Thursday, July 23, 2015

Lesson Plan: Mental Math with Decimals

This lesson utilizes enVision Math, but ideas can be adapted for other texts.  Many of the hyperlinks will direct you to a place to download the resources used throughout this lesson. (Note: You must have ActivInspire downloaded to view the Promethean Board slides)

Source: enVision Math 2.1
Subject: Math
Grade: 5th

Integration of Learning Outcomes

· Students will be able to compute sums and differences mentally using the Commutative and Associative Properties of Addition, compatible numbers, and compensation by making sense of problems and persevere in solving them, reasoning abstractly and quantitatively, attending to precision, and looking for and making use of structure.


· 5.NBT.7: Add and subtract decimals to hundredths using strategies based on properties of operations, and/or the relationship between addition and subtraction.

Anticipatory Set

· Ask: “What kinds of numbers do you find easier to add and subtract mentally?” Students will do a think-pair-share with a partner. Have 2-3 students share their responses. Mention that we will be doing metal math, and that we will break down the problems in order to solve them mentally and quickly.

· Students will work on a modified version of the Problem-Based Interactive Learning (PBIL).
o   PBIL: Suppose you want to buy new video games.  Just Dance costs $20.75. Minecraft costs $10.59, and Super Mario costs $18.25. Use mental math to find the total cost of all three games ($49.59).  Use mental math to find how much more Just Dance is than Minecraft. ($10.16)
§  Students will solve the problem by discussing with their group.  They must use mental math and talk through the process of how they solved it.  Have a few groups share their responses to the class.  Ask if students changed the subtraction problem at all to make it easier.  Model and demonstrate different ways to solve problems when necessary.


· Watch enVision’s 2.1 Video on Mental Math. Pause at the following slides and complete the following tasks:
o   How can you use mental math to add and subtract?  - Students will do a think pair share answering the question with a partner. 1-2 students will share their answers to the whole class.
o   Would the total change if the cashier rang up the video game and then the sunglasses, or the other way around?Students will solve the problems on their whiteboards.  Write out the two ways of writing the problem on the board.  ($11.45 +$3.39 = $14.84, $3.39 + $11.45 = 14.84)  Two students will solve the problem on the whiteboard in the front of the classroom while everybody else solves at their seat.  Pick the students from the token economy used for behavior management.  Circle the answers, noting that they are the same.
o   Commutative Property of addition: Underline “adding in any order.” Students will write down the vocabulary word and the definition in their math notebooks.  Have them skip a line to add later.
o   What property is shown below?Ask, “Is this the same as the commutative property of addition?  Are the numbers in the same order?”  (No)  Ask if any of the students know the name of the property. Go to next slide to reveal answers.
o   Associative Property: Underline “change the grouping of addends.”  Students will copy this into their math notebooks.  Have them skip a line to add for later.  Ask, “What is an addend?”  Call on students who raise their hands. 
§  Write on board: Addend: any of the numbers that are added together.  Students will copy this definition into their notebooks.
§  Write the following equation on the whiteboard.  Ask, “What are the addends?” (8, 3)  Label on board.
o   How could you describe the associative property using the example of the backpack, video game, and glasses? – Students will do a think pair share with a partner.
o   11.45 and 9.55 are compatible numbers.  Circle “compatible numbers” on board.  Students will write in notebook.
o   These are numbers that are easy to compute mentally.Underline “numbers that are easy to compute mentally.” Explain that they are compatible because the 5 makes it easy to add and subtract with. Have students write the definition of compatible into their notebooks.
§  Show how the problem solved.  Circle and label.  “First, he took the two biggest numbers.  Then, he took the whole number for each and added them together.  Then he added the cents together.”
§  Show how to add cents together by thinking in money terms.  “I know that 45 and 55 are both close to 50.  I’m going to take away 5 from 55 to make 50 and 50.  I know that $0.50 + $0.50 = 1.00 if I think about money and quarters.
o   Now finish adding mentally:   Circle where the 20 and 1 comes from.  Add mentally to get 21.  Then add $3.39 to 21.  “I know 21 + 3 = 24.  Then I have 39 cents left, so I add that to the 24 to get my answer.
o   Why can you re-arrange the order and grouping to get the same answer? – Students will do a think pair share to answer the question. Click the next slide to reveal the answer.
o   Communitative Property: change the order. – Students will add this to their definition in math notebook.
§  Ask: Is there a commutative property for subtraction?  Have a student raise their hand to answer.  Give example: Is 4.2 -2.6 the same as 2.6- 4.2?
o   Associative Property: change the grouping. –Students will add this to their definition in their math notebooks.

Play the YouTube video/song “Properties of Addition.”  Have students sing along.  (Say fifth grade instead of third grade.  Pause before identity property.)  If time runs out, play song while students transition to getting their materials out for the next class.

If there is extra time to spare, students can complete the even numbered problems on page 31 in their textbooks.


  • The video is paused and there are discussions at each part. This will help students follow along and work at a steady pace. The video/slideshow also helps give a visual aspect for visual learners.
  • The Problem-Based Interactive Learning was slightly changed to spark more student interests. 
  • The YouTube video/song will attract the musical multiple intelligences.
  • Mention that the students should break down problems and change them to simpler problems in order to help solve them mentally.
  • Students will write an “exit tweet.” Show the sample on the document camera so students know how to fill it out.

Formative/Summative Assessment
  • The exit ticket will be a formative assessment to see where the students stand.
  • The teacher will walk around, observe, and assist students while they are discussing problems within groups or working on practice problems.
  • There will be an end of the unit test that assess students on their skills.

  • enVision’s 2.1 Mental Math video
  • Promethean Board
  • Computer with projector and Internet access
  • Document camera
  • YouTube video

Reflection on Planning

I mostly used the teacher’s manual and Pearson’s website, following the curriculum to plan this lesson.  I felt that mental math would be hard to teach, so I felt that it would be best to stick to the book, especially since the district wants teachers to follow the textbook.

I tried to change the Problem-Base Interactive Learning by using video games as the product to hopefully interest students more.  I also used an “exit tweet” as a new alternative to an exit slip.  Students might be able to reflect better by using the template, and have fun by creating a hashtag.  It also gives them ideas about what to write about.  Plus, it gives the teacher feedback about what they learned or need assistance with.

I wanted to incorporate some fun video at the end that would wrap up what the students learned about the properties of addition.  I was looking for a cartoon, but came across the Properties of Addition song.  It’s to the beat of a popular One Direction song, which I thought was perfect because a lot of the girls in the class like One Direction.  This might allow them to sing along. Plus it perfectly captured the properties and how they work.

Reflection on Instruction

I received pretty positive feedback from the exit “tweets.”  One of my favorites read “I was scared about mental math because I mostly use my fingers, but Miss Orr helped me learn mental math. Thank you Miss Orr.”  There were several exit tweets that said it was hard at first, but then they got the hang of it.  Most of them said that using mental math was easy, even the lower students.  There were a few who said they had trouble doing math mentally.  Others thought addition was easy, but subtraction was hard.

I was able to get further than I expected in the plan.  I wasn’t expecting students to get to the math problems in the textbook, but they did.  In the future, I might have wanted to spend time on subtracting using mental math.  That seemed to be where the most confusion was.  I could also spend more time showing different ways to combine numbers, especially when we went over the textbook problems.

The students were able to solve the PBIL.  Perhaps next time I could have the students write their answer on the whiteboard and hold them up instead of asking a few students for answers.

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