Differentiating Math Activities

Differentiating Math Activities

Section 1: Lesson Preparation

Teacher Candidate Name:

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Peter Philips

Grade Level:

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5th Grade

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Date:

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June 28th 2023

Unit/Subject:

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Number and Operations-Fractions

Instructional Plan Title:

Comparing and Ordering Fractions

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Lesson Summary and Focus:

In this lesson, students will learn to compare and order fractions, mixed numbers, and decimals to thousandths utilizing a number line. The main goal is for learners to comprehend the notion of fractions and their relative sizes, as well as to be able to utilize the >, =, and < signs to order and compare them (Indiana Department of Education, 2020; Siegler et al., 2010).

Classroom and Student Factors/Grouping:

There are many different types of learners in the classroom, each with different needs and abilities. Eduardo, a Hispanic English Language Learner, requires support in reading, while Fredrick has a Traumatic Brain Injury and receives Tier 3 RTI for reading and math. Emma and Nick have low socioeconomic status and limited internet access at home. These factors impact the lesson's preparation, delivery, and evaluation since they call for providing differentiated activities and adjustments to ensure that all learners can participate and successfully learn fractions.

National/State Learning Standards:

Indiana State Standard: 5.NS.1 - Use a number line to compare and order fractions, decimals and mixed numbers to thousandths. Write the results using >, =, and < symbols (Indiana Department of Education, 2020).

Specific Learning Target(s)/Objectives:

1. Given a set of fractions, decimals, and mixed numbers, the learners will accurately compare and order them utilizing a number line and the symbols >, =, and <.

2. The learners will be able to detail/explain their reasoning for the ordering and comparisons of fractions, decimals and mixed numbers.

3. The learners will identify equivalent fractions and utilize them in comparisons.

Academic Language

v? Fractions

v? Decimals

v? Equivalent fractions

v? Compare

v? Mixed numbers

v? Order

These terms/phrases will be explicitly imparted to learners through direct instruction, visual representations, and practice exercise/activities. Examples and non-examples will be provided to support comprehension (WGBH Educational Foundation, 2002).

Resources, Materials, Equipment, and Technology:

?? Number lines

?? Whiteboard and markers

?? Worksheets and handouts

?? Fraction manipulatives

?? Online interactive fraction tools (if available)

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Section 2: Instructional Planning

Anticipatory Set

v? Display a number line on the whiteboard.

v? Ask learners to recall their previous understanding/knowledge of fractions and share what they remember about ordering and comparing fractions.

v? Demonstrate a set of fractions on the number line and ask learners to discuss with a partner what they notice and any patterns they observe (Indiana Department of Education, 2020; Siegler et al., 2013).

Time Needed:

10 Minutes

Multiple Means of Representation

v? Provide guided notes with visual representations of fractions, decimals, and mixed numbers on a number line (Siegler et al., 2010; Siegler et al., 2013).

v? Utilize a graphic organizer to compare and contrast different types of numbers.

v? Demonstrate examples of comparing and ordering fractions, decimals and mixed numbers utilizing real-world contexts and manipulatives.

v? Provide visuals and anchor charts to facilitate comprehension.

Differentiation:

1. Eduardo (ELL, Low SES):

?? Provide picture dictionaries or bilingual dictionaries to support understanding of academic vocabulary.

?? Utilize visuals and real-life examples to enhance understanding.

?? Provide scaffolds and sentence frames for detailing/explaining reasoning.

2. Emma (Mid SES):

?? Offer additional practice problems for reinforcement (Siegler et al., 2010; TeachersFirst.com, 2023).

?? Encourage peer collaboration and discussions.

?? Provide avenues for hands-on exercises/activities and manipulative utilization.

3. Fredrick (Traumatic Brain Injury, Low SES):

?? Utilize visual aids and graphic organizers to support understanding.

?? Break down complex assignments/tasks into smaller steps.

?? Provide additional time and repetition for practice (Siegler et al., 2010; TeachersFirst.com, 2023).

4. Nick (Low SES, Medium Parental Involvement):

?? Provide avenues for kinesthetic and hands-on learning.

?? Offer challenging extension exercises/activities for advanced learners.

?? Provide clear and concise instructions.

Potential Issues and Solutions:

1. Potential Issue: Limited English proficiency for Eduardo (ELL, Low SES)

v? Solution: Provide picture dictionaries or bilingual dictionaries to support Eduardo's comprehension of academic vocabulary. Utilize gestures, visuals, and real-life examples to enhance understanding. Provide scaffolds and sentence frames for detailing/explaining reasoning.

2. Potential Issue: Difficulty in abstract thinking for Emma (Mid SES)

v? Solution: Offer concrete representations of fractions utilizing manipulatives and visual aids. Provide hands-on exercises/activities and manipulative utilization to support comprehension. Utilize real-life contexts and examples to make fractions more relatable and tangible (Siegler et al., 2010; TeachersFirst.com, 2023).

