give a few more examples, such as 54 and 36. What is the next landmark number? How far away are you? How did you figure that out?

Say: "Another question that is often on the board is "How many more cubes do you need to have __ cubes?" For example, if you have 27 cubes, how many more cubes do you need to have 50?"

Write an equation on the board with the kids' help: 27 + ? = 50. How would you solve this problem?

Share strategies. Try to get someone to imagine jumping on the number line, and draw what that would look like, in addition to writing a list of equations.

Day 3 (Thursday)
Learning Targets:
 * I can figure out a mystery number by asking questions and getting clues about about the number.
 * I can automatically figure out how far a number is from a landmark number. That means I can say how far a number is from a multiple of ten.

Do some landmark number practice with mental math. Ask them to solve questions like 27 + 5. What's the nearest landmark number? How many steps to it? If you're adding 5 and you've already gone 3 steps, how many more steps do you have to go? Draw a picture of a number line on the board, illustrating how to break the 5 apart and use it, plus the landmark number, to quickly find the answer.
 * Mini-lesson:**


 * Work time:**

Choice time: Roll-a-Square Guess my Number (may be independent or in a small group with a teacher for kids who need it)

Day 4 (Monday)
//Learning Targets://
 * I can automatically figure out how far a number is from a landmark number. That means I can say how far a number is from a multiple of ten.
 * I can use a KWC chart to understand a story problem.

Check in about landmark numbers. How do they feel they are doing in achieving the learning target?
 * Mini-lesson**

Give a quick quiz, including all the tens facts, and a few other landmark number questions. [|landmark numbers quiz.doc]

Introduce the KWC chart with a think-aloud.

"Today we are not solving math problems. Instead we are going to learn how to really understand what a problem is asking us, by paying close attention to the problem, visualizing what is happening in the problem, making connections, and being clear about what the problem is asking us to do."

Use this problem: "Tyesha is collecting shells to decorate a picture frame. She has 34 shells. In order to get all the way around the outside of the picture frame, she needs to have 50 shells. How many more shells does she need to have 50?"

Think-aloud about how you would fill out the KWC.

"What do I **know**? I'm going to visualize the story so I can really understand it. I can see a picture frame -- I know they are usually a square or a rectangle, and she wants to collect enough shells to go all the way around it. She can only get partway around with her 34 shells -- I can see that when I visualize, a frame with shells going just partway around the outside. Okay, I'm going to write down that Tyesha is decorating a picture frame with shells. I know she has 34 shells. I know she needs 50 shells all together. I am going to visualize the hundreds chart also. I can see where 34 would be, and where 50 is. I know 50 is more than 34, and she is trying to get to 50. (You might visualize a number line instead if you prefer.) So I think I know that 50 is the whole. I'm going to draw a part-part-whole box and fill in that I know the whole is 50, and I know one part is 34. So I know I am missing a part."

"What do I **want** to find out? I need to find out the missing part: how many more shells she needs to get to 50 so she can go all the way around the frame. I think this means I can write my equation like this: What goes with 34 to make 50? 34 + ? = 50."

"The C stands for **Special Conditions**. That means, are there things I need to be sure I remember? Are there any tricks, or important details? Hmmm. I want to be sure I remember that I am missing one part. I know the whole, so this is a missing part problem. That means I am going to add on to 34, or subtract, but I am not going to add 34 plus 50. I want to remember that. I also want to remember that this is a problem about shells. I will have to label my answer with the word //shells."//

Next, do a KWC chart together as a class (or in small groups). Use this problem: "Harrington and Savion were having a reading race to see who could read more books. Harrington had read 23 books. Savion had read 50 books. How many books does Harrington need to read to catch up with Savion?"

Remind them that they are NOT solving the problem. They are just practicing how to do a really good job of understanding the problem, so they can solve it well later.

Together, fill in the KWC chart.


 * Work time:**

Students work on KWC charts in pairs.

Blank KWCs: [|landmark numbers quiz.doc] Problems to choose from: [|KWC practice problems.doc]


 * Sharing:**

Find someone else who did a KWC for the same problem you did. First, tell each other how you visualized the problem. Then, share your charts and see if you are missing anything.

Check in about the learning target. Are you understanding how to fill in a KWC?

Day 5 (Tuesday)
Learning Target:
 * I can solve story problems efficiently by taking big jumps on the number line or using landmark numbers.
 * I can use a KWC chart to understand a story problem.

Connect: remind them of the KWC work they did yesterday. Today they will continue the work, but solve some of the problems. They may choose to solve problems they started KWCs for yesterday, or they may choose new problems.
 * Mini-lesson:**

Teach them how to work with a partner.


 * 1) Partners agree on a problem to solve.
 * 2) They work independently on the KWC.
 * 3) They share and compare. Do you agree or disagree? Do you want to add anything to your chart?
 * 4) Tell each other Good job! and exchange high fives.
 * 5) They each solve alone.
 * 6) They compare and share how they solved. Do you agree on the answer? Do you understand how your partner solved the problem?
 * 7) At the end, each pair shares their work with another pair.


 * Work Time:**

Solve problems: (students may choose from these new problems OR they may choose to solve problems they did KWCs for yesterday) [|unit6inv2session4.doc]

Have hundreds charts available but not to write on. Encourage them to count groups of tens on the chart, not by ones.


 * Sharing:**

Ask students to tell you the equations they wrote for each problem. Make a list on the board:

46 + ? = 70 etc

What do you notice about the equations? Do you see any patterns? Can you connect this to landmark numbers? (Show the numbers on the hundreds chart.)

