Fraction Story: Determining Importance

This lesson is part of a thematic unit on integrating literacy into mathematics.  The topic is fractions.

Title of Lesson

Fraction Story: Determining Importance

Course

Third Grade Math
Math: Fractions
Literacy: Determining Importance

Standard(s)

CCSS.Math.Content.3.NF.A.1           Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

CCSS.Math.Content.3.NF.A.2           Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.ELA-Literacy.RI.3.4           Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.

Objectives

I can determine what information is important in text.

I can show and understand that fractions represent equal parts of a whole, where the top number is the part and the bottom number is the total number of parts in the whole.

I can recognize and write fractions and explain what they mean using words or models.

 

Materials

Pencils
Hilighters
Worksheets (included below)
Whiteboards/Markers
Reference for determining importance in math word problems

Essential Question(s):

How can we determine what information is important in a story problem?
How can we visualize a fraction?
How can we show what a fraction is without using numbers?
How can we show what a fraction represents?

Inclusion Activity

5-10 minutes

Discuss the following:
When we are reading a text, what is a detail?
What is a big idea?
How do we determine what is important in a text as we read?

This is the overviewing step.

The goal is to ensure students can recognize the difference between details and the big idea, or general understanding of the text.  Use previous concepts to discuss the importance of details: for example, how we use details to visualize what we are reading.

Allow students to offer their ideas via an open discussion and help cement a firm understanding of what to look for in “important details” in text.

Discuss with the students how, when it comes to story problems, important details are the ones that will help us answer the question.  Those are the details we need to find as we begin our activity.

 

Sequence of Activities

Give each student a worksheet.

Worksheet includes the following scenarios:

Determining Importance: Fraction Story Problems

  1. Captain Bob wanted to see the world! He decided to go on a long journey, sailing from one end of the earth to the other.  One sunny day, Captain Bob boarded a plane.  He traveled ¼ of the journey by plane.  Next, he boarded a boat.  He journeyed the rest of the way by boat.  What fraction of the journey does Captain Bob travel by boat?  Which mode of transportation was longer?

  2. Captain Bob had a lot of free time while on his boat! There are two things Captain Bob likes to do best: swim and watch TV.  Whilst on the boat, Captain Bob spent 3/8 of his free time watching TV.  Soon, he grew board watching all those shows.  He decided to swim, instead!  What fraction of Captain Bob’s free time did he spend swimming?  What did he spend more time doing?

  3. Captain Bob liked the food better on the plane than he did on the boat. For example, there were so many different kinds of drinks to choose from!  Captain Bob likes to blend his favorite kinds of juice.  His favorite drink has 2/5 orange juice.  He also adds cranberry juice.  What fraction of Captain Bob’s drink is cranberry juice?  What juice did his drink consist more of?

  4. Captain Bob didn’t want to be lonely on his journey. He decided to invite his friends along for the fun!  7/10 of his friends joined him on the plane.  The rest of his friends were afraid to fly, so they chose to take the boat.  What fraction of Captain Bob’s friends were on the boat?  Which mode of transportation had more friends?

  5. Captain Bob was pretty lazy during his journey. With all that spare time, he didn’t have much to do!  However, Captain Bob loves to sleep.  He spent 2/9 of his time sleeping on the plane.  What fraction did Captain Bob stay awake?  What did he do more: sleep or stay awake?

  1. Work together on problem #1. Read the story problem aloud, or have the student read it aloud.  Using a highlighter, have students suggest what they believe are important details in the story problem.  As the students make their suggestions, be sure to ask them if the idea they are highlighting helps them to solve the problem.  Also, discuss why certain details are not important to solving the problem. For example: the sky being blue does not help us determine any part of a fraction.
    Optional: print only one word problem per sheet or half sheet and distribute one per student.  That way, they cannot see their fellow students’ problems.

 

  1. Once you see the students are comfortable picking out important details, assign one question per student. The questions will have extra details that are not all pertinent to answering the question.  This is the overviewing step: students will want to read through their word problems, skimming for important words, sentences, and ideas.  Allow them time to work on them individually, highlighting the important details they believe will help them solve the problem.  Remind them as they work to think of what they already know (prior knowledge) to guide them in choosing the right details.
  2. Once the students feel as though they have thoroughly read and reviewed their word problems, have them highlight the ideas. Inform students to be prepared to explain why they chose those details: this is the self-assess step.
  3. One by one, students will share their word problems. The students will only share the details from their word problems that they found important.  They will not share the other details/sentences of the word problem.  Listening students will use their whiteboards and the information read to them to solve the problem on their own.  If the students cannot solve their problems, use the compare and revise stage to assess the interpretation of important details and revise as needed.  Students should openly discuss if there was enough information to solve the problem, what information was missing if they could not solve the problem, and etc.
    Important: where necessary, give students any missing information so that they may solve the problems to completion.

