Grade: 3 Lesson Title: Equivalent Fractions

Transcription

1 Targeted Content Standard(s): Grade: 3 Lesson Title: Equivalent Fractions 3.NF.3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Targeted Mathematical Practice(s): 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure 8 Look for an express regularity in repeated reasoning Supporting Content Standard(s): (optional) 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Student Friendly Learning Targets I can Represent fractions as equal-sized quantities that are equivalent. Use fractions as a tool to understand, model, and explain equivalent quantities and relationships. I can recognize that the size of the whole is essential when making fractional comparisons. Purpose of the Lesson: Students will identify equivalent fractions using area models and number lines. Students compare fractions on the number line to recognize that equivalent fractions refer to the same whole and to the same point on the line. Explanation of Rigor: (Fill in those that are appropriate.) Conceptual: 3.NF.3 Students will recognize that equivalent fractions have the same size. Students will identify whole number and equivalent fractions represented with an area model and a number line. Procedural: 3.NF.3 Students will represent whole numbers and fractions and decompose whole number fractions greater than one using area models and number lines. They will explain how whole numbers and/or fractional units are equivalent relevant to size. Application: Vocabulary: partition equal parts numerator justify fourth (s) part and whole

2 fraction equal distance (intervals) equivalent equivalence reasonable denominator unit fraction sixth (s) eighth (s) fraction half (ves) third (s) comparison fraction bars (tools) fraction bar-the line separating the numerator and the denominator, also called a Vinculum Evidence of Learning (Assessment): Pre-Assessment: Formative Assessment(s): Are These Equivalent? Answer Key (Segment 3) Generating Equivalent Fractions Answer Key/Rubric (Segment 3) What s the Fractional Representation? (Part 1 & 2) Rubric (Segment 3) Go Fish - Observation Checklist (Level II) (Segment 4) Summative Assessment: Self-Assessment: Sequence of Segments Segment 1: Recognize that equivalent fractions are of equal size, but not always same shape. Segment 2: Recognizing equivalent fractions on a number line. Segment 3: Generate equivalent fractions using visual fraction models and the number line. Segment 4: Express whole numbers as fractions and decompose whole number fractions.

3 Lesson Procedures: Segment 1 Approximate Time Frame: 80 minutes (2 class sessions) Focus: (3.NF.3a) Recognize and show that equivalent fractions have the same size, though not necessarily the same shape. Math Practice Look For(s): Grade: 3 Lesson Title: Equivalent Fractions Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Assessment Reason abstractly. Students will recognize that fractions are the same regardless of orientation. Model with mathematics. Students will build equivalent fractions using the same model and represent the fractions in various ways. Attend to precision. Students will precisely fold manipulatives and accurately count squares to create and build equivalent fractions. Students will also explain how each model represents each fraction. Look for and make use of structure. Students will make connections between various types of models used to represent fractions. Potential Pitfall(s): Students often fail to understand that a fractional amount can be represented in various ways depending upon the number of pieces and the size of the whole. Students often think that as the denominator gets bigger the amount gets larger. This misconception often keeps students from generating accurate models of equivalent fraction ideas. Part 1: T: Form a square with 3 yellow color tiles and 1 red color tile. What fraction of the square is red? S: One-fourth. T: Use 3 more yellow color tiles and 1 red color tile. Lay the tiles side by side to form a rectangle. What fraction of the rectangle is red? Resources: Color tiles 3 X 3 Post-Its Grid and Dot Paper Geoboards and rubber bands Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Differentiation for Remediation: Teacher discretion regarding use of all models presented in lesson. Differentiation for English Language Learners: Teacher discretion regarding use of all models presented in lesson, however allow for more discussion and more step-by-step modeling along with students. Differentiation for Enrichment: Teacher discretion regarding use of all models presented in lesson as some activities may be done independently by students. Additional fractions may also be presented to students to create and build independently. Independent Practice (Homework): Teacher Notes/Reflections: Color tiles 3 x 3 Post-its Grid paper Dot paper without squares Geoboards

