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Lesson excerpt:

NC Mathematics Standard(s):

Operations and Algebraic Thinking

Represent and solve problems.

NC.2.OA.1 Represent and solve addition and subtraction word problems, within 100, with unknowns in all positions, by using representations and equations with a symbol for the unknown number to represent the problem, when solving:

o   One-Step problems:

§  Add to/Take from-Start Unknown

§  Compare-Bigger Unknown

§  Compare-Smaller Unknown

o   Two-Step problems involving single digits:

§  Add to/Take from- Change Unknown

§  Add to/Take From- Result Unknown

§   

Number and Operations in Base Ten

Use place value understanding and properties of operations.

NC.2.NBT.7 Add and subtract, within 1,000, relating the strategy to a written method, using:

·      Concrete models or drawings

·      Strategies based on place value

·      Properties of operations

·      Relationship between addition and subtraction

Standards for Mathematical Practice:

1.    Make sense of problems and persevere in solving them.

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

7. Look for and make use of structure.

Student Outcomes:

·         I can apply place value understanding to add and subtract three-digit numbers.

·         I can communicate my strategies to add and subtract three-digit numbers.

Math Language:

What words or phrases do I expect students to talk about during this lesson?

      addition, count, count on, hundreds, ones, subtraction, tens

Materials:

·         base ten blocks, activity sheets

Advance Preparation:

●     Gather materials

Launch:

Ten Less than a Three-Digit Number (8-10 minutes)

Have students sit in a circle. Choose a number between 300 and 400. Move clockwise. Each student should say the number that is ten less than the last number said. Record the numbers for students to see.

Example: If the start number is 432, the teacher would record 432, 422, 412, 402, 392, 382, 372, 363, 352, 342, 332, 322, 312, 302, 292, etc.

Ask, “What pattern do you see in our list?”

The number of tens decreases by 1 each time.  The ones place stays the same.  Ask, “What happened after we said 403?  Why did that happen?”

This activity can also be done increasing the tens place, counting by hundreds, counting by twenties, etc. The children should see that the ones place never changes and the tens place changes. Talk about why the hundreds place sometimes changes.

Model this counting on a number line by having students tell you what to label.

Ask, “If we were going to solve this problem, how would the number line help us think about the solution? The problem is: My brother had 432 baseball cards. He gave me 50 cards. How many cards does he have now?”

Have the students talk with a partner about solving this problem. Then have them share.

Ask, “Is there a way to solve this problem without using a number line?” Students might share using drawings of 100s, 10s and 1s. They may also use numbers in a series of equations to solve the problem. Examples:

432-10 = 422                                     432-30 =402

422-10 = 412                                     402-10 = 392

412-10 = 402                                     392-10 = 382

402-10 = 392

392-10 = 382

Ask, “How are these strategies alike?  How are they different?”

**Attached to this lesson plan are examples of ways students can record solution strategies.

Explore

Solving Story Problems (15-17 minutes)

Pose story problems to solve. There are options on the attached activity sheets. Explain that they are to write an equation and show how they solved each problem. As students work on the problems the teacher walks around the class observing students and asking questions. As the teacher observes and talks with students, she chooses the strategies from the student work that she wants shared during the lesson discussion.

Possible things to observe:

·      Can a student accurately write an equation to represent a problem?

·      What strategies do students use to solve the problem?

·      What tools, models, or representations do students use to solve the problem? (cubes, drawing 100s, 10s, 1s, number line, numbers in a series of equations, other strategy)

·      Can you tell by looking at their work how the problem was solved?

Possible questions to ask:

·    Why did you choose to solve it this way?

·    Where is your answer in this representation?

·    Why did you add (or subtract)?

·    Could you solve it using a different strategy?

Discuss

Discussion of Strategies Used to Solve Story Problems (10-12 minutes)

After most students have finished the problems gather the students back for a discussion of strategies. It is not necessary to discuss every problem. There are different reasons to choose problems to share. If there was a story problem that many students had difficulty with, discuss the problem.

Ask, “What was the story describing? Who can put the problem in their own words?” Then ask students to share strategies. The teacher should make sure the strategies shared highlight the mathematics she wants highlighted in this lesson. Using place value is a major focus of this lesson. Another reason to choose a problem to share is if there were a variety of strategies used by the students to solve the problem.

After several strategies are on the board, ask, “How are these strategies alike and how are they different?”

After discussing 1-2 problems as a class, ask partners to share one of the other problems with each other. Have each partner share the strategy. Tell students to also discuss how their strategies are alike or different.

Evaluation of Student Understanding

Informal:  Make a chart (before the lesson) on observations.

Possible topics to place on the chart are:

o   Can a student accurately write an equation to represent a problem?

o   What strategies do students use to solve the problem?

o   What tools, models, or representations do students use to solve the problem? (cubes, drawing 100s, 10s, 1s, number line, numbers in a series of equations, other  strategy)

o   Can you tell by looking at their work how the problem was  solved? Make notes on the chart as you observe.

Formal: Examine student work for various strategies and correct answers.

Meeting the Needs of the Range of Learners

Intervention: Students who have difficulty solving the story problems may need to use smaller

numbers so they can concentrate on the structure of the problem rather than the numbers. You can change the numbers to one-digit numbers or numbers less than 20. Example: There were 5 students on the playground. 3 students joined them. Then 2 students went inside. How many students are now on the playground?

Change the numbers in the story problems for students who need to work with 2-digit numbers.

Extension: Have students write story problems and have classmates solve the problems. Have students solve start unknown problems. An example: There were some students on the playground. 36 children joined them. In a few minutes 16 students went inside. Now there are 75 students on the playground. How many students were on the playground at the start? ( __+ 36 – 16 = 75).

Start unknown problems are harder for students to solve.

Possible Misconceptions/Suggestions: