Rounding and Estimation, Day 2
Lesson 9 of 10
Objective: Students Will Be Able To Round 4 digit numbers to the nearest 1000s and apply this skill to use estimation to check sums, differences, and products.
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: Place value and Number lines
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
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!
Two things to teach today using rounding to estimate: (use a ‘teach than practice, repeat’ approach to deliver these). It is important that you "do the math" with the model problems, as well as the problems students will tackle. We don't always make the best choices. Better to find out before using them with students.
Front End Estimation (addition): This form of estimation is used when making a quick estimate. You use the first digit of a group of numbers and add them up.
Example: 4587 + 2341 + 2541 + 3625 is front end estimated to:
5000 + 2000 + 3000 + 4000 = 14,000
Or 4235 – 2314 becomes 4000 – 2000 = 2,000
Estimation for a Product: Example 6235 x 7 would be 6000 x 7, 6 x 7 = 42 so 6000 x 7 = 42000. 6235 x 7 is approximately 42000. Have a conversation about why and when it might be useful to use this strategy.
Possible story: Working in candy factory. Ask the students what kind of candy. As employees of the candy factory, students' job is to put the candy into packaging. Over the course of a month, you’ve packaged 6235 packages of candy. Your boss wants to know an estimate on how much candy you package in 7 months.
Work It Out
Have students create their own story problems. There is power in having students create their own word problems. Creating their own word problems helps gain strength in reading word problems. They can also give their problems to other students or create them in teams. It also allows students the chance to create work that they feel successful in solving. You can have students work individually or in their math teams (3-4 people). Creating work on over-sized posters to display motivates students to do their very best work.
As students finish work, have a classroom gallery walk. As they "tour", students take their notebooks and do the math. I like to take these posters to our main hall and have a real gallery walk. Taking the students out of the classroom gives it a more 'professional' feel!
Today's closing is a reflection on the gallery tour. Students participate in a class discussion on what worked, what didn't, successes and struggles with today's work. It is important to honor each student's experience with doing this project.
Closing is essential to bringing all the learning around the original objective. It gives students a chance to reflect on what they learned. Ending a lesson without a closing is an incomplete lesson and a missed opportunity.
Give one problem each of estimating product and quotient:
398 x 4 (400 x 4 = 1600) 135 ÷ 7 (140 ÷ 7 = 20)
Have students do their work on a post it note, and put it on the Post It Poster!
Look-Fors: Rounding to numbers that do not work: 398 x 4 becomes 390 x 4. While not entirely incorrect it would be efficient and demonstrates a lack of understanding of the concept of rounding.