Comparing Numbers to 10,000,000

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Objective

Students will be able to compare numbers by recognizing place values.

Big Idea

Students will begin to notice patterns in groups of numbers, using place value to make comparisons between numbers up to 10,000,000.

Language Objective and Prior Knowledge

Language Objective:  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: 4th graders worked with all forms of numbers, up to 100,000.

Math Blast - Lesson Activator

15 minutes

Math Blast Number of the Day 7

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 5th 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.

See, Think, Wondering

5 minutes

1

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!

Elevator Speech

10 minutes

Important Tip of the Day: Get to know your students and work their interests and skills into your lessons!

After the See, Think, Wonder, ask the students what is the largest number in the Number Spiral, what is the smallest, and which number is in the middle?

Say: You know yesterday when I made the huge mistake on my paycheck? Who thinks they know what I did wrong? I forgot place value is what I did wrong. Well, there is another mistake a lot of us make with place value.

Let’s say you are looking to buy a new car. You want something that looks cool and goes fast. You find two cars that you really like but you want to make sure that you spend the least amount of money. One red car cost $10,001 and the navy car cost $9,991, which in should you buy? Why? (Have a discussion and allow students to debate each other’s reasoning.

Well, it looks like I would buy the car for $9,991 as it is cheaper than the other car. (I like to show how to compare numbers by stacking them vertically. This helps students see it visually.)

Now that we have our car we need to buy gas, but I've noticed that the price of gas has been changing. So I decided to write the price of gas each week. The first week it as $3.25, the next $3.50, the third week $3.75 and the last week it was $4.00.

When I looked at my information I realized that there is a pattern. First, is the price of gas going down or up (UP!)

How much is it going up each week? (+.25)

So what would we say the pattern is?

Work It Out

40 minutes

Students work on comparing numbers and also recognizing patterns in numbers increasing or decreasing.

Create a list of numbers to compare making sure they are close in value. Vary the challenge by crossing decades, centuries, millennia, and using the same numerals in different places.

Also, give students another group of numbers to practice looking for and identifying patterns. For example: +10 patterns, +1000 patterns, +150 (a bit more challenging), and so on.

Students work in groups to create their own lists of numbers and identify the patterns. Students are quicker to understand patterns if they also are challenged to create their own!

Teach New Game: My Hand beats Your Hand. It is a game of comparisons! To teach a game, use interactive modeling with a student partner(s), rather than read and/or provide directive directions. Make sure to check student understanding before sending them off to play.

It is important to engage students into their learning by using games. They are fun but have important skills involved. This is also a great way to work on targeted Mathematical Practice standards of the Common Core.

The Closing

5 minutes

Wow, owning a car isn't a cheap investment is it? But I am glad that we helped each other get the best deal and not over pay.

We also did some great work realizing that there was a pattern for the gas pricing. Why do you think it might be important to see a pattern, like in our gas pricing. Knowing what things might cost next week allows us to do....what?

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.

Quick Assessment

5 minutes

The Post-It Poster

Write:

 1,010             1,110                  1,210                1,310          

Ask, What is the pattern?

Students place their answers on the Post-It Poster.

Look-Fors: Students that say the pattern increases by 1, this will usually indicate lack of place value understanding.