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Learning Objectives: What should students know and be able to do as a result of this lesson?
As a result of this lesson, students will be able to explain, model, and apply the equivalent representations of fractions with denominators of 10 and 100 in the equivalent decimal form. This is not limited to fractions to decimal, but will include modeling decimals to fractions representation as well.
Prior Knowledge: What prior knowledge should students have for this lesson?
The understanding that a fraction is a representation of a part of a whole.
Part-whole meaning of fractional parts.
Meaning of Numerator and Denominator in a fraction. (3.NF.1)
The understanding of the 10-to-1 relationship between adjacent digits in our numeric system (both to the left & right). (2.NBT.1a)
Guiding Questions: What are the guiding questions for this lesson?
Does your model accurately represent the given fraction or decimal? How do you know these are equivalent?
Describe how you knew how much of the 10 x 10 grid to shade in. What strategies did you call upon to help you complete this task?
How can you prove that your representations are true?
Teaching Phase: How will the teacher present the concept or skill to students?
Teacher will begin the lesson by writing the number 56 on the board or projector to begin the discussion that the number 56 can be composed of 5 tens and 6 one,s as well as various other ways, such as 4 tens and 16 ones to model the 10-to-1 relationship (that a ten can be exchanged for 10 ones, and so on). This will lead the teacher to then remind students that the same relationship exists for the place values to the right of a decimal point.
Teacher can then ask the students what it means to have (one-tenth) of something. Students can share with their table or shoulder partner to explain and justify their answers. Students should explain that it means that something is broken up into ten equal parts (called tenths) and one-tenth would be one of those pieces. Teacher will distribute base-ten blocks of all values and give students the task of determining a whole (that would be a thousand cube, flat, or rod) and then determine what one-tenth of that would be (a flat, rod, or cube).
Teacher will then distribute a 1 x 10 and then later, a 10 x 10 grid and give the students the task of shading in what one-tenth of each grid would look like. Teacher will then ask if the grid is one-whole and you shaded in one-tenth, what would the shaded fraction look like? ( one-tenth as a fraction)? What would the decimal representation of the grid be? (0.1).
Teacher will then give students several more examples such as four-tenths, nine-tenths, etc. Give students a fraction then ask, can you predict what the decimal will be without shading in the grid? Try five-tenths. Students should accurately come up with 0.5.
Teacher will ask: Students, what grid could you use if I give you a fraction with 100 as the denominator? (10x10 or 1x10 grid) Example, (forty-six hundredths). Talk with your partners and determine how the fraction can be shaded on your 10x10 grid and how you can model that fraction as a decimal. (0.46)
Could you model three-tenths as a fraction on a 10x10 grid? Would that change the decimal value? (0.3 or 0.30- value unchanged)
Try (seven-hundredths). What would that look like? What digit would be in the tenths place? Hundredths? How do you know?
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Teacher will ask a student to shade in portion of a 10x10 grid (on guided practice attachment) and call upon a different student/group to explain and write the equivalent fraction and decimal representation.
Once students have completed the representations on the grid and the equivalent fraction or decimal, teacher will facilitate the discussion of how students were able to notate the fraction and decimal from the grid. (See guiding questions for facilitation tips/questions). Could students be given a fraction (with 10 or 100 as a denominator) to write the corresponding decimal without a grid? Does the denominator give students any indication as to the number of digits in the corresponding decimal will have?
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The independent practice will require the students to work in pairs or groups.
Step 1: Students will take their partners papers and shade in various amounts of the 10 x 10 grids then pass back to their partner.
Step 2: Students will take the paper that their partner shaded in and record the fraction and decimal amount represented on the corresponding grids. On the reverse side of the student independent work document (or in students' math journal), the student will justify how they know that their decimal and fraction amounts match the gridded representation.
The fraction to decimal center (attached) could also be accessed by students upon completion for independent work. Struggling students can be pulled into a small group for remediation. Students in need of challenge can be given the extension piece.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students can participate in a gallery walk of other students work.
Throughout independent work, teacher is taking note of specific fraction/decimals (most likely fractions with single-digit numerator over 100, ex: four-hundredths) that s/he wants the students to discuss in anticipation of either student struggle, or various comparison strategies utilized among the class.
Teacher will facilitate students sharing by emphasizing the strategies used by students in order to correctly identify corresponding fractions and decimals.
The teacher will check for student understanding of the skill by checking student's independent work and journal responses. Also, teacher can pose questions to students to gauge their understanding of fractions and equivalent decimals as well as utilization of discussed strategies in order to compare fractions to decimals by representing them on a decimal grid. Through monitoring/checking students work and gauging the understanding of representing fractions as decimals the teacher will make instructional decisions regarding the amount of time to spend on the skills and if more practice is needed.
The teacher can formatively assess the student's prior knowledge at the beginning of the lesson immediately when posing an "activating prior knowledge" task where students share their understanding of the value of the given two-digit number (56). Students should be able to explain the various ways to compose the number 56 and that it can be composed of 5 tens and 6 ones as well as various other ways such as 4 tens and 16 ones to model that the 10-to-1 relationship (that a ten can be exchanged for 10 ones, and so on). The teacher will use this information to guide their instruction and make necessary changes within the lesson based on the students needs. For example: If some students are unable to accurately determine the 10-to-1 correspondence between place values in whole numbers and decimals, the teacher will need to either reroute the lesson back to determining place values of whole numbers and decimals, work on representations with building numbers with base-ten blocks, or pull a small group of struggling students to work on the required prior knowledge of this lesson first; before delving into building decimals from fractions.
Feedback to Students
Students will continuously receive feedback during the lesson when sharing their reasoning about the values of fractions, modeling the representations of fractions, and sharing their strategies for comparing fractions. Teacher will provide feedback to students when asking questions to gauge their understanding. If students are making errors, teacher can provide thought-provoking questions to guide students to think about their fractions and equivalent decimals representations.
Feedback to Students: Students will continuously receive feedback during the lesson when sharing their reasoning about the values of fractions, modeling the representations of fractions, and sharing their strategies for comparing fractions. Teacher will provide feedback to students when asking questions to gauge their understanding. If students are making errors, teacher can provide thought-provoking questions to guide students to think about their fractions and equivalent decimals representations.
Summative Assessment: The teacher will check for student understanding of the skill by checking student's independent work and journal responses. Also, teacher can pose questions to students to gauge their understanding of fractions and equivalent decimals as well as utilization of discussed strategies in order to compare fractions to decimals by representing them on a decimal grid. Through monitoring/checking students work and gauging the understanding of representing fractions as decimals the teacher will make instructional decisions regarding the amount of time to spend on the skills and if more practice is needed.
Accommodations & Recommendations
Students with special needs will need fraction grids already shaded for the independent work. Depending on the disability, the student's task can be to match the fraction to the correct representation. The fraction/decimal center would be beneficial for this task.
Possible extensions of the lesson include providing select students with fractions with 4 and 5 as a denominator. Challenge the student to try and shade and write those fractions as decimals using their background knowledge of equivalent fractions.
Several copies of fraction/decimal center (lamination optional)
Pair or group your students for introduction and guided practice portions of this lesson.Standards for Mathematical Practices (SMPs) recommended (but not limited to):MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others- requesting students to share their thinking with their groups to justify their strategies with others.MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning- Throughout the lesson, the goal is for students to discover and make.MP sense of the connection to fractions and decimals. Students should, by the end of the lesson, be able to explain the accurate corresponding fraction or decimal without the grid due to regularity in guided and independent practice.
Source and Access Information
Name of Author/Source: Tara Davies
District/Organization of Contributor(s): Hillsborough