## homework consecutive sums.docx - Section 3: Homework

# Number System Assessment

Lesson 11 of 23

## Objective: SWBAT simplify expressions by combining like terms and using the distributive property and to solve variable expressions using the correct order of operations

## Big Idea: Students solve when given the value of a variable and simplify when the values of variables are unknown.

*59 minutes*

#### Warm up

*15 min*

The warmup today is a math family group warm up Practice quiz number system for the test they are about to take. They should work together to make sure everyone in their family gets questions answered and clarified. They work on combining like terms, distributive property, and order of operations with variables. I

circulate to make sure students are remembering to put the terms in the correct standard order and also that students are multiplying by all terms inside parentheses. I also want to make sure they notice that I have given the value for the last two and that they can actually solve and not just simplify. After we go over the warmup I ask students to share helpful advice they received from a

math brother or sister with the class. This helps uncover common misconceptions or errors. It also helps them explain their ideas clearly (mp3) and view one another as a resource.

#### Resources

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#### Assessment

*30 min*

Students work on the simplifying quiz. When they are finished they turn it over in the center of the table group and I bring them their homework which they can work on the remainder of the period. I used to have students get up and turn in their tests and pick up their homework. The problems with that

are that it is distracting and intimidating to other students who worry that everyone else is finishing quickly and will know how long it took them to finish. In addition, it keeps me circulating through the class to keep voices down.

When I grade tests I never put the score at the top. Instead I just mark problems wrong. I put the score in my grade book, but I find that if they see the score they just look at it and turn it over so no one will see. They don’t try to figure out what they did wrong and fix it. When I mark it wrong with out the score they are more likely to compare their tests and ask what they did wrong. I always make them fix the mistakes and hand it back. If they still get one wrong I go over it with them. If a particular problem was tricky for a lot of them, I go over it with the class.

#### Resources

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#### Homework

*14 min*

The homework homework consecutive sums.docx tonight is a brain stretcher, which I remind students may be too tough to figure out completely with a single brain. I encourage them to get families involved at home and bring ideas about what they tried and may have learned when we come back together in the next class. It consists of a single problem, the consecutive sums problem, which asks what type of numbers can not be made as the sum of consecutive positive whole numbers. Students may want to ask about the vocabulary, but I encourage them to think about what they think the meaning is and use my examples for how to get started. I am willing to redirect them back into the problem to get clues for how to start and I just tell them to try something and see if anything can be noticed or learned from it that might suggest what to try next. This is all about building perseverance and making sense of the problem. (MP1)

The other reason I give them this particular problem is because it deals with factors (the numbers that can't be made as consecutive positive whole number sums are the powers of 2) and we are moving on to using the distributive property to factor expressions.

When students are all finished with the assessment we can start making sense together of the warmup. (If all students haven't finished I collect the tests for those who need more time and can finish it during a warm up section of our next class.) We read through the problem and then I ask what sum, consecutive number, positive number, and whole number mean (one at a time). If they can't define it I ask if they can give me an example of what it is and isn't. I also ask if my examples help them understand. Once we clarify vocabulary I ask what the problem is saying and what we are trying to figure out. When we determine that it is claiming that some numbers can be made by adding positive consecutive whole numbers and some can't I set up a chart with two sides for can and can't. I ask which ones we already know we can make and write down the information from my examples. When we determine that what we are trying to find out is the types of numbers that can't be made this way I ask what we might try or what some students may already have started trying. Some students may have already started adding numbers together so I ask what numbers they were able to make so we can add to the "can make" list. I make sure to ask how they did it so that the class can critique whether their method fits the criteria. This helps to clarify the task. I tell them to start adding and see what numbers they make.

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- UNIT 1: Order of operations & Number properties
- UNIT 2: Writing expressions
- UNIT 3: Equivalent Expressions
- UNIT 4: Operations with Integers
- UNIT 5: Writing and comparing ratios
- UNIT 6: Proportionality on a graph
- UNIT 7: Percent proportions
- UNIT 8: Exploring Rational Numbers
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- LESSON 1: Farmer John and Farmer Fred Day 1 of 2
- LESSON 2: Farmer John and Farmer Fred Day 2 of 2
- LESSON 3: Let's Break It Down
- LESSON 4: Halloween Candy to Zombies
- LESSON 5: Extending Farmer Frank's Field with the Distributive Property
- LESSON 6: Who's Right?
- LESSON 7: To Change or Not to Change
- LESSON 8: Let's Simplify Matters
- LESSON 9: Clarifying Our Terms
- LESSON 10: Breaking Down Barriers
- LESSON 11: Number System Assessment
- LESSON 12: Garden Design
- LESSON 13: Ducks in a Row!
- LESSON 14: The Power of Factors
- LESSON 15: Forgetful Farmer Frank
- LESSON 16: Common Factor the Great!
- LESSON 17: Naughty Zombies
- LESSON 18: Reducing Fields
- LESSON 19: Common Factor the Great Defeats the Candy Zombies!
- LESSON 20: The Story of 1 (Part 1)
- LESSON 21: The Story of 1 (Part 2)
- LESSON 22: Simple Powers
- LESSON 23: Equivalent expression assessment