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2012-13 and 2013-2014 Transitional Comprehensive Curriculum

Grade 5Mathematics

Unit 4: Number Theory and Equivalent Fractions

Time Frame: Approximately four weeks

Unit Description

The focus of this unit is equivalent fractions, comparison of fractions, and the number theory properties that provide the basis for such equivalencies and comparisons. Activities presented in this unit will give students opportunities to represent fractions in various ways that will help them gain fluency with manipulating proper and improper fractions and mixed numbers. This unit also gives them activities that allow them to use their understanding and skills and apply them to real-world, problem-solving situations.

Student Understandings

Students develop an understanding of different representations of fractions such as parts of wholes, parts of collections, locations on number lines, as ratios, and as divisions of whole numbers. Students recognize and generate equivalent forms of commonly used fractions, mixed numbers, and decimals. Students use models, benchmarks, and equivalent forms to judge the size of fractions.

Guiding Questions

1. Can students identify fractions using region models, set models, and linear models?

2. Can students identify or develop equivalent fractions related to a given fraction?

3. Can students write ratios as fractions?4. Can students convert between decimals and fractions or mixed numbers?5. Can students compare fractions?

Grade 5 Mathematics Unit 4Number Theory and Equivalent Fractions 4-1

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Unit 4 Grade Level Expectations (GLEs) and Common Core State Standards (CCSS)Grade-Level Expectations

GLE # GLE Text and BenchmarksNumber and Number Relations2. Recognize, explain, and compute equivalent fractions for common

fractions (N-1-M) (N-3-M)4. Compare positive fractions using number sense, symbols (i.e., <, =, >),

and number lines (N-2-M)6. Select and discuss the correct operation for a given problem involving

positive fractions using appropriate language such as sum, difference, numerator, and denominator (N-4-M) (N-5-M)

CCSS for Mathematical ContentCCSS# CCSS TextOperations and Algebraic ThinkingNumber and Operations in Base Ten5.NBT.3 Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Number and Operations- Fractions5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b

= a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

ELA CCSSCCSS# CCSS TextWriting Standards W.5.2a Write informative/explanatory texts to examine a topic and convey ideas

and information clearly.a. Introduce a topic clearly, provide a general observation and focus,

and group-related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.

Speaking and Listening StandardsSL.5.1c Engage effectively in a range of collaborative discussions (one-on-one,

in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

c. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.



SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

Language StandardsL.5.6 Acquire and use accurately grade-appropriate general academic and

domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships.

Sample Activities

Activity 1: All About One-Half (GLEs: 2, 4, 6)

Materials List: paper, pencils

Have students use brainstorming (view literacy strategy descriptions) to determine what they know about the fraction . Some examples are the following: = , 1 is the

numerator, 2 is the denominator, < 1, > , + = , ; in simplest terms, = 0.50,

of $10 is less than of $1000, is 1 ÷ 2, etc. This activity provides insight about

students’ knowledge of fractions. Have each student draw a picture of . Using their drawings, discuss the different models for fractions such as area or regions, sets, linear models, or as a division problem.

Activity 2: What about Fractions? (GLEs: 2, 6; CCSS: L.5.6)

Materials List: What about Fractions? BLM, pencils

Before beginning the fraction activities, have students complete a vocabulary self-awareness (view literacy strategy descriptions) chart. Provide students with the What about Fractions? BLM. Do not give students definitions or examples at this point.

Word/Phrase + – Example Definitionnumerator

denominator

mixed number

improper fraction

equivalentfractionsimplest form


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Ask students to rate their understanding of each word with either a “+” (understands well), a “” (some understanding), or a “–” (don’t know). During, and after completing fraction activities, students should return to the chart and fill in examples and definitions in their own words. Some words may have a “–”, a “”, and a “+” by the end of the activities. The goal is to have plus signs for all words at the end of the activities.

Activity 3: Fractions of Shapes (GLEs: 2, 4, 6)

Materials List: Circle BLM, Square BLM, pencils, fraction tiles or circles (optional), The Internet (optional)

Using a display of the Circle BLM, demonstrate dividing the circle in half. Label each half with 1

2 using colored overlays. To give the activity a more real-like feel, call the circle a pizza. Discuss the terms numerator and denominator. The denominator shows the number of pieces that the pizza has been cut into and the numerator shows the number of pieces that you get to eat. Draw a line perpendicular to the first line through the center of the circle and ask students what the pizza is divided into now (fourths). Continue drawing lines to show eighths and sixteenths. Shade parts of the circle and ask what fraction would describe it. An example would be 1

4 , which could also be called 28 or 4

16 .

