##
* *Reflection: Developing a Conceptual Understanding
Rounding and Estimation, Day 1 - Section 4: Elevator Speech

When I start to teach this lesson, I always revert to the number line. I'll be honest here - models do not work for me as I tend to think of math very viscerally. I struggle with using models but this one works! Just teaching the 'rules' of rounding isn't enough, because students tend to just fill in holes to fix gaps in their own understanding, but once they see the number line they start to connect.

As for models, if there is one suggested in a lesson that doesn't work for you, find one that does. There are always a 100 different ways to explain things. You might even ask your students to develop their own models. You might even learn something form them...I do!

*Challenges*

*Developing a Conceptual Understanding: Challenges*

# Rounding and Estimation, Day 1

Lesson 8 of 10

## Objective: Students Will Be Able To Round 4 digit numbers to the nearest 1000s and use estimation to check sums, differences, and products.

*80 minutes*

**Language Objectives:** Students will be able to write numbers out in word form and say numbers in standard form, using correct vocabulary of place value terms.

**Prior Knowledge: **Place value and number lines.

#### Resources

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Math Blast is a quick, fun, fast-paced math game! It doesn't require a lot of materials - just the PowerPoint, music, white boards, and dry erase markers. I begin every day with a Number of the Day.

Math Blast is also a great place to work on Common Core skills, especially critical thinking skills, discourse and collaboration!

I usually play music while students are working (it is the "Blast" in Math Blast). They have to the end of the song to fill in their board.

In the beginning this is more time than most need, but they will use all of the time when the numbers get bigger. Math Blast is a great way to pre-teach a concept and is really good scaffolding, especially for those struggling learners. I like to add new concepts that will be learning in the near future into Math Blast. This way students are familiar with new concepts when I go to teach them. If they haven't figured out the work through Math Blast they will have at least seen the concept.

I allow table mates to support each other, this is also a good way to support struggling learners.

The basic content my Math Blast covers is:

- Begin with prior knowledge tasks, factoring GCF, LCM. In 5
^{th}grade this is really good to have understanding for going into fractions. - I always add some rounding and estimation, good tools to know and it is pre-teaching our next lesson.
- I always like to end with a word problem to challenge and support students' skills in answering a problem with what the question is requesting them to do.

The closing piece of Math Blast is See, Think, and Wondering.

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#### See, Think, Wondering

*5 min*

I end Math Blast and lead into my lesson with a See, Think, Wondering. The art I choose always relates to the unit I am teaching.

See, Think, Wonder is a dynamic way to get your students to think deeper about a subject without them knowing that they are doing it.

The SEE part is pretty basic thinking. *I see….*

The THINK part is intended to get students to think about things in ways they haven't before. This is a fun way for students to make connection to the things we're learning in math. In my class, we'll be thinking about math and art. I use art because I am passionate about art. Use examples of things that ignite your passion! *This art makes me think about…*.

And the WONDER requires enough engagement with the topic (the art) to be able to come up with a question. *This art makes me wonder if….*

See, Think, Wonder is my way to getting their brains ready to think about math and I find that the transition is great. It is also a quick chance to expose my students to different types of art.

Note: I've added a See, Think, Wondering separate from the Math Blast in case you want to do it by itself. It is also attached at the end of the Math Blast PowerPoint.

Note: You don’t have to use art; I use art because I am passionate about art. Use examples of things that ignite your passion!

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#### Elevator Speech

*10 min*

**Concept: **Rounding numbers isn’t always easy for students to understand. Concrete models are a great way for students to see not only how, but why we round things. Using models to explain ‘*closer to this -- than that*’ is a great way for students to see and understand rounding. Than, when you bring numbers into the picture you can relate them back to the models. I like to use students as my first model.

Get 5 students to come to the front of the room and line them up. Student A on far left, Student B far right, Student C directly ½ between A & B. Student D should be between A & C and

Student E between C & B. Ask the class, *Which student is in the middle?* Then ask if Student D is closer to A or B? Ask the same of Student E.

Now draw a number line on the white board, label the left end 3,000 and the right end 4,000. Draw a line in the middle and ask the class what number belongs there (3,500).

Ask, *If you have the number 3,678, where would it go on the number line?*

Then ask if 3,678 is closer to 3,000 or 4,000.

You should do this at least a few more times with different numbers. Once students demonstrate that they can identify (approximate) locations on an empty number line, and use that information to compare numbers to determine which thousand (or hundred, or ten - you may have to go back to these lower numbers) you can tell them the easiest thing to do is just look at the number to the right of the place value you are rounding.

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#### Work It Out

*40 min*

Students tackle a real world problem today, working on a list of home projects and their cost. Students round and add to come up with an estimate of the cost to have all the work done. Because students don't have real world experience with what sorts of home projects might be needed, make a list of things such as : new roof, fence, deck, new counter tops, shower remodel, new carpet, gutter cleaning, etc. Use pricing with challenging numbers. For example, use $1587, not $1000. Give students a reason to see why rounding and estimating is a great tool.

Note: Taking math real world is SO Common Core. Context is important for learning, and the Common Core emphasizes the importance of real life application of learning. It is fun and engaging.

Note: Rounding and estimation are important skills to develop for the real world. But rounding and estimating are thinking skills, that develop those Mathematical Practices the Common Core lists as critical to success in mathematics.

#### Resources

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#### Closing It

*5 min*

Make a connection with rounding and estimation as a way student's can check their own work quickly. Talk about why this skill might be useful and a good one to have.

The closing is just as important as the launch. This is where you pull it all together and help the students connect to their learning. It is also a great place to take about common misconceptions, if there are any, from their learning. Don't skip this piece; always make sure you leave time for this. Students need a chance to pull it all together.

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#### Quick Assessment

*5 min*

Write a 5 digit number (ex: 56,489) and have students round to the nearest 1000s,and write on sticky note, and put their responses on the Post-It Poster.

Look-Fors: Rounding the wrong number, and how it connects to misconceptions/errors in place value understanding. Also look for basic mistakes in rounding such as: 57,000 when it should have been 56,000.

The Post It Poster assessment system has been an effective tool in my teaching. It allows me to get a quick check on growth of student understanding in response to each lesson. I've structured it so that students can "feel safe", with a focus on content, not individuals.

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- LESSON 1: Math Blast...It's A Numbers Game
- LESSON 2: Math Norms: Setting the Stage for Math Workshops!
- LESSON 3: Place Value: The Games of Total Recall
- LESSON 4: Working with Numbers up to 10,000,000 Day 1
- LESSON 5: Working with Numbers to 10,000,000 Day 2 - Standard to Word form with Numbers
- LESSON 6: Everything In Its Place: Place Value
- LESSON 7: Comparing Numbers to 10,000,000
- LESSON 8: Rounding and Estimation, Day 1
- LESSON 9: Rounding and Estimation, Day 2
- LESSON 10: Rounding and Estimation, Day 3