Fractions and Decimals: Part 2

Transcription

1 Fractions and Decimals: Part Objective To provide experience with several graphic models for renaming fractions as decimals. epresentations etoolkit Algorithms Practice M Facts Workshop Game Family etters Assessment Management Common Core State Standards Curriculum Focal Points nteractive Teacher s esson Guide Teaching the esson Ongoing earning & Practice Differentiation Options ey Concepts and Skills Convert between fractions, mixed numbers, and decimals. [Number and Numeration Goal ] Order rational numbers. [Number and Numeration Goal ] Order fractions and decimals on a number line. [Number and Numeration Goal ] ey Activities Students use the Probability Meter and FractionStick Chart to approximate decimal equivalents for fractions. They begin filling in a table of decimal equivalents. Materials Math Journal, pp.,, and the inside back cover Study ink transparencies of Math Masters, pp. and slate straightedge Converting mproper Fractions with Division Math Journal, p. Students review and practice converting improper fractions to mixed numbers using division. Math Boxes Math Journal, p. Students practice and maintain skills through Math Box problems. Ongoing Assessment: ecognizing Student Achievement Use Math Boxes, Problem. [Number and Numeration Goal ] Study ink Math Masters, p. Students practice and maintain skills through Study ink activities. ADNSS Playing Number Topt (Place Decimals) Student eference Book, p. Math Masters, p. per partnership: each of number cards (from the verything Math Deck, if available) Students practice forming and comparing decimals. NCHMNT Writing Fraction and Decimal quivalents for a Shaded Grid Math Masters, pp. and transparency of Math Masters, p. Students write equivalent fractions and decimals for the shaded portion of a grid. XTA PACTC Minute Math Minute Math, p. Students compare fractions, decimals, and percentages. Advance Preparation For Part, make transparencies of Math Masters, pages and. For the optional nrichment activity in Part, make one transparency of Math Masters, page for each group of six students. Cut apart the transparency grids so that there is one per student. Teacher s eference Manual, Grades pp.,, esson

2 Getting Started Mathematical Practices SMP, SMP, SMP, SMP, SMP, SMP Content Standards.NBT.a,.NBT.,.NF. Mental Math and eflexes Ask questions like the following. Students refer to the Probability Meter on Math Journal, page and respond by writing number sentences. Which is greater, _ or _? _ > _ Which is greater, _ or _? _ > _ Which is greater, _ or _? _ > _ What fraction is equal to.? _ =. What fraction is equal to.? _ =. What fraction is equal to.? _ =. What fraction is equal to.? _ =. What fraction is equal to.? _ =. What fraction is equal to.? _ =. Math Message How would you use the Probability Meter on journal page to show someone what _ dollar is worth? Study ink FollowUp Allow partners five minutes to compare their answers and correct any errors. Ask volunteers to share their strategies for rounding the area of Malta to the nearest tenth km. Highlight that rounding to the nearest tenth rounds. km to the nearest whole number. km. % %. %. %.. % %. %. %. %. %. %. %.... %.. %.. %. %.... CTAN X T M V CHANC U N,,,,,,,,,,, Teaching the esson Math Message FollowUp (Math Journal, p. ) WHOCASS DSCUSSON Ask volunteers to show how they used the Probability Meter to find the value of _ dollar. Use their explanations to discuss the meter s decimal labels as dollar notation. n dollar notation, hundredths are equivalent to pennies or cents: _ is., or cents. The fraction _ is directly opposite the decimal.. Point out that. is cents and. is _ of _, or _ of cent, so _ dollar is worth $., or _ cents. What is _ dollar worth? $., or _ cents What is _ dollar worth? $., or _ cents What is _ dollar worth? $., or _ cents Writing Fractions as Decimals (Math Journal, p. ; Math Masters, p. ) WHOCASS ACTVT %.. %.. %. V U N Use a transparency of Math Masters, page to demonstrate how the FractionStick Chart can be used to approximate the decimal names for fractions. %. %. MPOSSB. X T M U N Probability Meter Unit Fractions, Decimals, and Percents

