Warm-up: Notice and Wonder: Two Curious Tables (10 minutes)
The purpose of this warm-up is to elicit observations about patterns in addition tables containing sums of two-digit addends that are multiples of 10. Each table is partially filled out to show certain behaviors of the sums and highlight some properties of operations. For example, the sums in the first table can illustrate the commutative property (\(10 + 30\) and \(30 + 10\) both give 40). The sums in the second table can help students to intuit the associative property (\(50 + 10 = (40 + 10) + 10 = 40 + (10 + 10) = 40 + 20\), though students are not expected to generate equations as shown here).
While students may notice and wonder many things about the addition tables, focus the discussion on the patterns in the tables and possible explanations for them. When students make sense of patterns in sums and try to explain them in terms of the features of the addends and how they are added, they look for and make use of structure (MP7).
- Groups of 2
- Display the tables.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
What do you notice? What do you wonder?
- “How do you think the tables work? How do we know what numbers go in the cells?” (Each number in the row at the top is added to each number in the first column on the left.)
- For each of the following questions, give students a minute of quiet think time. Illustrate their responses with equations, if possible.
- “In the first table, why are the sums in the middle row and the middle column the same set of numbers?” (The same pairs of numbers are added. The first number in the middle row and in the middle column are 40 because they are both the sum of 10 and 30, just added in different orders: \(10 + 30\) and \(30 + 10\).)
- “In the second table, why are the sums from the lower left corner to the upper right corner all 60?” (Each time, the first number being added goes up by 10 and the second number goes down by 10, so the sum stays the same.)
Activity 1: Monuments and Falls (25 minutes)
The purpose of this activity is for students to solve word problems that involve adding or subtracting numbers within 1,000, using strategies they are familiar with from earlier grades. The goal is to elicit and highlight strategies that rely on place value understanding, in preparation for upcoming work on addition and subtraction algorithms, which also rely on place value.
Monitor for the following strategies as students work on the last problem about the Eiffel Tower:
- Starting at 328 and counting on by place to 674. This could be represented on a number line or a series of equations.
- Starting at 674 and counting back to 328. This could be represented on a number line or as a series of equations.
- Subtracting 328 from 674 using base-ten blocks, subtracting hundreds from hundreds, tens from tens, and ones from ones, trading a ten for more ones as needed.
As students interpret quantities in context, reason about ways to represent them, and consider the solutions in terms of the situation, they practice reasoning quantitatively and abstractly (MP2).
Materials to Gather
- Groups of 2
- “We are going to solve some problems that involve famous places and great heights.”
- “Take a couple of minutes to quietly read the problems and look at the pictures. Be prepared to share what you think the problems are about and how they are alike or different.”
- 2 minutes: quiet think time
- Share responses.
- Give students access to base-ten blocks.
- “Work with your partner to solve these problems.”
- 5-7 minutes: partner work time
- Monitor for the strategies used to solve the Eiffel Tower problem and identify students who use different strategies to share during synthesis.
- As student work, consider asking:
- “How could you represent the problem?”
- “What does this represent in the problem?”
- “What strategies could you use to solve the problem?”
Solve each problem. Explain or show your reasoning.
Iguazu Falls in South America marks the border between Paraguay, Brazil, and Argentina. It is the largest waterfall in the world.
The waterfall has two parts. The water falls 115 feet in the first part and 131 feet in the second part. How far down does the water fall altogether?
In Washington, D.C., there are many monuments that honor important people in American history.
The Lincoln Memorial is 99 feet tall. The Washington Monument is 555 feet tall.
How much taller is the Washington Monument than the Lincoln Memorial?
The Eiffel Tower in Paris, France, has 674 steps that go from the ground to the second floor. There are 328 steps from the ground to the first floor.
How many steps are there from the first floor to the second floor?
Advancing Student Thinking
- “What is this problem about? What can be counted or measured in this situation?”
- “How could you represent the problem with base-ten blocks?”
- Select previously identified students to share in the sequence shown in the Student Responses.
- “How are these strategies the same?”
- “How are these strategies different?”
- If no students mention using place value to find sums or differences, ask them about it.
Activity 2: Journal About Connections (10 minutes)
The purpose of this activity is for students to reflect on the strategies they used in the first activity. This is an opportunity to check in with students about the strategies from grade 2 they are comfortable using and those they find more challenging.
Supports accessibility for: Fine Motor Skills, Social-Emotional Functioning
- Groups of 2
- “Take some time to respond to one of these journal prompts. You can respond to more than one prompt if you have time.”
- 5-7 minutes: independent work time
- “Now, take a few minutes and share your response with your partner.”
- 2 minutes: partner discussion
Respond to one of these journal prompts:
- What math did you do today that connected to something you did in an earlier grade?
- Describe something you really understand after today's lesson.
- Describe something that was confusing, challenging, or that you’d like to learn more about.
- Invite 2-3 students to share their journal responses with the class.
“Today we used different strategies to solve problems that involve addition and subtraction within 1,000.”
“What is a strategy you like to use for addition or subtraction and why?” (I like to use base-ten blocks to subtract because it helps me see when I need to trade for more ones.)
“What is a strategy for addition or subtraction that you would like to learn more about?” (I would like to learn more about the counting up strategy that can be used in subtraction problems.)
Cool-down: How Much Taller? (5 minutes)
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