Give the students the Square BLM (maybe call it a pan of brownies) and have them divide it the same way (halves, fourths, eighths, and sixteenths). Have students make up various problems and use them in number sentences. Having colored fraction tiles and circles for the students will make this activity easier. Next, have students write comparison statements using their fractional pieces. For example, they could write 1 1

2 4 . Informally introduce addition and subtraction, by saying 1 1 2

4 4 4 . You want students to see that 1 1

4 4 equals 24 , not 2

8 . Continue informally with addition and subtraction questions. Each time, write the equation on the board.

The website www.nctm.org has a lesson on the region model of fractions. Go to the lesson, http://illuminations.nctm.org/LessonDetail.aspx?ID=L343, Fun with Pattern Blocks Investigating Fractions with Pattern Blocks

Activity 4: Creating Equivalent Fractions (GLE: 2)

Materials List: Equivalent Fractions BLM, paper, pencils, The Internet (optional), fraction circles (optional)

Use student sets of fraction circles, if available. If not, provide each student with the Equivalent Fractions BLM. Have students cut out the three circles. Have students create a model of 1

2 by having them fold one circle along a diameter to make two congruent parts.


http://illuminations.nctm.org/LessonDetail.aspx?ID=L343

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Using another circle, have students fold it into four congruent parts. Now, have students repeat folding with a third circle to create eighths. Once the folding is complete, have students cut the fractional parts and label them. Using the fractional parts, have students create number sentences by showing that 1 2

2 4 , 1 24 8 . Having students working in pairs,

challenge them to create as many equivalencies as they can with their models. The activity can be repeated with thirds, sixths, and twelfths. Students can think of a clock to estimate 3

1 and 32 . They can draw lines from the center to 12:00, to 4:00, and to 8:00 to

make thirds. Another way to fold the circles to get sixths is to fold the circle in half and then make two folds to make equal sections. Make sure that the edges meet to ensure equal sections. This divides the circle into six equal parts.

As an extension, students can visit http://www.learningplanet.com/sam/ff/index.asp to practice matching equivalent fractions in a game format. The game is called Fraction Frenzy.

Activity 5: Sets of Fractions (GLEs: 2, 6)

Materials List: paper, pencils, The Internet (optional)

Have students draw 3 small circles on their papers and shade 2 of the circles. Ask what fraction represents the number of shaded circles. ( 2

3 ) Ask what the numerator, 2, represents and what the denominator, 3, represents. Underneath the first set, have students draw a second set exactly like the first set. Ask questions, such as: How many circles in all? How many circles are shaded? What fraction represents the number of shaded circles? ( 4

6 ) Discuss the fact that these fractions are equivalent.

Show that 2 sets of 23 means 2 sets of 2 4

62 sets of 3 or . Continue modeling with other fractions, emphasizing equivalent fractions. The website www.nctm.org has a lesson on the set model of fractions. Go to the lesson, Fun with Fractions: Another Look at Set Model Using Attribute Pieces, http://illuminations.nctm.org/LessonDetail.aspx?ID=L339.

Activity 6: Fractions as Division: Writing Ratios (GLEs: 2, 6; CCSS: 5.NF.3)

Materials List: paper, pencils, paper cups, 2-color counters

Have students count different items in the classroom, such as the number of boys, girls, teachers, desks, chairs, doors, windows, and clocks. On the board, make a table of their counts. Discuss that ratios are comparisons of two quantities, and that they can be used to compare a part to another part, a part to the whole, or the whole to a part. Ratios can be written in 3 forms. Examples are 15 to 14, 15 : 14, and . Have students choose 2 items to compare, such as boys and girls in the classroom, and have them write as many ratios as they can about the two quantities. Each ratio should be written in all 3 forms.


1514



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Provide pairs of students with 20 two-color (e.g., red/yellow) counters and a paper cup. Have the first student shake the counters in the cup and then empty the counters onto a desk. Ask the other student to determine the ratio of red counters to yellow counters. Once the ratio has been determined, the first student should give another equivalent ratio. For example, if the 20 counters are emptied from the cup and produce 14 red counters and 6 yellow counters, then the ratio is . An equivalent ratio would be 7 red counters to 3 yellow counters. This can be shown by creating 2 stacks of red counters with 7 in each stack versus 2 stacks of yellow counters with 3 in each stack. Once the ratio is in simplest terms, repeat the shake. When adequate time is given, have students write about a situation in their own lives in which they could use a ratio to describe the situation. Have them share the experience with the class.