3 xample: What decimal is about equal to _? Step : Use the thirds row, and locate the fraction _. Count the _ bars from left to right: _ is the right edge of the second bar. Step : Place one edge of a ruler or straightedge at _ ; that is, along the right edge of the second _ piece and perpendicular to the Decimal Number ine inches Date SSON Time Writing Fractions as Decimals Use a straightedge and the above chart to fill in the blanks to the right of each fraction below. Write a decimal that is equal to, or about equal to, the given fraction. Directions for filling in the blank to the left of each fraction will be given in the next lesson. Sample answers: Math Journal, p. Step : Find where the straightedge crosses the number line. t crosses at about., so _ is about.. efer students to journal page. Ask them to use the chart and number line on the page to mirror the steps as you demonstrate finding the decimal name for _. Ask students how they would use the chart to find the decimal name for _. Use their responses to emphasize that with mixed numbers it is necessary to approximate only the fraction part. The whole number part is unchanged when they write the decimal name, so _ is about.. Assign students to complete the estimates for each problem on the journal page. Circulate and assist. When most students have finished, review the answers and strategies, and discuss any problems that students found particularly difficult or interesting. NOT The FractionStick Chart is a useful visual device but is not intended to provide precise equivalencies between all fractions and decimals. n esson, students will use their calculators to find decimal equivalents for fractions. Name Date Time SSON FractionStick Chart and Decimal Number ine Math Masters, p. esson

4 Name Date Time Denominator SSON Numerator Table of Decimal quivalents for Fractions xample: To find the decimal equivalent for, use the row for the denominator. Go to the column for the numerator. The box where the row and the column meet shows the decimal.. Math Masters, p..... Filling n a Table of Decimal quivalents for Fractions (Math Journal, inside back cover; Math Masters, p. ) Denominator PATN ACTVT A partially completed table of decimal equivalents for fractions appears on the inside back cover of the journal and on Math Masters, page. Use a transparency of Math Masters, page to show students how the table works. ach number across the top of the table identifies the numerator of a fraction. ach number down the left side of the table identifies the denominator of a fraction. The box where a row and column meet is used to show the decimal equivalent for that fraction. Have students complete rows,,,, and. The fractions for the assigned rows are easy fractions. Most students will know their decimal names or will be able to calculate them mentally. Students will complete the rest of the rows in succeeding lessons. Numerator nside back cover of Math Journal. Completed rows,,,, and. Date SSON Time n the problems below, the hexagon shape has a value of. Write the improper fraction name for each diagram. Use division to find the mixed number. Show your work. xample:... Converting mproper Fractions to Mixed Numbers mproper Fraction Mixed Number Show your work. Use division to convert the following improper fractions to mixed numbers or whole numbers.. _ =. _ =. _ = Whole hexagon _ Try This. Jenny said that she could convert _ to a mixed number by repeatedly subtracting _ and seeing what was left over. Tell whether you agree or disagree with this method, and explain why. Sample answer: agree. ach time Jenny subtracts _, she is taking away a whole. f she writes the number of wholes she subtracts and then writes the remainder as a fraction, she will have the correct mixed number, _. When students have written the decimal names, ask volunteers to describe any patterns that they notice in the table. Sample answers: The rows represent whole numbers, halves, thirds, fourths, etc. The first column represents unit fractions. All boxes on the diagonal from the upper left to the lower right have a value of, with decimals greater than in the boxes to the right of this diagonal and less than in the boxes to the left. Decimals become larger as you move across rows and become smaller as you move down columns. Ongoing earning & Practice Converting mproper Fractions with Division (Math Journal, p. ) NDPNDNT ACTVT Students review and practice converting improper fractions to mixed numbers using division. Math Journal, p. _MCS_G_S_G_SMJ_U_X.indd // : AM Unit Fractions, Decimals, and Percents

