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# The Numbers Game: Playing by the Rules

Lesson 2 of 20

## Objective: SWBAT use index cards to build numerical expressions to solve word problems and to explore their knowledge of the properties of operations with whole numbers, fractions, and decimals.

*37 minutes*

#### Do Now

*10 min*

Students enter the room silently and sit in their seats. Their Do Now is already on their desk with a single sticky note attached. The first problem is a complex multi-step word problem that involves ranges. If students ask for help on this question, I help only with the first step to get them going: "If you know that there are 175 legions and 4,000 soldiers in each, how can you determine the number of soldiers in all 175 legions?" I also point out that the answer to this question should be a range itself to match the information given (**MP1**, **MP7**).

The second question asks students to reflect about where they want to go to college and stand to go place their sticky note in one of three designated areas of the room. If students finish early, I ask them to take a silent gallery walk and check out what their teammates said about college locations.

When time is up, we review the word problem together with the power point. The questions that are set up on that presentation ask students to think about the operations necessary to solve each step. I also show students how to write numerical expression to figure out this type of problem. The information is organized as a T-chart to give students a strategy for problem solving.

I then transition to a small "get-to-know-me" activity. Today is our school's "College T-shirt" day, so I take the opportunity to talk to students about where I went to college, making sure I talk a ton about the freedom and the food. Students then get 3 minutes to walk around the room looking and talking about what other teammates wrote on their notes. I ask students to keep their eye on the clock for the time when they are expected back in their seats.

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#### Group Problem Solving

*20 min*

Students work in groups of 4 or 5 on a Task that will ask them to construct numerical expressions from given Word Problems on index cards. Some cards will give instructions about specific properties students must use to construct their number sentences. Students earn "achievements" after correctly solving each problem. Achievements can be cashed in for prizes. Each student will carry their own card and 1 achievement will be earned by all group members for each correct problem. Each student must also return a worksheet with their work for each problem. This serves as both an accountability piece and a diagnostic piece for me to look at later.

**Before the activity:**

- Share with students my love for games and list some examples. Explain why you think learning math is like playing a video game (rules, puzzles, more than one way, etc.)
- Hand out vocab cards needed for lesson: numerical expression, commutative property, associative property. Students must keep these in their index card boxes. Instruct students to refer to these cards during group work. Briefly discuss that properties are like rules numbers have to follow.
- Explain that today's groups are not "forever groups" and that students will have an opportunity to give me feedback about today's teammates and other students whom they feel they would work well with in the future.
- Explain the "game". Give the expectation.
- Student questions?

**During the activity:**

**Teacher**:

- walks around listening to conversations and answering questions
- asks students about the use of the associative and commutative property in each word problem
- for example: "Could you add/multiply/divide/subtract this part first? Why? Which property/rule is in use if I am allowed?
- writes down expressions on sentence strips for gallery walk at the end of class
- gives out "achievements" (star stickers on their index cards)

**Students**:

- read instructions silently for 1 minute.
- work together to construct their numerical expressions. All students must be participating in the task. I visually look for this (and tell students I'm looking for this) by ensuring that ALL students are holding index cards and placing them in the desired order.
- raise their hand to ask a question no one else in their group was able to answer. (Ask 3 before me)

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Everyone takes a seat and I introduce them to their **Math Journals**. Each KIPPster will receive one composition book and will also have one math journal checked for a grade each week. Focus will be placed on the effort shown in the journal responses. I advise students to elaborate on as much of their thinking process as possible to earn good scores on their journal entries. If they are ever confused about a concept, I encourage them to write all the questions they feel that they need answered in order to understand the concept. Then, we read the journal questions together.

Students are then introduced to the **Gallery Walk**. They must walk around the room quietly (whispering is allowed, like at a museum), while thinking about which questions they're going to answer. Students are encouraged to take notes. After they walk around once, they return to their seats to write.

Students are instructed to answer any TWO of the following questions:

- Did you notice any equivalent numerical expressions in two different groups' answers to the same question? Which ones?
- Describe how the Commutative Property could be applied to any of the expressions you saw.
- Describe how the Associative Property could be applied to any of the expressions you saw.
- Do you notice any unique solutions at any groups' station? Is there an expression that makes sense to you? Why?