Activity 7: Fractions as Division: Ratios in Patterns (GLEs: 2, 6; CCSS: 5.NF.3)

Materials List: pattern blocks, paper, pencils

Display a repeating pattern such as this:

core

The pattern should show the core and 3 repetitions. Create a table such as this:

Number of blocks In Core After 1st

RepetitionAfter 2nd

RepetitionAfter 3rd

RepetitionNumber of Triangles 1 2 3 4Number of Squares 4 8 12 16Ratio of Triangles

to Squares14

28

312

416

Ask students if they see any relationships between the number of triangles and squares. They should say something such as, for every triangle there are 4 squares. Ask questions such as these: If you continued the pattern completing each repetition until you had 5 triangles, how many squares would you have? (20) Write a ratio between the number of triangles and squares. If you continued the pattern until you had 28 squares, how many triangles would you have used? (7) Write this as a ratio of triangles to squares. Explain that all of these ratios show the same comparison, and are called equivalent ratios. Using pattern blocks, have students make their own patterns and a table for their patterns. Lead students to see that they can simply use the original ratio and multiply the numerator and denominator by the same number to get an equivalent ratio.


…

146


Activity 8: Fractions as Division: Ratios in Recipes (GLE: 2; CCSS: 5.NF.3)

Materials List: Sample Recipes BLM, paper, pencils

Display the sample recipe for lemonade from the Sample Recipes BLM. Have students write ratios for different ingredients, such as 6 cups of water to 2 cans of juice is a 6:2 ratio. Ask them what the equivalent ratio would be if they doubled the recipe or tripled it. (12:4, 18:6) Distribute the Sample Recipes BLM to students. Have students make a table showing equivalent ratios for different pairs of ingredients from any of the recipes. If there are two ingredients that are multiples of 2, ask students what would be the ratio if they divided the recipe in half. If other recipes are desired, write ratios from the ingredients that are whole numbers.

Activity 9: Using Fractions to Describe (GLEs: 2, 6)

Materials List: paper, pencils

Have students think of a topic they would like to investigate, such as a favorite color. Allow students to survey at least 10 of their classmates and create a pictograph to represent the data they collect. Have them to summarize the results with fractional statements and orally present those summaries to the class. An example is given below.

3/10 of the students chose blue, 2/10 or 1/5 of the students chose brown, 2/10 or 1/5 of the students chose green, 1/10 chose orange, 1/10 chose purple, and 1/10 chose red. Encourage students to ask questions of the group such as: Is there any other color chosen by 2/10 of the group? What fraction of the students chose red? What fraction of the students did not choose purple?

Activity 10: Fractions on a Number Line (GLEs: 2, 4, 6; CCSS: W.5.2a, SL.5.1c)

Materials List: math learning log, paper, pencils, The Internet (optional) Students at this level are familiar with fractions as they relate to a ruler. Use the directed learning-thinking activity (DL-TA) (view literacy strategy descriptions) to help the students understand fractions on a number line. DL-TA is used to foster students’ ability




to make predictions, teach self-monitoring techniques for independent learning, and increase attention in the concepts being taught.

Provide students with a blank sheet of 128 11 inch paper. Tell them that they are going to

look at the parts of a ruler. They are going to enlarge the section between 0 and 1. Allow students to make predictions about folding the paper and how the fold in the paper will relate to this section. Ask questions, such as “Considering this sheet of paper is a section of the enlarged ruler, what do you think will happen to this section when it is folded?” A prediction could be “The paper will be divided in half.” Have students to write their predictions in their learning logs (view literacy strategy descriptions). Learning logs are used to help students keep track of learning during class, and the collaboration process and can be created in various ways including a composition notebook or loose leaf paper bound with construction paper. Upon completion, learning logs provide a guide for follow-up activities and evaluation methods. Have students turn their paper sideways and draw a line across the top of the paper from end to end. Draw a line on each side of the paper that starts at the top line and runs about halfway down the page. Label the left line as 0 and the right line as 1. Have students fold the paper in half. Show the students which way to fold. Elicit discussion about their predictions. Ask them if their prediction has to be changed based on the outcome of the fold. On the fold line, draw a line from the top line about half as long as the 0 and 1 lines. Ask questions, such as these: When you folded the paper, how many sections were formed? (2) How far is it from the 0 line to the fold line? ( 1

2 unit) What should we label the fold line as? ( 1

2 ) How much farther is it to the 1 line? ( 12 unit more) How many halves

are in 1? (2)

0 121 2

2

Ask the students to make another prediction concerning subsequent folds. Ask questions, such as “What do you believe will happen to the paper when folded again?” An answer could be, “Both halves are divided in half creating fourths.” Continue having students fold the paper in halves. Ask students to return to their predictions after each fold to see if they have to create a new prediction. Label the halves fourths and eighths. Consider folding all the way to sixteenths depending on the ability of the class. As each fold line is labeled, emphasize equivalent fractions.