5 Math Boxes (Math Journal, p. ) NDPNDNT ACTVT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in esson. The skill in Problem previews Unit content. Ongoing Assessment: ecognizing Student Achievement Math Boxes Problem Use Math Boxes, Problem to assess students ability to compare fractions. Students are making adequate progress if they write the fractions correctly from least to greatest. [Number and Numeration Goal ] Date SSON Math Boxes. Complete the table. Fraction Decimal Percent.... Put the following decimals in order from least to greatest ,.,,...,. Put the following fractions in order from least to greatest. % % % Time. stimate an answer for each problem. Sample answers: a.. stimate b.. stimate c.. stimate d.. stimate. Determine whether the following sentences are true or false. Write T or F. a... b. c. T F F d. F. Circle the letters for the pairs of equivalent fractions. Study ink (Math Masters, p. ) NDPNDNT ACTVT,,,,,,,, Math Journal, p. a., b. c., d., e. f., Home Connection Students practice converting between decimals, fractions, and mixed numbers. Name Date Time STUD N Decimals, Fractions, and Mixed Numbers. Convert each decimal measurement to a mixed number. ongest oad and ail Decimal ength MixedNumber ength Tunnels in the U.S. Cascade Tunnel (Washington). Flathead Tunnel, or (Montana). Moffat Tunnel (Colorado). Hoosac Tunnel (Massachusetts). BAT Transbay Tubes, or (San Francisco, CA). Source: The Top of verything. The longest oneword name of any place in America is Chargoggagoggmanchauggagoggchaubunagungamaugg. This name for a lake near Webster, Massachusetts, is letters long. t is a Native American name that means ou fish on your side, ll fish on mine, and no one fishes in the middle. Use this word to answer the problems below. a. What fraction of the word is made up of the letter g? b. What fraction of the word is made up of the letter a?, c. What fraction of the word is made up of the letter c? or. n the space above, write the decimal equivalents for the fractions in Problem. Practice Study ink Master.,.. Math Masters, p., or., or.. Number Topt (Place Decimals) Materials number cards ( of each) PlaceValue Mat (Decimals) (Math Masters, p. ) Players or more Skill Place value for decimals Object of the game To make the largest digit decimal numbers. Directions. This game is played the same as Number Topt (Digit Numbers). The only difference is that players use a placevalue mat for decimals.. Players take turns turning over the top card from the deck and placing it on any of their empty boxes. ach player takes turns, and places cards on his or her row of the game mat.. Players play rounds for a game. Shuffle the deck between each round. The player with the smallest total number of points at the end of the rounds wins the game. Phil and Claire played Number Topt using the placevalue mat for decimals. Here is the result. PlaceValue Mat (Decimals) Ones. Tenths Hundredths Thousandths Phil. Claire. Claire s number is larger than Phil s number. So Claire scores point for this round, and Phil scores points. Student eference Book, p. Games esson

6 Name Date Time SSON Fractions and Decimals Write the fraction name and decimal name for the shaded portion of each square. Use your transparent grid to check your answer. For Problem, color the grid to show a fraction and then write the fraction and decimal name for the shaded portion of the square Differentiation Options ADNSS Playing Number Topt (Place Decimals) (Student eference Book, p. ) PATN ACTVT Min To provide experience with decimal place value and ordering decimals, have students play Number Topt (Place Decimals). See Student eference Book, page for directions. After playing the game, have students choose two decimals from their record sheet and write them using number names.... Math Masters, p. Answers vary.. NCHMNT PATN ACTVT Writing Fraction and Decimal quivalents for a Shaded Grid (Math Masters, pp. and ) Min Name Date Time To apply students understanding of fractions and decimals, have them complete Math Masters, page. Distribute the transparent grids. Students write the fraction and decimal names for the shaded portions of squares and use a transparent grid to check their answers. Students then shade a copy of Math Masters, page to create their own designs and estimate the fraction and decimal names for the shaded portions. Have students copy their favorite design from Problem and display their designs in the Fractions, Decimals, and Percents Museum. SSON Grids XTA PACTC Minute Math SMAGOUP ACTVT Min To offer students more experience with comparing fractions, decimals, and percentages, see Minute Math, page. Math Masters, p. Unit Fractions, Decimals, and Percents