4 S: One-fourth. T: Are the fractions of the red tiles equal? Turn and talk to your neighbor. NOTE: Some students may think the fractions are not equivalent because the shapes are different sizes. If necessary, have students rearrange color tiles to cover original square. Build upon this concept using 3 x 3 Post-its to represent the whole partitioned into halves. Procedure: 1. Give each student 3 Post-its. 2. Have them fold each Post-it in half three different ways: Figure A Figure B Figure C T: Shade in half of each note. How do you know that one-half is shaded on each note? T: Are you sure that Figure A and Figure C are both one-half? How do you know? Turn and talk. T: Other than folding the Post-its in half, what else can you to prove you have two equal parts? NOTE: Look to have students cut or tear one Post-it apart and lay it on top of another to show that it represents the same size. If necessary, use grid paper to represent Figure C. Give students grid paper and direct them to make a 4 x 4 square. Draw a vertical line like in Figure A dividing the square into two equal parts. Students count how many squares are in ½ of the square grid. Next, draw another 4 x 4 square. Then using a straight edge or ruler, draw a diagonal line like in Figure C dividing the square into two equal parts. Students count how many squares are in ½ of the square grid. Grid Paper Representation Grid A (See Figure A) Grid C (See Figure C) Guide students through number of squares in each of the sections. Focus on half-squares.

5 T: Is half of Grid A equal to the half of Grid C? How do you know? Part 2: As needed, build upon concept using geoboards and dot paper with squares to represent the whole partitioned into fourths. Procedure: 1. Give each student a geoboard, rubber bands, and dot paper. 2. Students will represent fourths in different ways on the geoboard: Note: Consider the whole geoboard as 1 whole. T: Using your rubber bands, partition your board into fourths. Students share. T: What do you notice about the different models? Model A Model B Model C Model D Model E T: Record your partitioned model on the dot paper. T: Choose another partitioned model. Represent it on your geoboard and record it on the dot paper. Model A Model B Model C Model D Model E Students will share their justification regarding equivalencies. If no one has made Model E, challenge students to make a figure that is partitioned into fourths differently than Models A, B, C, and D. ADDITIONAL GUIDING QUESTIONS: T: How can you prove that a fourth in your first dot paper model is the same size as a fourth in your second dot paper model? (Students should recognize the response is that both models have the same number of squares.) T: How do you know that a fourth in Model A and D are equal?

6 Segment 2 Approximate Time Frame: minutes Focus: (3.NF.3a) Recognize and show that equivalent fractions refer to the same point on the number line. Math Practice Look For(s): Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Assessment Model Mathematics: Students use number line templates or draw number lines to represent fractions and show equivalency/non-equivalency. Use Appropriate Tools Strategically: Students use number lines to represent various fraction pairs and compare the distance travelled to determine equivalency. Attend to Precision: Students precisely draw hash marks on number lines to represent halves, thirds, fourths, sixths, and eighths. Look for and Make Use of Structure: Students recognize that if fraction a/b = fraction c/d and fraction c/d = fraction e/f, then fraction a/b = fraction e/f, i.e. If 1/2 = 2/4 and 2/4 = 3/6, then ½ = 3/6. Resources: Number line template (Halves, Fourths, Eighths with/without hash marks) Personal dry erase boards or paper Dry erase markers Fraction Cards (Halves, thirds, fourths, sixths, eighths) Straight edge Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Differentiation for Remediation: Provide visual models and/or anchor charts for vocabulary. Provide additional modeling and guided instruction to represent equivalent/non-equivalent fractions on number lines. Peer tutoring to model and represent equivalent/nonequivalent fractions on number lines. Use number lines with labeled hash marks. Create a giant number line with masking tape. Students can represent fractions by standing on various locations on the number line. Differentiation for English Language Learners: Provide visual models and/or anchor charts for vocabulary. Provide additional modeling and guided instruction to represent equivalent/non-equivalent fractions on number lines. Differentiation for Enrichment: Provide exploration time for representing equivalent fractions for fifths, tenths, etc. Assign students to create a game to practice identifying/representing equivalent fractions on a number line.