Day 6 (Wednesday)
Learning Target: I can use a KWC chart to understand a problem.


 * Mini-lesson:**

Model the KWC again. (think-aloud) Model how to fill out the Special Conditions using the prompts. Do one as a group. Stress putting as many relevant things in each column... kids earn "points" for each item.

Children chose problems they have not done yet and fill out the KWC. They compare / add / change with a partner. They may do more than one problem but they are not solving any today.
 * Work time:**


 * Sharing:**

Play "What's the label?" Tell a very easy story problem (like 5 + 5). Say, "The answer is 10. What's the label?" Do many times, to practice identifying the correct label.

Day 7 (Thursday)
Learning targets:
 * I can solve story problems efficiently by taking big jumps on the number line or using landmark numbers.


 * Mini-lesson:**

Model solving a problem and showing your work. Students must solve a problem in a number of ways. Think about solving efficiently. Review where you can find the label for your answer: Show a problem and ask them to analyze where can they find the label? In what part of the question?


 * Work time:**

Solve problems. Work with a partner or show a partner your work and make sure you agree. Ask each other questions before starting a new KWC.

Push students to use landmark numbers to solve the problems.


 * Sharing:**

Stop students and have them choose the most efficient strategy they used. Have some students show their work on the board. Highlight landmark numbers strategies and the number line.

Day 8 (Monday)
Learning targets:
 * I can solve story problems efficiently by taking big jumps on the number line or using landmark numbers.
 * I can use a KWC chart to understand a problem.
 * I can automatically figure out how far a number is from a landmark number. That means I can say how far a number is from a multiple of ten.

Get back into the swing of things.

Some finish KWC and solve Some finish solving Some share most efficient solution, then play Roll a Square.


 * Sharing**: (Save 15-20 minutes for this)

53 + 17 (use discussions in the book, page 84-85 and 89-91.) Focus on these strategies:
 * tens and ones
 * keeping one number whole and adding the other number in parts
 * hundreds chart (visualizing) (Counting up by groups)
 * number line (visualizing)

Day 9 (Tuesday)
Strategies "Carousel" day.


 * Mini-lesson:**

Talk about weight lifting and how, if you want your arms to get strong, you have to lots of kinds of weights and exercises. Biceps, triceps, push-ups, etc. Otherwise you'd have one part of your arm that was really big and strong and the other parts would be tiny!

Today we are going to see how many kinds of exercises we can do for our brains to solve different kinds of story problems. It is like adding to our toolbox: we are going to see what is in our toolbox.

Model how to proceed through the Carousel.


 * Each student is given an addition problem.
 * There are different strategies for each kind of problem around the room. Each strategy has a certain color of index card. When you get there, you look at the strategy. There is one example of the strategy there. You write on an index card your name, and the problem you are solving. Then you use that strategy to solve the problem
 * When you finish at that station, continue on to the next station.
 * At the end, you will have a stack of index cards showing all the ways you know how to solve your problem: all the tools in your toolbox, all the exercises you can do to strengthen your math muscles!


 * Work time:**

These strategies should be at centers around the room.
 * count up by ones
 * keep one number the same and add on the other number by tens and ones
 * add the tens and then add the ones (be sure to write equations)
 * take big jumps on a number line
 * take big jumps on a hundreds chart and write the equations down (here you need hundreds charts for them to use, but they should write out the equations)

When you have gone to all the centers, find someone else who has finished. Show him or her the one way you solved the problem that was newest, or made you think the most. Explain it to him and her.


 * Sharing:**

Teachers hang up the index cards on posters by the strategy the card represents, except that students keep the one they shared with a partner. For sharing time, students find the poster that fits the strategy they shared. There should be small groups at several of the posters.

In pairs or threes, students write down one thing to remember in order to use this strategy well. These can also be attached to the posters.

Day 10 (Wednesday)

 * Mini-lesson**

Ask students to put all their strategies from yesterday in front of them. Have them pick 2 that they can make a connection between. Tell them this will help them remember the strategies, if they can make connections between them.

Ask them to write down what is the same about the 2 strategies. Share a few.


 * Work time**

Same as Tuesday, but using Missing Part problems. (ie: 37 + ? = 50)

Strategies that are up:
 * Count up by ones
 * Count up by groups
 * Take big jumps on a number line
 * Take big jumps on a hundreds chart

When you have gone to all the centers, find someone else who has finished. Show him or her the one way you solved the problem that was newest, or made you think the most. Explain it to him and her.


 * Sharing:**

Reflection sheet. [|strategy reflection.doc]

Other ideas
(Maybe assign strategies to try? or do that later?) -- ie. you choose a problem, then choose a strategy from a hat.

Session 2.6 as written in the book Assessment day assessment: [|stickerbooksassessment.doc] Introduce sticker problems, lesson 2.4

Tell the story on page 76 about the sticker book and how there are 100 stickers per page. Have students help you model a few sticker pages. Go over the first problem, and ask what the sticker page would look like with 46 stickers (as written on page 78 of curriculum guide).

Low group should do page 28 in student workbook (practice with groups of tens and ones), then solve some sticker problems. easier problems: [|stickerbooks1easier.doc]

Everyone else can solve missing part problems about the sticker books, below.

problems: [|stickerbooks1.doc]

Session 2.5

More sticker problems. Finish the ones from Friday, and do a few more. Roll-a-Square

problems: [|stickerbooks2.doc]