# Adding Three-Digit Numbers on an Open Number Line with Froggie Game

Students will be able to use different strategies to add three-digit numbers using an open number line.

(5 minutes)
• Tell students that part of learning to be a strong mathematician is understanding that there are usually many strategies to solve a problem, and knowing multiple strategies gives you more options.
• Write this problem on the board: 44 + 150. Ask students what strategies they could use to solve this addition problem. Have then discuss with a partner or small group then share ideas as a class.
• See if your class can come up with at least three strategies to solve it.
(5 minutes)
• Tell students that you are going to teach them three strategies to solve three-digit addition problems using an Open number line, then they are going to play a game to practise.
• Explain that an open number line is blank so that you can add your own numbers, as needed.
• Draw an open number line on the board to model, then use it to solve 44 + 150.
• Tell students that the first strategy can be called Larger than smallerBecause you start with the larger addend then add the smaller number digit by digit. It is easier when you start with the larger addend, so circle 150 in the problem.
• Now put a point on the number line on the left and label it '150.' Explain that you are going to add the value in the tens place (40) then the ones place (4).
• Put your marker on the point marked 150 then jump four times to the right on the number line. Mark each jump '+10' above the arc then label the new total below the number line (190).
• Now add the ones, making four small jumps to the right, labeling each one '+1' and adding 194 (the sum) below the number line.
• Create a chart noting this strategy and an example for future reference.
(15 minutes)
• Show students the Compensation strategy. Write '63 + 29' on the board. Demonstrate how you temporarily add one to the second number, changing it to 30. This allows you to add three tens (63 + 10 + 10 + 10 = 93) then take that one away, going backwards on the number line one, making the sum 92.
• The last strategy can be called the Combination strategyBecause you combine the hundreds in both numbers than the tens and then the ones, one at a time. Take 132 + 256 for example. Start at 300, then 50 then jump forward 80 (mark the sum 380 under the number line). Then add the 8 in ones on the line. You should be at 388 on the number line.
• Distribute the practise Adding Three-Digit Numbers on an Open Number Line worksheet. Review the three strategies using the problems provided. Each time, discuss which strategy might be most helpful. You might try a few strategies with one problem to contrast how they work differently.
(25 minutes)
• Distribute the Go Froggie! worksheet. Review the directions as a class and answer any questions.
• Assemble students into pairs or triads and distribute one die per group - if you have extra dice, three per group would make each turn faster.
• Allow about 20 minutes for students to play the game.
• *Support: Make a guide with examples of each strategy and allow students to use it as a reference.

Enrichment: Have students try using the open number line tool as a strategy for subtraction. Does it work for other operations?

(5 minutes)
• On the back of one of their sheets, have students use an open number line to solve 345 + 642. Demonstrate the solution and spot check student work for the accurate sum.
(5 minutes)
• Discuss, "Why is it good to know more than one strategy to solve a problem? In what other areas of life do we need to utilize different strategies to be successful? Consider different problems we have or how we get what we want."

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