Ask the student to consider their predictions as they relate to equivalent fractions. Have students to return to their predictions and discuss the predictions made with partners. Discuss the fact that the first fraction that was written for each fold line is the simplest form of that fraction. Have students also compare fractions such as 1

4 and 24 , and 1

4 and




12

. Ask students to find similarities in fractions such as 12 and 2

4. Informally ask questions

involving addition and subtraction. What is 1 18 8 ? What is 3 1

8 8 ? What is 3 14 4 ?

The website www.nctm.org has lessons on the linear model of fractions. Go to the lessons, http://illuminations.nctm.org/LessonDetail.aspx?ID=L545, Fun with Fractions: Inch by Inch or http://illuminations.nctm.org/LessonDetail.aspx?ID=L540, Fun with Fractions, Making and Investigating Fraction Strips to assist in teaching with visual models.

Activity 11: Decimals, Fractions, and Mixed Numbers (GLE: 2; CCSS: 5.NBT.3a)

Materials List: Decimal Squares BLM, Thousands Cubes BLM, thousands cube, paper, pencils

Provide each student with a copy of the Decimal Squares BLM. Display the square. Begin by discussing the first large square. Have students tell what they know about it. (It is made up of 100 smaller squares. There are 10 rows and 10 columns (10 × 10). There are 10 squares in each row, and 10 squares in each column.) Have students work with the first decimal square by having them shade the small square at the top left on their Decimal Squares BLM. Ask questions such as these: How many small squares are shaded? (1) How many squares in all? (100) What fractional part of the large square is shaded? ( 100

1 ) Show students that 1/100 can also be written as the decimal, 0.01. On a sheet of paper, have students write 1/100= 0.01. Shade the next square in that column. Have students do the same. The amount is now 2/100. On their paper, have students write 2/100 = 0.02. Consider looking at other equivalencies such as 2/100 = 1/50. Continue using the same square to shade and record different decimal amounts until the entire square is shaded. Pay particular attention to 10/100, 20/100, 25/100, 75/100, and 100/100.

Once they have shaded one entire large square, have students shade one small square in the second large square. Students should see that the amount shaded is 101/100, 1 1/100, or 1.01. Continue shading other amounts of the second square showing amounts larger than one whole.

Display the thousands cube and have students find the cube on their Thousands Cube BLM. Have students tell what they know about a thousands cube. (It is made up of 1000 smaller cubes. There are 10 rows, 10 columns, and a height of 10 or 10 × 10 × 10 cubes or 1,000 cubes.) Have them think about 1 of the small cubes. Ask questions such as these: How many of the small cubes are in the large cube? (1,000) What fractional part of the large cube is one small cube? (1/1000) Show students that this can also be written as the decimal, 0.001. On a sheet of paper, have students write 1/1000 = 0.001. Ask students what fractional part of the large cube would 2 cubes represent (2/1000). On their paper, have students write 2/1000 = 0.002. Continue shading and recording different


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amounts. Pay particular attention to 100/1000, 200/1000, 250/1000, 500/1000, 750/1000, and 1000/1000.

Activity 12: Decimals in Expanded Form (GLE: 2, CCSS: 5.NBT.3a)

Materials List: Place Value Chart with Decimals BLM, thousands cube, paper, pencils

Have students work in pairs. Give each student a copy of the Place Value Chart with Decimals BLM. Ask students to consider the number 125.25. Help the students write the number in expanded form by asking them how many hundreds are shown. (1) Show them how to write the 100 in 125.25 (1 × 100). Ask them how many tens are shown (2). Show them how to write the 20 in 125.25 (2 × 10). There are five ones in 125.25. Show them how to write the five in 125.25 as (5 × 1). Ask them how many tenths are in the number 125.25? (2) Show them how to write the tenths in 125.25 (2 × 0.1). Ask them how many hundredths are in the number (5) and show them how to write the hundredths (5 × 0.01) Tell the students to write the number in expanded form (1 × 100) + (2 × 10) + (5 × 1) + (2 × 0.1) + (5 × 0.01). The expanded form equals 100 + 20 + 5 + 0.2 + 0.05 or 125.25.