At the end of 3-4 minutes, we can do partner share and 1 student shares. Two students pass out homework and we pack up for the next class.

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*Responding to Tammie Cotenas*

Hi Tammie, thank you for your feedback!

I've attached an answer key (PDF) with possible expressions for each word problem in the "Group Problem Solving" section of this lesson. Remember to be open to lots of different representations of these expressions, not just the ones in the answer key. This flexibility in thinking and answering in math can be very beneficial to students.

In terms if the number of items, it really depends on the structure of your class and the time allotted. I created this lesson when I was teaching 90 minute blocks, so I do have to admit I had the luxury of time. You would be surprised though, my classroom management routines had to be tight to make as much time as possible for this task. I requested that student groups complete at least 4 of the word problems and I gave them 20-25 minutes to do so. If any groups finished early, I gave them the choice: either complete one additional problem or come up with a different and equivalent expression for the completed problems.

Before the gallery walk, ask students to make sure their expressions and problems are labeled accurately and neatly on the worksheet included in the resources section. They should also clear their desks of any other objects and make sure the aisles are clear before everyone starts moving around. I would also give them a couple of minutes to silently preview the questions above so they are ready to focus their observations during the gallery walk. They ARE in fact looking at the expressions created during the group work time, so they are student generated. I liked doing this activity at the beginning of the school year because it was an active way to diagnose my students' skills. It's jam packed with deliverables so your classroom management has to be on point and there should be some form of accountability. For example, I would let students know that they needed to answer ALL of the questions above and this journal entry would be a **completion** grade as an exit ticket at the end of class. Again, their responses gave me a good sense of the skills they were bringing in at the beginning of the year.

I remember it being tough, but I did push myself NOT to reveal all of the answers. At the beginning of the school year I wanted to focus on learning about my students and increasing the student to teacher talk ratio. Many also come on with fixed mindsets about their abilities in math. If anything stood out as completely incorrect or made it obvious that a student was struggling with this skill, I would have a private one-on-one with that student, letting them know how excited I was to help them this year and reassuring them that their mistakes were valuable to the learning process.

Hope this helps, please let me know if you have any other questions and thank you for your feedback! :)

| 7 months ago | Reply*Great lesson. I too am wondering about an answer key. Thank you. | 7 months ago | Reply*

*Great lesson. I too am wondering about answer keys. Also, could you give me a little more information on the gallery walk...how many items? what are they looking at? For this lesson I'm assuming they are looking at expressions....are these student generated or teacher generated? Thank you. | 7 months ago | Reply*

*Great lesson. I too am wondering about answer keys. Also, could you give me a little more information on the gallery walk...how many items? what are they looking at? For this lesson I'm assuming they are looking at expressions....are these student generated or teacher generated? Thank you. | 7 months ago | Reply*

These are great lessons! I can't wait to use them with my 7th grade class. I was wondering if you provide an answer key? I would like to focus more time on the lesson and less time on solving the problems. Thank You!

| 2 years ago | Reply*expand comments*

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- LESSON 1: The Numbers Game: Playing by the Rules
- LESSON 2: The Numbers Game: Playing by the Rules
- LESSON 3: Exponents: It's Gotta Be the Power of 3
- LESSON 4: Rolling with the Order of Operations
- LESSON 5: Bingopposites
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- LESSON 9: Lines Around the World: Combining and Graphing Integers on a Number Line
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- LESSON 11: What's up with that? The Connection Between Addition and Subtraction of Integers
- LESSON 12: Note the Arrows: Modeling Addition and Subtraction of Integers on Number Lines
- LESSON 13: Man Your Station! Adding and Subtracting Integers in Real World Situations
- LESSON 14: Lines and Patterns: Difference, Change, and Multiplication
- LESSON 15: We Are a Family!
- LESSON 16: Trashketball!
- LESSON 17: Quiz Day
- LESSON 18: Rewind! Reviewing Integer Operations and Critical Thinking
- LESSON 19: Unit 1 Test
- LESSON 20: Error Analysis: Unit 1 Test