 

Instructional Strategies

Learning groups/cooperative learning
Group discussion/brainstorming

Assessment

Formative: Listening to students offer their understanding of the concepts.  Review responses on worksheets.

Summative:  Topic test

Differentiation

ELL: Provide full worksheets of all problems.

ELL: Allow students to verbalize their understanding, their important ideas, and/or the way they solve their problems.

ELL: Allow students to use the whiteboards to draw their understanding and/or show their problem-solving.

Summary, Integration, and Reflection

Discussing as a team what parts of each story problem were important and why.  It is also important to discuss which parts of the story problems were unnecessary to solving the problem, as in, which were unimportant details.

 

By |April 11th, 2019|3rd Grade, Math|

Fraction Story: Connecting to Text

This lesson is part of a thematic unit on integrating literacy into mathematics.  The topic is fractions.

Title of Lesson

Fraction Story: Connecting to Text

Course

Third Grade Math

Fractions

Standard(s)

CCSS.Math.Content.3.NF.A.1           Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

CCSS.Math.Content.3.NF.A.2           Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.ELA-Literacy.RI.3.4           Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.

Objectives

I can: connect math concepts to something in my own life experience.

I can: connect math concepts to other match concepts I have learned or used before.

I can: connect math concepts to something that is occurring or has occurred in the world.

Materials

Device
YouTube: My Half Day read aloud
“Making Math Connections” worksheets (created by Kristina Wyatt, included below)
Pencils

Essential Question(s):

What text-to-self?  What is math-to-self?
What is text-to-text?  What is math-to-math?
What is text-to-world?  What is math-to-world?

Inclusion Activity

5-10 minutes

Prepare students for a conversion of the “text-to-_____” concept to “math-to-_____” concept.  Discuss what text-to-self, text-to-text, text-to-world means, respectively, and have each student provide an example.  This lesson relies on students’ prior knowledge of text-to-____ concepts.

Tell a short story (preferably containing fraction concepts for this lesson) or conduct a short read-aloud to encourage thinking.

Example:  Tell a story about grocery shopping and buying five out of the ten apples available in the produce section.  Elaborate as needed until students can produce “text-to-_____” examples of their own.

If students continue to struggle, model your own examples.

Once comfortable with the “text-to-_____” foundation, discuss how we can alter the strategy to be “math-to-_____” instead (using self/math/world).  Review the worksheet which gives definitions for “math-to-_____” connections.  Model examples of each from the same fraction story.

 

Sequence of Activities

Distribute the Making Math Connections Worksheet.

Either with individual devices or one central device, show the video My Half Day read aloud.  This is a fraction story with several examples of fractions throughout.

Since this lesson will be used for a small group, pause after each page to allow students to offer any “text-to-_____” examples they come across.  Have students share and record the examples in their worksheets (optional: if students are struggling, have them record all working examples.  If students are comfortable, have them record only their own).  Teacher: be sure to contribute your own  examples as well.

Continue through the story.  Once completed, replay the story one more time without pausing so students can write down any other examples they may have missed or need clarifying.

Instructional Strategies

Literacy strategy: connecting to text
Learning groups/cooperative learning
Group discussion/brainstorming

Assessment

Formative: Listening to students offer examples of connections during the inclusion activity as well as throughout the read-aloud.  Reviewing responses on worksheets.

Summative:  Topic test

Differentiation

Inclusion activity: teacher model examples or offer written examples.

Provide a script from the read-aloud.

Have students record all connections made on the worksheet, and not just their own.

ELL: Allow students to draw their connections or speak them into a recorder.

ELL: Provide advance notes, script, examples, etc. for them to review prior to the activity.

 

Summary, Integration, and Reflection

Students openly discuss the connections they made.  If connections did not meet the criteria, we discussed why/why not and, in some cases, adjusted them so that they did meet criteria.

