Comparing and Ordering Decimals

Lesson Content

• Lesson Plan Template:

  General Lesson Plan

• Learning Objectives: What should students know and be able to do as a result of this lesson?

  
  

  Students will be able to take a set of decimals cards - with both 10ths and 100ths - and order them least to greatest based on:

  • Benchmark decimals 0.5, 0.25, and 0.75
  • Comparisons referring to the same whole
  • Visual representations of decimals (drawings)

  Students often have misconceptions that when a decimal in hundredths is compared to a decimal in tenths, the hundredths decimal is always greater because they treat them as whole numbers - the longer the number, the greater the value. For example, they might see 0.57 as greater than 0.8 because the whole number 57 is greater than the whole number 8. It is important that when students are comparing decimals that they convert the decimals to equivalent decimals before comparing them. For example, 0.8 is the same as 0.80 - now when comparing the two numbers, it becomes clearer that 0.57 is indeed smaller than 0.8

• Prior Knowledge: What prior knowledge should students have for this lesson?

  
  

  Student should know/understand:

  • fractions as parts of a whole
  • meaning of numerator and denominator
  • equivalent fractions with denominators of 10ths and 100ths
  • reasoning of relationship between fractions and decimals
  • tenths, hundredths, multiplication
  • comparisons/compare, <, >, =

• Guiding Questions: What are the guiding questions for this lesson?

  
  

  Guiding questions for this lesson include:

  • Would 0.8 be closer to one whole or zero?
  • Explain why you placed 0.27 before 0.5?
  • What strategies did you use to help you decide?
  • What helpful numbers are nearby that you could use to decide where to place a decimal?
  • How could a drawing be helpful?
  • What is the relationship of the quantities?

• Teaching Phase: How will the teacher present the concept or skill to students?

  
  

  Prior to the lesson, have the students separated into groups of four. Each group should have the following levels of students: (#1)- High, (#2)- High Medium, (#3)-Low Medium, (#4)-Low...When splitting each group into pairs (shoulder partners) always team them - High (1)/Low-Medium (3) and High-Medium (2)/Low (4). This leads to more engaged learning for all members of the group.

  1. When beginning the lesson, have individual students draw a number line at their desk. Instruct them to label the benchmark decimals of 0.5, 0.25, and 0.75. Circulate to assess individual student understanding. Students making incorrect marks need to receive immediate coaching. (Make a note to pull these children into a small group and remediate.)
  2. Upon completion of the task, the teacher reinforces the concept by drawing a number line on the board at the front of the room and having students locate the benchmark decimal points.
  3. Give each team of students a post-it note decimal (see Post_It_Note_decimals.pdf). Working cooperatively the teams determine where their post-it notes would appear on the number line.
  4. Call on the #1 and #2 students from each team to come to the board and place the team's post-it note on the number line - justifying the choice of placement.
  5. Provide Feedback, Praise, and Coaching (if necessary).

• Guided Practice: What activities or exercises will the students complete with teacher guidance?

  
  
  1. Student groups receive a second post-it note (see Post_It_Note_decimals.pdf).
  2. Working cooperatively the teams determine where their post-it notes would appear on the number line.
  3. Student groups talk amongst themselves and decide where each of their decimals should be placed on the class number line and discuss the reason for the decision.
  4. The #3 and #4 students will come up to represent their teams. This is considered guided practice because these students will need coaching and guiding questions (see Guiding Questions section for appropriate questions) to complete the task.
  5. Feedback and praise are given.

• Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?

  
  

  ACTIVITY PREP: It will take a bit of time to prepare the materials for this activity. I suggest you do it a day or two prior to the lesson.

  • The decimal cards for this activity: Ordering_Cards_Set_And_Answer_Key.pdf
  • You will need to copy the decimal cards onto card stock (I chose a different color for each sheet) For example: J-1 blue, J-2 yellow, J-3 green, J-4 white, J-5 red. The answer key I put on a different color.
  • I suggest laminating the cards for durability. Each team is given a zip-loc bag containing one set of each color cards as well as an answer key.

  ACTIVITY:

  1. Teams find a workspace area on the floor. It needs to be a large enough area that all four students can sit side-by-side. Sitting across from each other would make two of the students looking at the cards upside down and reading them in the wrong direction.
  2. The #1 team member (the captain) selects a set of cards from the bag. The cards are spread apart for all members to see. The students take turns selecting a card and identifying its position when ordering from least to greatest - justifying the choice.
  3. Once the cards are ordered least to greatest, the captain selects a team member to check the answer key. The captain calls out each decimal to the checker. The checker responds by saying "Check!" if the decimal is correct. If the captain comes to a decimal that is NOT CORRECT, the answer key is immediately placed back into the bag and the cards are mixed-up again and the process begins again. This is done repeatedly until the order is done correctly.
  4. When the first round is completed, the captain places the cards back into the bag and the #2 team member (the NEW captain) now selects a new set of cards from the bag. The process begins again.
  5. The activity continues until all card sets have been completed. There are 5 card sets in each bag. Once each student has had a turn as a captain, the team plays "Rock-Paper-Scissors" to see who the final captain will be.

• Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?

  
  

  During the activity, the teacher circulates to each group asking probing questions to individual students to justify answers. For example:

  • "Joel, why did your group chose to put .67 after .5?"
  • "Christy, why did your group decide to put 0.16 at the beginning rather than at the end?"
  • "Denise, where do you think 0.89 should go next? Why?"

• Summative Assessment

  
  

  The teacher will check for student understanding by evaluating students' Independent Work on a summative worksheet (Lesson_3_summative_assessment.pdf). Also, the teacher can pose questions to students to gauge their understanding of the correct ordering of decimals - from least to greatest.

• Formative Assessment

  
  

  The quick pre-assessment for this lesson is to have the individual students draw a number line and mark the benchmark decimals: 0.5, 0.25, and 0.75 - along with the points of 0 and 1. The number lines should show the decimal marks at the correct intervals. Students struggling with this need to be pulled into small groups and worked with using manipulatives such as base 10 grids to help with recognizing and comparing decimals.

• Feedback to Students

  
  

  Students will receive feedback during the Guided Practice portion of the lesson when placing their decimals on the class number line. They will also receive feedback when asked questions to gauge their understanding during the group activity. If students are making errors, teacher can provide thought-provoking questions and suggestions to guide students to think about their decimals. (see Guiding Questions section)