7 Potential Pitfall(s): Students may struggle with precise hash mark placement for intervals. Step 1: Representing Fractions on a Number Line (5 min.) T: What does equivalent mean? S: Equal. T: When fractions are equivalent, they take up the same part of the samesized wholes. Quick review: Students create models using available concrete model representations, i.e., fraction circles, grid paper, connecting cubes. Students turn and talk with partners to explain how their representations are equivalent. Choose one or two students to share ideas with the class. Draw a number line on the board that represents a number value. Independent Practice (Homework): Homework Activity Sheet: L3-2: 3.NF.3a Recognize and show that equivalent fractions refer to the same point on the number line. Teacher Notes/Reflections: T: The distance of a whole number shown on a number line represents the value of a number. What is the value shown on this number line? S: 3 Draw a number line with uneven hash marks. T: What do you notice about this number line? (Guide students to realize necessity to utilize precision when placing hash marks on the number line.) T: Equivalent fractions take up the same distance on a number line. Step 2: Represent Equivalent Fractions on a Number Line (10 min.) Provide students with number lines that can be folded to create fractional units. Number line models can be pre-cut or allow time for students to cut number line models before continuing instruction. T: Use a number line model with a beginning hash mark point of 0 and an ending hash mark point of 1. Fold your number line in half and label the hash mark representing ½. (Check student drawings.) T: Using another number line model with a beginning hash mark point of 0 and an ending hash mark point of 1 on your number line, fold your number line in fourths and label the hash mark representing 2/4. (Check student drawings.) T: What do you notice? (Guide students to realizing ½ is equivalent to 2/4.) Choose 1 or 2 students to share models and ideas with the class. Example:

8 T: When fractions are equivalent they take up the same distance on the number lines. You can see that ½ lines up evenly with 2/4. 1/2 and 2/4 travel the same distance on the number line, therefore they are equivalent. T: (Write 1/2 = 2/4.) This number sentence shows that 1/2 is equivalent to 2/4. Step 3: Represent Non-equivalent Fractions on a Number Line (nonexamples) (10 min.) Write 2/3 and 2/6 on the board. T: These fractions have the same numerator. Are fractions with the same numerator equivalent? Make a prediction and share with your neighbors. Then use a number line to check your prediction. Allow students a few minutes to make predictions, share, and draw number lines. T: Turn and talk to your partner. Share and discuss your number line representations. T: What does a numerator represent? S: Numerators tell us how many parts of the whole there are. T: What does a denominator represent?

9 S: The denominator tells us how many equal parts the whole is divided into. Choose 1 or 2 students to share number line models for 2/3 and 2/6 and ideas with the class. T: The denominators in these fractions are different. What can we conclude about denominators and equivalent fractions? S: When the numerators are the same, but the denominators are different, the fractions will not be equivalent because the whole is divided differently and the fractions do not travel the same distance on the number line. T: Write 2/3 2/6. This number sentence shows that 2/3 is not equivalent to 2/6. If necessary, test the statement with another fraction pair such as 3/4 and 3/8. Step 4: If A is Equivalent to B and B is Equivalent to C, then A is Equivalent to C (5 min.) Write 2/4 and 3/6 on the board. T: Use number line models with a beginning hash mark point of 0 and an ending hash mark point of 1. Represent 3/6 on one number line. Next, represent 3/6 on another number line beginning hash mark point of 0 and an ending hash mark point of 1 below it. (Check students number lines for accuracy.) T: You can see that 2/4 is equivalent to 3/6. (Write 2/4 = 3/6). T: Think about this: At the beginning of the lesson we showed that 1/2 = 2/4. If 1/2 = 2/4, does 1/2 = 3/6? Students can place their number lines for 1/2, 2/4 and 3/6 above one another to prove that the distance traveled is the same on all three number lines.

10 Step 5: Make a Set: Equivalent or Not Equivalent (10-15 min.) Materials: Fraction Cards; Personal dry erase boards, paper, or number line templates Objective: Compare 2 fractions to determine equivalency. Players: 2-3 Directions: Print the fraction cards. Laminate for durability and cut. Shuffle all the cards and place the deck face down. Each player takes 2 cards from the deck and turns the cards. Next, they both draw number lines to represent the fractions on their cards. If the fractions on both cards are equivalent, they keep the cards. If the fractions are not equivalent, the player can discard either one or both cards. Round 1 ends when all players have compared their fractions to determine equivalency. Play continues with players comparing fraction cards until all of the cards are gone or until they have finished a given number of Rounds determined by the teacher. The player with the most cards wins. Circulate among teams as they play to monitor understanding and representations. Note: You may combine fraction card sets for larger decks.