Making Math Connections Worksheet
(created by Kristina Wyatt)making connections (Fractions)

 

 

By |April 11th, 2019|3rd Grade, Math|

Fraction Story: Vocabulary

This lesson is part of a thematic unit on integrating literacy into mathematics.  The topic is fractions.

Title of Lesson

Fraction Story: Vocabulary

Course

Third Grade Math

Fractions

Standard(s)

CCSS.Math.Content.3.NF.A.1           Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

CCSS.Math.Content.3.NF.A.2           Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.ELA-Literacy.RI.3.4           Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.

Objectives

I can: show and understand that fractions represent equal parts of a whole, where the top number is the part and the bottom number is the total number of parts in the whole.

I can: recognize and write simple fractions and explain their components using words.

Materials

Device
Quizlet.com or flashcards
Headphones or ear plugs
Paper and pencil
Math textbook
Diagram printout

Essential Question(s):

What are different types of fractions?
How are fractions used in our daily lives?

Inclusion Activity

5-10 minutes

This is our first lesson, so begin the activity by telling the students: “We will be working together over the next several weeks.  Our mini lessons are going to revolve around fractions and writing a fraction story.  But first, I need your help!  I need you to teach me what you know about fractions.”

Provide the diagram I have created (attached below) for a visual that the students can write on.  Each vocabulary word is depicted, so that the students may label the diagram with the correct terms.  (Optional: provide a word bank if the students miss any of the terms depicted).

As they work through the diagram, have the students compile a vocabulary list of terms relating to fractions that will be inputted into digital flashcards.  Discuss terms and their definitions, what they look like, and how they are used.  Have a math textbook on hand (or use the teacher’s provided anchor chart) to reference, just in case.

Using a device such as a laptop to access quizlet.com, enter the terms as they come up with them, including their definitions.  Be sure to guide them when necessary, as your premade cards will be sure to differ from their definitions (you don’t want them to be too different, but it is expected and good that wording varies slightly.  This will encourage complex thinking for literacy).

Sequence of Activities

Prepare: Using Quizlet.com, prepare two sets of flashcards ahead of time.  You should have three rounds total, including the terms the students define on their own:

  • Definitions (with term as the answer)
  • Picture (with term as the answer)
  • Terms (with definition as the answer)

Also prepare a couple of tie-breaker cards that are number line questions (adapted to fit Mrs. Lang’s current lessons revolving around number lines).  Show a series of fractions on a number line with one highlighted to be guessed.

Be sure to have students turn in their diagrams momentarily before they start the game.

Activity (15-20 minutes): Divide into equal numbered teams.  Explain that the object of the game is to get as many flashcards correct.  The opposite team should wear headphones to make it fair (or ear plugs if headphones are not on hand).

Use a number line flashcard to choose who goes first (whoever raises their hand/gets it correct first).  Each team should then choose the order in which they’ll answer.  One student per turn gets to answer, in order.  Pace should be quick.  Teacher should keep tally of correct answers.

First round: Begin with the definition cards, where the definition is given and the students must guess the term.  Explain that the definitions may differ from what they’ve come up with, but the meaning should be the same – another way of describing the same term (literacy differentiation).  Once the round is complete,

Second round: Test using the term cards.  The students should be able to give a basic definition that does not have to match word-for-word with the given definition on the back of the cards.

Third round: Test using the picture cards.  For example: the numerator flashcard should have a fraction on the front with the numerator circled.  The students should identify that the answer is numerator.

If a tie-breaker is necessary, use the number line cards.

Optional: provide a prize or incentive for the winning team.  Or, for every correct answer (countable by your tally), give a piece of candy or one eraser from the dollar store bags of miniature erasers, etc.

Wrap-up (5 minutes):  Discuss with students the challenges of the game.  Was it difficult defining given terms?  What did they notice between my definitions and theirs?  Were there any words that stuck out to them and helps them to remember?  Which terms were the most difficult to remember?  Which method (of the three rounds) worked best for them?  (Compare and contrast the number right for each round).   Also, be sure to ask the students what they liked about the game and what they thought could be done differently.

Instructional Strategies

Learning groups/cooperative learning

Group discussion/brainstorming

Assessment

Formative: Guiding the students through the Inclusion Activity where they define the terms.  Observe responses (ensure that each student has a chance to define 1-2 terms, respectively).

Summative:  Topic test

Differentiation

Variation in the number of terms allows for struggling and/or advanced learners.

