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#### Learning Objectives

Students will be able to use their knowledge of place value to add and subtract decimals.

#### Introduction

*(5 minutes)*

- Explain to students that they will put their knowledge of adding and subtracting decimals to use with this game.
- Ask students what the most important rule is when adding or subtracting decimals.
*Answer: lining up the decimal point.* - Write the problem
**2.21 + 0.54**on the board as a review. Have students help you solve the problem step-by-step.

**Beginning:**

- Allow students to use their home language (L1) or new language (L2) in their discussions.
- Provide visuals, such as a place vaue chart with decimal places, and visuals for new vocabulary (e.g., decimals, hundreths, tenths, fractions, etc.) to help them understand the decimal review.

**Intermediate:**

- Write the academic language they can use throughout the lesson on the board as you introduce the language in the lesson (i.e., write sentence frames or new vocabulary).

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Tell students the goal of the game is to create an addition expression whose sum is as close to 1.00 as possible. Explain that students will be broken up into groups of 4.
- Each group of students will receive a deck of cards. An ace will stand for the number 1, and 10 will stand for the number 0. Face cards are considered "wild cards" and can be used to represent any number of the student's choosing.
- At the start of the round, each student will draw four cards. Their goal is to construct two decimals that, when added together, are as close to a whole, or the number one, as possible. The sum can be greater than, equal to, or less than one. Students will use the cards to determine which digits will go in the tenths and hundredths place of each decimal.
- Give students an example. Have a 10, 2, 6, and 7 set aside. Draw these four cards and think aloud as you decide how to arrange the cards. For example,
*I know*Try several different combinations before showing students that the best answer is**6 + 7**is 13, which is much greater than 10, and because ten tenths = one whole, I don't want to put those two in the tenths place. I know**7 + 2**is 9 which is pretty close to 10, so I will try putting those in the tenths place.**0.76 + 0.20 = 0.96**. Make sure to show students how to subtract**1.00 â€“ 0.96**to show exactly how close the sum is to one.

**Beginning:**

- Give students vocabulary cards and allow them to draw visuals for the new terms (e.g., decimals, hundredths, tenths, fractions, etc.). Provide reference materials in their L1 to look up new terms.

**Intermediate:**

- Provide vocabulary cards for the key terms and ask students to rephrase the definitions as they learn them.
- Have ELs restate the think-aloud on how to choose the place value for numbers so the sum is close to 1.00.

#### Guided Practice

*(10 minutes)*

- Have three student volunteers come up to play a practice round with you for the rest of the class to see.
- Students should write their decimal addition equations on the board and solve them for the class to see. Students should then show how they subtracted 1.00 from their sum (if the sum was greater than one) or how they subtracted their sum from 1.00 (if the sum was less than one). Remind students that the person with the smallest difference is the one who wins.
- Make sure that at least one student (or you) receives a wild card to demonstrate how to replace the wild card with any numeral.

**Beginning:**

- Have students work with sympathetic partners that can understand their L1. Tell them to restate the process one of the volunteers used to find the smallest difference.
- Encourage them to use the vocabulary cards for assistance in their discussions.

**Intermediate:**

- Allow students to work with a partner to redo one of the presenter's addition and subtraction problems to show they understand the process.
- Have them restate the directions and steps for the group game.

#### Independent working time

*(20 minutes)*

- Split the class into groups of four.
- Hand out the decks of cards and graph paper. The graph paper should be used to record the addition and subtraction problems, as it allows students to more easily line up the decimal places.
- Students should complete as many rounds as they can in the 20 minute time frame.
- Circulate around the room to make sure students are on task.

**Beginning:**

- Preview how to solve the addition and subtraction problems on graph paper and have students tell the process they use to solve the problem.

**Intermediate:**

- Tell students to explain how they know whether they should subtract from 1.00 or subtract 1.00 from the number greater than 1.00 (e.g.,
**1.20 â€“ 1.00**or**1.00 â€“ 0.72**).

#### Differentiation

**Support:**

- Students may have the other members in the group help them as they solve the problems. It may be beneficial to strategically choose groups, rather than having students choose their own, to ensure there is an "expert" in each group who can help guide struggling students.

**Enrichment:**

- Give advanced students extra practice problems that have numbers in various place values, not just the tenths and hundredths places. For example:
**1.3 + 2.06 + 12**, or**18.2 â€“ 7.005**.

#### Assessment

*(5 minutes)*

- Pass out a notecard to each student. Have them complete the following problems:
**1.00 â€“ 0.33**and**0.74 + 0.65**. This will allow you to see each individual student's understanding of addition and subtraction with decimals, as well as their understanding of regrouping and place value. - Observe if they lined up the decimal points correctly and carried over a group of ten when regrouping was required.
- Additionally, while circulating the room during independent work time, look to see that students have a solid grasp of number sense and place value. Are students making intentional choices about which numerals to put in each place value, or are they simply guessing?

**Beginning:**

- Allow students to continue to work with the graph paper to solve the problems. Have them explain how they lined up the decimals.

**Intermediate:**

- Tell students to turn and talk to a partner and share their final answers. Encourage them to use sequencing words to explain their process, but also have them say how they know they got the correct answer ("I know my answer is correct because...").

#### Review and closing

*(5 minutes)*

- Have students talk with a partner who was not in their group about the most challenging part of the game.
- Have students share some of their challenges as well as strategies they used when determining which number should be placed in each place value.

**Beginning:**

- Model how to use the vocabulary terms to describe a challenging aspect to finding the smallest difference.
- Have students share their explanations with their partners before sharing with the whole class.

**Intermediate:**

- Have students restate a student's explanation and then add to it ("I agree the most challenge part was
**____**. I also think...").