11 Segment 3 Approximate Time Frame: minutes Focus: (3.NF.3b) Generate simple equivalent fractions by using visual fraction models and the number line. NOTE: Fraction pieces utilized in this Lesson have been constructed previously in Lesson 1. Math Practice Look For(s): Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Assessment Model Mathematics: Students use both paper strips to represent fraction bars and number line templates to represent fractions and show equivalence. Use Appropriate Tools Strategically: Students use fraction bars to compare whether two fractions are the same size and use number lines to represent various fraction pairs that are on the same point on the number line to show equivalence. Attend to Precision: Students precisely fold paper and shade in parts of the whole/mark parts of the whole with an X and place the paper above the appropriate number line to represent halves, thirds, fourths, sixths, and eighths. Resources: 5 Paper strips 2 x 7.5 Number-line Templates (Halves, Fourths, Eighths; Thirds, Sixths) L3-3 Glue stick Fraction Bar Manipulatives Fraction Circle Manipulatives Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Differentiation for Remediation: Repeat halves, fourths and eighths; thirds and sixths. (These students may benefit from refolding paper strips but if it is too challenging, actual fraction bar or fraction circle manipulatives may be used instead.) 1. Once students have glued the halves, fourths, and eighths above the number line, model how to draw a line from the half-strip up through the fourth-strip up through the eighth-strip at the midpoint (1/2 or 2/4 or 4/8) of each of the three strips. 2. Label the number line with the following fractions: ½, 2/4, 4/8. Write them in that order each one, underneath another for that point on the number line. 3. Have students explain the relationship of ½, 2/4, and 4/8. 4. Repeat for thirds and sixths. Differentiation for English Language Learners: Students may have difficulty expressing the standard form of each fraction, i.e., they may read ¼ as one-four rather than one-fourth. Explain that if we were referring to 4 as whole number we would say four, but here we are talking about a part of a whole or its position on the number line in relation to 1 or the whole. Therefore, th or rd is added to number word. Exception: When you refer to more than one-half, halves is used instead of half.

12 Begin by having students read one-half and then write the standard form ½ next to the word form for this fraction. Repeat for the fourths, eighths, thirds, and sixths, as each of these fractions are introduced. Potential Pitfall(s): Students need to fold precisely and make defined creases in order to see the parts clearly. Students need to carefully align fraction paper strips above the number line. Differentiation for Enrichment: Ask: When equivalent fractions are compared, what do you notice about the numerator and denominator? Explain why you think that occurs. Fold paper strips into fifths and tenths and compare the fractions. Fold a strip of paper into twelfths and compare it to the other fraction paper strips. Ask: 3/12 is equivalent to what fraction?; 9/12 is equivalent to what fraction?;10/12 is equivalent to what fraction? Have students write statements such as the ones found in Independent Practice (Homework) along with an answer key that has a picture model, number line, and an explanation as to why you should agree or disagree with each statement. Independent Practice (Homework): For each of the statements below, explain why you agree or disagree. 1/6 and 2/12 is equal to 1/3 ½ and 2/4 is equal to 1 2/8 and ¼ is equal to ½ Steps: Part A (Halves, Fourths, and Eighths) Templates found in Lesson Resources and fraction pieces that were constructed earlier in Lesson 1. Teacher Notes/Reflections:

13 Halves: T: Place your half pieces on the number line. What do you notice? T: With a pencil draw a line on the fold, then shade in one of the two parts. T: Name the fraction of the part you shaded. S: One out of two parts; a half; one-half T: Label the shaded part ½. Glue your ½ strip onto the number line paper. On the number line below your shaded section, write ½. Fourths: Repeat with fourths, marking the fourths with x. T: When two fractions of the same whole are compared and they are the same size, we can say they are equivalent. (Glue the fourths strip above the halves strip.) T: On the number line below, record the fractions that are represented on this strip. (1/2, ¼, 2/4, ¾) T: Why are ½ and 2/4 represented by the same point on the number line? S: Possible Responses: The shaded parts of the whole are the same for the two fractions being compared; the fractions being compared are the same size; the fractions are equal; the fractions are equivalent. Eighths: Repeat with eighths. T: What do you notice about this strip? S: Possible Responses: There are eight parts; all 8 parts are the same size; the parts are equal. T: Line-up the left edge of the strip, above the fourths paper strip that we had glued down previously. Glue down the eighths paper. What do you notice? S: Possible Responses: It takes 8 parts to make a whole; each part is even smaller than when we folded the paper into four equal parts; the 2 parts with X s are the same size as 4 of the 8 parts; ½ is the same as 4/8; the part with only one X is the same as 2 of the 8 parts; ¼ is the same as 2/8; ¾ is the same as 6/8. T: On the number line below, record the fractions that are represented by the strip. (1/8, 2/8, 3/8, 4/8, 5/8, ¾, 6/8, 7/8) T: Why are ½ and 4/8 are represented by the same point on the number line? T: Why are ¼ and 2/8 represented by the same point on the number line?

14 T: Why are ¾ and 6/8 represented by the same point on the number line? Part B (Thirds and Sixths) Repeat process for Thirds and Sixths: NOTE: Are These Equivalent? Answer Key and Generating Equivalent Fractions Answer Key/Rubric can be done following instruction. Teacher Notes/Reflections:

15 Segment 4 Approximate Time Frame: minutes Focus: (3.NF.3c) Express whole numbers as fractions and recognize equivalence in the various ways of writing 1 as a fraction, i.e. 1 = 2/2 = 3/3 = Decompose whole number fractions using whole number equivalence with various models, including number bonds. Math Practice Look For(s): Lesson Format: Whole Group Small Group Independent Modeled Guided Collaborative Assessment Model Mathematics: Students use fraction circles, fraction bars/strips, number lines, and number bonds represent fractions and show equivalence to whole numbers. Use Appropriate Tools Strategically: Students use fraction bars/strips and number bonds to compare whether a fraction are the same size and use number lines to represent various fraction pairs that are on the same point on the number line to show equivalence. Attend to Precision: Students precisely partition shapes and number lines to represent 2/2, 3/3, etc. are equivalent to 1 whole. Look for and Make Use of Structure: Students recognize that if the denominator and numerator of a fraction represent the same number of parts, the fraction is equivalent to a whole. Resources: Differentiation for Remediation: Various concrete and visual manipulatives: (fraction circles, colored tiles, student-created fraction bars/strips, number lines) L3-4 Blank number line template Literature Connection: Full House, Dayle Ann Dodds L3-4 What s the Fractional Representation (Part I and II) Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation Provide visual models and/or anchor charts for vocabulary. Review partitioning number lines. Peer tutoring to model and represent fractions equivalent to 1 whole on number lines. Use number lines with labeled hash marks. Create a giant number line with masking tape. Students can represent fractions by standing on various locations on the number line. Distribute symmetrical duplicate letters of the alphabet or other various symmetrical figures to small groups. Students may choose 2 matching figures to represent 2/2 = 1. Differentiation for English Language Learners: Provide visual models and/or anchor charts for vocabulary. Provide additional modeling and guided instruction to represent fraction equivalence to 1 whole. Differentiation for Enrichment: Provide exploration time for representing fractions equivalent to a whole fifths, tenths, etc.