Display the number 349.256. Have students share with their partners how many hundreds, tens, ones, tenths, hundredths, and thousandths are in the number (3 hundreds, 4 tens, 9 ones, 2 tenths, 5 hundredths, 6 thousandths). Ask students to work with their partners to write the number in expanded form (3 × 100) + (4 × 10) + (9 × 1) + (2 × 0.1) + (5 × 0.01) + (6 × 0.001) = 349.256.

Display the number 589.314. Have students share with their partners how many hundreds, tens, ones, tenths, hundredths, and thousandths are in the number (5 hundreds, 8 tens, 9 ones, 3 tenths, 1 hundredth, 4 thousandths). Ask students to work with their partner in writing the number in expanded form (5 × 100) + (8 × 10) + (9 × 1) + (3 × 0.1) + (1 × 0.01) + (4 × 0.001) = 349.256.

Display the number 9,734.244. Have students share with their partners how many hundreds, tens, ones, tenths, hundredths, and thousandths are in the number (9 thousands, 7 hundreds, 3 tens, 4 ones, 2 tenths, 4 hundredths, 4 thousandths). Ask students to work with their partners to write the number in expanded form (9 × 1000) + (7 × 100) + (3 × 10) + (4 × 1) + (2 × 0.1) + (4 × 0.01) + (4 × 0.001) = 9,734.277.

Have partners work together to create numbers of their own and have their partner write the number in expanded form.

When appropriate time is given to the activity, have students write a summary in their math learning logs, (view literacy strategy descriptions), about three things they have learned with this activity.




Activity 13: Understanding Fractional Relationships with Cuisenaire Rods (GLE: 2; CCSS: W.5.2a, SL.5.1c, SL.5.4)

Materials List: paper, pencils, Cuisenaire Rods or Cuisenaire Rods BLM, scissors, Cuisenaire Rods Process Guide BLM

With the use of Cuisenaire Rods and a process guide (view literacy strategy descriptions), students will visually “see” and manipulate fractions and discover new fractional relationships. The process guide scaffolds students’ comprehension within unique formats. The students’ thinking during the process is stimulated and involvement in the problem-solving process is enhanced as students focus on important ideas and concepts as they progress through learning about the topic.

Place students in pairs. Give each pair a set of Cuisenaire Rods or a copy of the Cuisenaire Rod BLM. If using the BLM, students will need to color and cut the rods apart. In some sets of Cuisenaire Rods, the rod for 4 is pink and in others, it is purple. Allow students time to become familiar with the rods. Provide the students with the Cuisenaire Rods Process Guide BLM and have them survey the guide. Explain the guide’s features (explore, examine, reason and compare) and then tell them that they will use the process guide to work through understanding fractional relationships.

Guide the students through the process by helping them work through the questions. Allow for discussion and listen as they explain how they reach their answers and explain





how they know. Guide students to an understanding of how the rods are related and which rods or series of rods are equivalent. Facilitate their completion of the guide providing feedback and additional explanation as needed.

Activity 14: Fractions Near 0, 12 , and 1 (GLE: 4)

Materials List: paper, pencils, fraction circles or strips

Provide each group of students with a set of fraction circles or strips. Have them place a 12 piece in the center of the table. Display a table similar to this one.

Fractions Near 0 Fractions Near 12 Fractions Near 1

Call out a fraction. Have students model the fraction and decide where to place the fraction in the table above. Once about 10 fractions have been called out, ask students to look for patterns in each column. What is alike about the fractions in each column? How can you decide if a fraction is near 0, 1

2 , or 1? These ideas will help students when comparing fractions and estimating fractional amounts.

Activity 15: Comparing Fractions (GLE: 4; CCSS: W.5.2a, SL.5.1c, SL.5.4)

Materials List: paper, pencils, fraction circles (or other manipulatives such as strips or tiles) math learning logs

Give each group of students two sets of fraction circles. Have them place 2 whole units in the center of the table. Have one student display 1

4 on one of the circles, and a second student display 3

4 on the other circle. Write 14 __?__ 3

4 on the board. Ask students to discuss which fraction is larger and why. Continue having students model fractions with the same denominator. You want them to see that if the denominators are the same, the larger numerator will show the larger fraction. Tell the students to think of eating a pizza. If two pizzas are cut into the same size pieces (the denominator), they get more pizza if they get more pieces (the numerator.)