3. Potential Issue: Processing challenges for Fredrick (Traumatic Brain Injury, Low SES)

v? Solution: Utilize graphic organizers, visual aids, and graphic representations to support understanding. Break down complex assignments/tasks into smaller steps and offer clear instructions. Provide additional time and repetition for practice to cater for Fredrick's processing needs.

4. Potential Issue: Lack of interest or motivation for Nick (Low SES, Medium Parental Involvement)

v? Solution: Provide avenues for kinesthetic and hands-on learning to engage Nick. Offer challenging extension exercises/activities for advanced learners to keep him motivated. Link fractions to real-world examples and contexts that align with Nick's interests or experiences (Siegler et al., 2010; TeachersFirst.com, 2023).

5. Potential Issue: Challenges generalizing skills for all learners

v? Solution: Provide avenues for practice and application in different settings and contexts. Utilize a variety of examples and non-examples to boost comprehension. Encourage learners to detail/explain their reasoning and link concepts to real-life scenarios. Offer ongoing evaluation/review and reinforcement to boost skill generalization.

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Time Needed:

15 Minutes

Multiple Means of Engagement

A. Engage learners in a hands-on exercises/activity where they place/position fractions, including equivalent fractions, on a number line.

B. Divide learners into small clusters/groups and assign each cluster a set of fractions to order and compare utilizing the number line.

C. Facilitate a class engagement/discussion, asking quizzes that promote conceptual comprehension:

1. Can you detail/explain why a fraction with a larger numerator and smaller denominator is greater than a fraction with a smaller numerator and larger denominator?

?? This question prompts learners to link the size of the numerator and denominator to the value of the fraction and stresses the notion of relative size.

2. How would you order and compare the fractions 3/5, 4/7, and 5/8? What approach would you utilize and why? (Siegler et al., 2013)

?? This question encourages learners to think about their preferred approaches for ordering and comparing fractions and articulate their reasoning, fostering metacognition and critical thinking.

3. Imagine you have a pizza divided into 12 equal slices, and another pizza divided into 8 equal slices. Which pizza has larger slices, and how can you justify your answer utilizing fractions? (Siegler et al., 2010; TeachersFirst.com, 2023)

?? This quiz presents a real-world context and challenges learners to apply their comprehension of fractions to make comparisons and support their reasoning with mathematical evidence.

4. Suppose you have a number line from 0 to 1 and need to place the fractions 1/3, 1/4, and 1/6 on it. How would you determine their positions, and what would the relative distances between them tell you about their sizes?

?? This question promotes spatial reasoning (WGBH Educational Foundation, 2002) and encourages learners to utilize number lines as a tool for ordering and comparing fractions, stressing the significance of the denominator in determining the size of the fractional elements/parts.

5. Can you think of a scenario in your daily life where comprehending fractions, including ordering and comparing them, would be essential? Detail/Explain your answer (Siegler et al., 2013).

?? This question links fractions to real-life applications and invites learners to consider the practical relevance of their learning, promoting engagement and fostering knowledge transfer to significant contexts.

Differentiated Activities:

Fraction Tasks: Equivalent Fractions

v? Eduardo: Utilize visual manipulatives and models to explore and identify equivalent fractions (Siegler et al., 2010; TeachersFirst.com, 2023).

v? Emma: Utilize fraction circles or bars to identify/find and compare equivalent fractions.

v? Fredrick: Utilize division or multiplication to identify/find equivalent fractions.

v? Nick: Solve word challenges/problems involving equivalent fractions (Siegler et al., 2013).

Ordering and Comparing Fractions

v? Eduardo: Utilize number lines and visual models to order and compare fractions with like denominators (Siegler et al., 2010; TeachersFirst.com, 2023).

v? Emma: Order and compare fractions with unlike denominators utilizing a common denominator or by converting to decimals.

v? Fredrick: Order and compare fractions with unlike denominators utilizing multiplication or division (Siegler et al., 2013).

v? Nick: Solve word challenges/problems that involve ordering and comparing fractions.

Time Needed: 25 Minutes

Multiple Means of Expression

I will avail the following options for learners?to show their understanding of ordering and?comparing fractions to accommodate diverse learners during the lesson and avail alternative means of expression:

Summative Assessments:

?? Written Response: Learners will complete a written response to justify ordering and comparing the fractions. This can be a quick response, a paragraph, or an essay.

?? Multimedia Presentation: Learners may choose to create a multimedia presentation (e.g., PowerPoint or video) to demonstrate their comprehension of ordering and comparing fractions.

?? Hands-On Project: Learners can work on a hands-on project where they manipulate and graphically display fractions to order and compare. This can be a physical model, a piece of art, or a diorama (Siegler et al., 2010; TeachersFirst.com, 2023).

?? Portfolio: Learners will compile a portfolio illustrating their work, including visual representations, completed worksheets, and explanations of ordering and comparing fractions.

?? Written Test: Learners will take a written test that includes multiple-choice, fill-in-the-blank, and short response questions to evaluate their comprehension of ordering and comparing fractions.