16 Potential Pitfall(s): Some students may think that fractions and whole numbers can t represent the same amount of space or distance. Independent Practice (Homework): Students may have difficulty partitioning number lines. Step 1: Fraction Equivalence to Whole Numbers with Fraction Circles Review equivalent fractions. The teacher or a couple of students will model 1/3 and 2/6 using fraction circles or draw circles on the board. Teacher Notes/Reflections: T: What does a numerator represent? S: Numerators tell us how many parts of the whole there are. T: What does a denominator represent? S: The denominator tells us how many equal parts the whole is divided into. T: What have we learned about equivalent fractions thus far? S: They represent the same space or distance on a number line, so 1/3 is equivalent to 2/6 because they represent the same space. Write 1/3 = 2/6. Distribute 2 blank circles per student and crayons or use fraction circles. T: Can you use your circles to show that 2/2 equal 1? Be prepared to share your thinking. Use the terms denominator and numerator in your explanations. Choose 1 or 2 students to share ideas and models with the whole class. Step 2: Fraction Equivalence to Whole Numbers with Fraction Strips and Number Bonds. Distribute a set of fraction strips. T: Will we see the same results with these fraction strips? Does 2/2 still equal

17 1 on these manipulatives? Work with your partner and be prepared to share and discuss your ideas and models. Choose 1 or 2 students to share ideas and models with the whole class. T: So does 2/2 equal 1 on the fraction strip? S: Yes, because the denominator tells us the whole strip is divided into 2 equal parts, and the numerator tells us we are referring to 2 of those parts. If 2 parts of 2 equal parts are shaded/covered, the whole strip is colored/covered with 2 halves. Both strips represent the same amount of space, so 2/2 is equivalent to 1 whole. T: Write 2/2 = 1. This number sentence shows that 2/2 = 1 whole. T: We can also represent this number sentence with a number bond. Note: A number bond is a mental picture of the relationship between a number and the parts that combine to make it. A whole is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part. Definition from Model Number Bond for 2/2 = 1 whole. Students recreate number bond models on dry erase boards. T: The whole is represented by the the whole circle on top. It is made up of 2 halves represented by the 2 circles. Using fractions strips, continue representing other fractions equivalent to 1 whole. T: Does 4/4 equal 1? Use the strips to show your thinking. Choose 1 or 2 students to share ideas and models with the whole class. T: Does 4/4 equal 1 on the fraction strip?

18 S: Yes, because the denominator tells us the whole strip is divided into 4 equal parts, and the numerator tells us we are referring to 4 of those parts. If 4 parts of 4 equal parts are shaded/covered with 4 fourths, the whole strip is colored/covered. Both strips represent the same amount of space, so 4/4 is equivalent to 1 whole. T: Draw a number bond and write an equation to represent 4/4 = 1 whole. T: Does 8/8 equal 1? Use the strips to show your thinking. Choose a student to share and model thinking. S: Yes, because the denominator tells us the whole strip is divided into 8 equal parts, and the numerator tells us we are referring to 8 of those parts. If 8 parts of 8 equal parts are shaded/covered with 8 eighths, the whole strip is colored/covered. Both strips represent the same amount of space, so 8/8 is equivalent to 1 whole. T: Draw a number bond and write an equation to represent 8/8 = 1 whole. Note: You may want to represent 3/3 and 6/6 for reinforcement. Step 3: Recognize Patterns of Equivalent Fractions to 1 Whole T: If 2/2, 4/4, and 8/8 are equivalent to 1 whole, what do you know about the equivalence of fractions and wholes? S: If the denominator and numerator represent the same number of parts, the fraction is equivalent to a whole. T: Represent this with your fraction strips. Check student models.

19 Possible student representations: Note: Students may consider other fraction possibilities, such as 5/5, 16/16, or 124/124. Step 4: Model Patterns of Equivalent Fractions to 1 Whole Using Number Lines Note: Students should be familiar with partitioning number lines. T: Using a blank number line, represent 3/3 = 1 whole. Turn and talk. Share and discuss your representations with your partner. Choose 1 or 2 students to share ideas and models with the whole class. Students should recognize that 3/3 and 1 whole travel the same distance on the number line and 3/3 is above 1, therefore 3/3 = 1 whole. Students continue using blank numbers lines to represent other fractions equivalent to 1 whole, i.e. 1/1, 2/2, 4/4, 6/6, 8/8. Check student models. Optional Activity: Students may play Go Fish or Fraction Concentration without the cards representing a fraction with a numerator greater than 1 and denominator of 1, i.e. 2/1, 3/1. Administer Assessment: L3-4 What s the Fractional Representation (Part I and II)