Continue the activity with fractions in which the numerators are the same, but the denominators are different. Help them see that if the numerators are the same, the fraction with the smaller denominator will be larger. If a pizza is cut into 2 pieces, the pieces will be larger than a pizza that is cut into 6 pieces. Both of these ideas are critical to working with fractions. Next, give fractions that do not have the same numerator or denominator. To help them compare fractions, encourage students to model the fractions using the fraction circles or a number line. Encourage students to use number sense when comparing fractions. 2

5 is less than 12 and 5

7 is greater than 12 , so 52

5 7 .



In their math learning logs, (view literacy strategy descriptions), have students use pictures, numbers, and/or words to find ways to show that 3

2 of a pizza is larger than 52

of that same pizza.

Place students in groups of four. Ask them to demonstrate their understanding of equivalent fractions by completing a RAFT writing (view literacy strategy descriptions) assignment. This form of writing gives students the freedom to project themselves into unique roles and to look at content from unique perspectives. From these roles and perspectives, RAFT writing can be used to describe a point of view, envision a potential job or assignment, or solve a problem. It is the kind of writing that when crafted appropriately, should be creative and informative.R – Role (role of the writer – employee)A – Audience (to whom the RAFT is being written – manager of Toby’s Typical

Toppings Pizzeria)F – Form (the form the writing will take – a menu)T – Topic (the subject of the focused writing – to create a menu for the pizzeria to include

whole pizza prices and fractional pizza prices. Fractions should not be less than ½.)

The groups should share their RAFTed menus with the class. Students should listen for accuracy and logic in each RAFT. Afterward, the menus might be posted on the bulletin board or classroom walls to remind students about practical ways of comparing fractions.

Activity 16: How Big Is the Fraction? (GLEs: 2, 4; CCSS: SL.5.1c)

Materials List: How Big is the Fraction? BLM, paper, pencils

Distribute the How Big Is the Fraction? BLM to students.

= 0Between0 and 1

2= 1

2Between

12 and 1 = 1 Between

1 and 2

Call out fractions, decimals, and mixed numbers and have the students place them in the proper columns. Examples include 2

4 , 06 , 4

4 , 53 , 1

21 , 0.5, 1.2.

After an adequate amount of numbers is called, have students use the discussion strategy (view literacy strategy descriptions) Think Pair Square Share about the process of the activity and the knowledge gained. This strategy allows students time to think alone for a short period of time and then share their thoughts with someone. Ask the students questions such as the following: “Were there any similarities in the decimal numbers called and the fractions that were between 0 and ½ ?” “How was this activity like creating the enlarged ruler?” “Were there any numbers difficult to place? Why or Why not?” Give the students some wait time to think about the responses to the questions






asked. Ask the students to share their thoughts with a partner. Allow both to share their thoughts. Then, allow the students to share their thoughts with another pair to create groups of four. Elicit responses requiring the students to share their partner’s response for class discussion after discussions have been made.

Sample Assessments

General Assessments

Portfolio assessments could include the following:o Anecdotal notes made during teacher observationo Either one of the journal entries, or one of the explanations from the

specific activitieso Corrections to any of the missed items on the tests

On any teacher-made written tests, include at least one of the following.o One problem that requires the use of manipulatives or drawings such as

this: Show how to compare 12 and 3

4 using manipulatives or drawings.o One problem that requires students to explain their reasoning such as this:

Explain how to find three fractions equivalent to 13 .

o One problem involving real-life such as: Name 3 places where you see fractions or decimals in real-life.

Journal entries could include the following:o Answer the following question and explain your reasoning. Can 1

4 ever be larger than 1

2 ?

Activity-Specific Assessments

Activities 3 and 4 : Have the student draw 4 congruent rectangles and use these rectangles to show that 81 2 4

2 4 8 16 .

Activity 8 : Tell the student that a good recipe for cookies calls for 2 cups of brown sugar and 4 cups of flour. The student should write a ratio of brown sugar to flour and find equivalent ratios if the recipe is doubled, tripled, or cut in half.

Activity 10 : Have the student discuss how he/she can easily tell that 18 is to the

left of 12 on the number line.

Activities 14 and 16 : Have the student name a fraction, mixed number, or decimal equal to 0, between 0 and 1

2 , between 12 and 1, equal to 1, and between 1

and 2.


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