Omit more difficult rounds.

Adding multiple choice answers to the flashcards.

Allowing students to work together to come up with answers.

Summary, Integration, and Reflection

Discussing as a team what worked and what didn’t work is a great way to reflect on the activities.  Also, allowing students to make their own flashcards based on what you came up with together in the Inclusion Activity can and should be done, to be helpful for future lessons.

Vocabulary

Number line
Fraction (proper fraction)
Numerator
Denominator
Improper fraction
Whole number
Mixed fraction
Equivalent fraction
Unit fraction
Part
Share

fraction number line

By |April 11th, 2019|3rd Grade, Math|

Flip, Turn, or Slide and Congruence (3rd grade lesson plan)

This lesson begins to teach students the geometric concepts of flip, turn, slide, and congruence.  Students will learn the accompanying vocabulary and  demonstrate the concepts using hands-on learning and graphing.

Title of Lesson

Flip, Turn, or Slide and Congruence

Course

Grade 3 Geometry

Standards

3.G.A.1           Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of those subcategories.

Student Learning Goal(s)

  • Students will know the following vocabulary: triangle, congruent, symmetry, transformation, slide or translation, flip or reflection, turn or rotation, pre-image, image.
  • Students will be able to demonstrate the above vocabulary and construct each independently.

Bloom’s Taxonomy

Remember previous geometrical concepts that apply to this lesson (e.g. quadrilateral,
rhombus, rectangle, square, and others).
Understand new vocabulary and concepts.
Apply vocabulary and concepts in the activity.
Create diagrams of the vocabulary proposed.

Assessment

Formative assessment: following the teacher’s demonstration using an overhead projector and pentominoes (or other shape/geometric materials) to demonstrate the vocabulary, students will attempt to mimic what they have learned and form their own diagrams and recordings.  Teacher will check for understanding.
Summative assessment: following the lesson and subsequent days of practice, an evaluative test would be administered.  An evaluative test can range from (a) simple testing or quizzes with work shown, or (b) via a geometry journal project where students will create a reference book defining and diagraming the vocabulary.

Procedures/Lesson Sequence

  1.  Discuss each term with the students as a class.  Each student will record the term and definition (one per page) in their geometry journal.
  2. Check prior knowledge: use overhead magnetic pentominoes to have students demonstrate their knowledge of the terms.
  3. Conduct hands-on activity: provide students with individual sets of pentominoes and graph paper (optional).  Students will practice translations, reflections, and rotations.
    1. Provide a list of steps students must follow to produce each diagram.  For example, problem #1 would state: from point A, show 2 slides and 2 flips across the graph paper.  Students will then trace the starting point (pre-image) as well as their ending point (image).  These pages of graph paper should be included in their geometry journal.
  4. Closing: Have students share and describe how they found their answers.

Materials

Graphing paper, pentominoes (or other shape/geometric materials), overhead projector, pencils, journal or folder designated for geometry terms.

Technology

An overhead projector is required to demonstrate the vocabulary using pentominoes or other overhead shape/geometric materials.  This technology engages students as it gives a real-time, hands-on example of the vocabulary being discussed.  Students may also be asked to use the projector and pentominoes themselves when called upon to demonstrate their learning.

Adaptations

  • Pre-teach all vocabulary and concepts.
  • Provide study guides and worksheets to provide references and foster memorization.
  • Write vocabulary and definitions on the board so that students may easily transcribe without error into their journals.
  • Use visuals via the overhead for visual cognition.
  • Use simple terms in association with difficult vocabulary (i.e. “slide” for translation, “flip” for reflection, and “turn” for rotation).
  • Have students repeat directions for the steps, and provide substantial pause between steps while vocalizing.
  • Write steps on the board and have students transcribe them into their journals.
  • Have students use pentominoes so as to easily visualize the steps.
  • Have students use graphing paper to produce precise diagrams.
  • Circulate the room and provide assistance or thinking points with students if they struggle.
  • Instruct students to raise their hands and ask questions if they find themselves “stuck.”
  • Have students work with buddies to produce their diagrams, then copy into their own respective journals.
  • If students have difficulty writing, provide print-outs of the steps for students to cut and paste into their journals (graph paper also aids in writing legibly).

 

Image credit: ExcelMathMike

By |March 14th, 2016|3rd Grade, Geometry, Lesson Plans, Math|
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