T4T Adding on the Number Line
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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
Additional/Supporting Standards:
Number and Operations in Base Ten
Understand Place Value
NC.2.NBT.3 Read and write numbers, within 1,000, using base-ten numerals, number names, and expanded form.
Use place value understanding and properties of operations.
NC.2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
Student Outcomes:
· I can use a number line to represent addition and subtraction word problems.
· I can solve addition and subtraction word problems using strategies related to place value.
· I can communicate how I solved problems to my teacher and classmates.
Math Language:
What words or phrases do I expect students to talk about during this lesson?
addition, count on, group, hundreds, ones, subtraction, tens
Materials:
· strategies sheet, activity sheet, base ten blocks
· Additional Activities: number cards (1-9, 4 of each number), 100 boards
Advance Preparation:
● Gather materials.
Launch:
1. Unpacking Strategies for Adding (13-15 minutes)
Read the problem to the class but cover the strategies. (see attached sheet)
Miguel is 41 inches tall. His sister, Maria is 78 inches tall. How much taller is Maria than
Miguel?
Ask, “What do we know?” After students share ideas, students will compare and contrast the strategies shown on the page. Ask students to discuss how each student solved the problem and how the strategies are alike and how they are different.
Optional: Have students solve the problem or discuss how to solve the problem before sharing the strategies shown on the page.
Explore
2. Exploring Adding on the Open Number Line (15-17 minutes)
Have students solve 2-3 problems independently (suggestions are listed below) using an open number line. Have the problems written on chart paper or write them on the board. Discuss each problem. After reading the first problem, ask students to retell the story. Then ask students for suggestions on how to solve the problem. Have students solve the problem in their math journal or notebook paper. As students are solving the problems observe what they are doing. As the teacher is observing also think about which strategies should be shared in the class discussion.
Possible questions to ask as they work:
· Why did you start with this number?
· How do you know when to stop jumping on the number line?
· When you jump by 10s how do you know the next number?
· How did you figure out your answer?
After students successfully complete the first problem, have them do one more. If a student is struggling, change the numbers in the problem.
Possible problems to solve:
· Maria had 45 erasers. Her mom gave her 37 more. How many does she have now?
· David shot baskets in his driveway. Before dinner he shot 26 baskets. After dinner he shot 48 baskets. How many did he shoot?
· If a student is struggling change the first problem to
Maria had 15 erasers. Her mom gave her 10 (or 20) more. How many does she have now?
Discuss
3. Discussion of Strategies Used to Solve Story Problems (8-10 minutes)
After most students have solved the first (and possibly the second problem) have a class discussion
about one of the problems.
Gather the class back together. Draw one student’s strategy on the board. Have the students explain how he/she solved it. Ask if there are any questions.
Draw another student’s strategy on the board. Have the student explain how he/she solved it. Ask if there are any questions.
Ask the class, “How are these strategies alike?” Then ask, “How are these strategies different?”
If needed, share one more strategy. Have the student share his/her thinking on how it was solved. Ask the class to compare the three strategies. Are two of them more alike than the third?
Do they all have something in common?
Additional Activities for Centers or Small Group Work (20-30 minutes)
Create and Solve Your Own Story Problems
Students need number cards. Students select two number cards and make a two-digit number (3 and 6 could be 36 or 63). Students then put that number into a story problem and choose whether they will add or subtract the numbers.
I had 63 pieces of candy and my friend (gave me/ gave away) 20 more. How many do I have now? (63 + 20 or 63 - 20).
Students solve several problems that involve adding and subtracting multiples of ten. They can use ten strips or base ten blocks. Have students make a representation of the problem in their math journal or on a whiteboard.
Depending on the time of year, students may be ready to add and subtract hundreds or tens from a three-digit number. Students would draw 3 number cards instead of 2 for this activity and put the number within the context of a word problem.
Building Three-Digit Numbers
Give students number cards and base ten blocks. Students pick three number cards and make a three-digit number: a 5, a 4, and a 3 could be 543, 534 or other possible numbers. Students then build those three-digit numbers with base ten blocks, record the number and make a picture of the blocks. They continue to do this during the center.
Moving on the Hundred Board
Students need a hundred board and number cards. They then draw 2 number cards and make a 2-digit number. Place a marker on the hundred board. They draw two more number cards and determine how to move on the hundred board to find that number. For example, if 52 is where the first marker is placed and then the next two cards drawn are 2 and 6. The student moves from 53 to 26 or to 62. He records the move. 52 +10 = 62 or 52 – 10 -10 -2 – 4 = 26. Of course, there are multiple ways to move to different numbers.
Evaluation of Student Understanding
Informal: Check student understanding through questioning during the lesson. Also, formative assessment is done while students are working on the exit ticket. As students are working, questions to ask are;
· Why did you start here?—pointing to the number line.
· Where will you stop on the number line?
· What is the problem asking?
· How can you use the number line to find the answer to the question?
As you observe:
· Are there students who are still counting by ones?
· Do students understand where to start and stop on the number line?
· Are there students who take larger jumps? For example, in the problem 45 + 37 did students start at 45 and jump 30 to 75 and then 7 more? The jump of 7 could have been 7 ones or a jump of 5 to get to 80 and then 2 more.
Formal:
Exit ticket: There are 37 girls in the gym. If 28 more girls show up, how many girls are there now?
Meeting the Needs of the Range of Learners
Intervention: Have students solve the tasks with base ten blocks or 100 boards. Consider using smaller numbers (less than 50) or using problems in which the sum of the ones digits is 9 or less so they will not have to reorganize tens and ones.
Extension:
Have students work with numbers beyond 100, including numbers with 3 addends.
Possible Misconceptions/Suggestions:
Possible Misconceptions |
Suggestions |
Students may struggle adding or subtracting by multiples of 10. |
Work with smaller numbers (50 or less) and provide them with base ten blocks or ten frame cards to support their work. Use the attached ten strips to help student count by tens. For example, show 3 dots and then a ten strip. Ask how many? Then add another ten. How many? Continue adding ten strips and counting by tens 3,13,23,33,43, etc. |
Students may struggle determining whether to add or subtract. |
Students act out the problem. Students need concrete objects such as base ten blocks or ten strips. Use smaller numbers and have students discuss the action of the problem to determine whether they should add or subtract. |