Formative Assessments:

v? Thumbs Up-Thumbs Middle-Thumbs Down: Learners will indicate their level of comprehension by demonstrating a thumbs-up, thumbs-down or a thumbs-middle sign during the lesson particularly class discussions (Siegler et al., 2010; TeachersFirst.com, 2023).

v? Exit Ticket or Entrance Slip: Learners will complete a brief written response or work out a problem involving ordering and comparing fractions at the beginning or end of the lesson.

v? Mini-Whiteboard Responses/Answers: Learners will utilize mini-whiteboards to write and display their responses to questions or problem-solving assignments/tasks.

v? Pair-Share Discussions: Learners will engage in pair-share interactions/discussions where they explain their thinking and share their comprehension of ordering and comparing fractions.

Differentiated Assessments for Each Student:

1. Eduardo (ELL, Low SES):

?? For the written response, provide graphic organizers or sentence frames to support Eduardo in organizing his thoughts and expressing his ideas.

?? Allow Eduardo to create a visual representation (e.g., diagram, drawing) to illustrate his comprehension in the multimedia presentation.

?? Provide hands-on and manipulatives exercises/activities for Eduardo's hands-on project to enhance his understanding of ordering and comparing fractions.

2. Emma (Mid SES):

v? Offer Emma a choice between a written response and a multimedia presentation, allowing her to choose the mode of expression that best aligns with her interests and strengths.

v? Provide Emma with extra resources (e.g., templates) to improve the quality of her multimedia presentation (Siegler et al., 2010; TeachersFirst.com, 2023).

v? Provide rubrics and specific criteria for self-evaluation and peer feedback on her portfolio.

3. Fredrick (Traumatic Brain Injury, Low SES):

?? Provide Fredrick with additional support during the written response, such as guided prompts or sentence starters (Siegler et al., 2010; TeachersFirst.com, 2023).

?? Allow Fredrick to illustrate his comprehension through a hands-on project that caters to his kinesthetic and tactile strengths.

?? Provide extra time and repetition for formative evaluations, ensuring Fredrick has ample avenue to participate and demonstrate his comprehension.

4. Nick (Low SES, Medium Parental Involvement):

v? Offer Nick a choice between a hands-on project and a written test, considering his preference for hands-on learning (Siegler et al., 2010; TeachersFirst.com, 2023).

v? Provide clear instructions and examples for the hands-on project to facilitate Nick's comprehension and ensure he meets the criteria.

v? Incorporate peer discussions and collaboration in formative evaluations to encourage Nick's active engagement and participation.

Time Needed:

25 Minutes

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Extension Activity and/or Homework

1. Extension Activity:

For learners who have grasped the concept of ordering and comparing fractions quickly, provide them with an extension exercise/activity to deepen their comprehension. They can explore fraction operations by subtracting and adding fractions with like and unlike denominators. The task could involve solving word problems that require them to find the difference or sum of fractions. Example question:

?? Question: Sarah ate 3/4 of a pizza, and her brother ate 2/3 of the same pizza. How much pizza is left? (Siegler et al., 2010; TeachersFirst.com, 2023)

2. Homework:

Assign homework that underlines the concepts of ordering and comparing fractions. Provide a mix of multiple-choice quizzes and open-ended challenges/problems to evaluate their comprehension. Encourage learners to illustrate their work, utilize visual models, and detail their reasoning in solving the problems. Example questions:

?? Compare the following fractions using >, <, or = (Siegler et al., 2013):

a) 2/5 ____ 3/5

b) 4/7 ____ 5/7

c) 2/3 ____ 4/5

?? Order the following fractions from least to greatest:

a) 1/2, 3/4, 2/5

b) 2/3, 5/6, 3/4

?? Solve the following word problems:

a) Sarah ran 2/3 of a mile, and her friend ran 4/5 of a mile. Who ran a greater distance?

b) A pizza is divided into 8 equal slices. If John ate 3/8 of the pizza and Lisa ate 2/8 of the pizza, who ate more? (Siegler et al., 2010; TeachersFirst.com, 2023)

Time Needed:

10 Minutes

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References

Indiana Department of Education. (2020, December). Indiana Academic ???? Standards Mathematics: Grade 5 . Indiana Department of Education. ??????? https://www.in.gov/doe/files/Grade-5-Math-Standards-Dec-2020-?????? R.pdf

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013, January). Fractions: The New Frontier for theories of numerical development. ??????? Trends in Cognitive Sciences. ? https://www.sciencedirect.com/science/article/abs/pii/S136466131200??????? 2653?via%3Dihub

Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., ... ??????? & Wray, J. (2010). Developing Effective Fractions Instruction for ? Kindergarten through 8th Grade. IES Practice Guide. NCEE 2010-4039. ???? What Works Clearinghouse.

TeachersFirst.com. (2023). Teachers first - thinking teachers teaching thinkers. TeachersFirst’s Numbers & Operations - Grades 3-5. ??????? https://www.teachersfirst.com/spectopics/numberop35.cfm

WGBH Educational Foundation. (2002). Difficulties with Mathematics. PBS. ????????? https://www.pbs.org/wgbh/misunderstoodminds/mathdiffs.html