Fractions, Decimals and Percents Mini-course

Session Six

Connecting Fractions to Decimals

Objectives

• To use paper strips as a manipulative for illustrating the connections between fractions and decimals.

• To use calculators as a tool to investigate patterns in the decimal representation of fractions.

• To Introduce the NCTM Reasoning and Proof Standard.

Homework Discussion

• Share your solutions for correcting the errors on Decimal Problems 1.

Paper Strip Activity

• Line up your decimal strip and fraction strip ( labeled in tenths) from last weeks class

• Notice that 6/10 =0.6 This means that they are equivalent.

• In the next activity you will find many other fraction and decimal equivalents.

Fraction Family Strips

• Beginning with the strip for fourths, cut this out. The strip is already marked with the divisions for fourths.

• Now cut out and label each strip according to the fraction family. Without using a ruler to measure, mark the strip. You can fold it or compare it to the marks on another strip.

• Marks do not need to be accurate but do your best!

Paper Strips continued..

• Share with others how you made your divisions/ markings on the strip.

• Now tape the fractions strips in order ( halves, thirds, fourths, fifths, eights, twentieths) onto construction paper lining up each strip side by side. Put ZERO on the bottom edge of the paper for each strip.

• Now name all the equivalent fractions that you see.

• How can you use these strips to compare fractions?

Decimal Strips• How could we use the fraction strips to

find the decimal equivalents.

• Using the decimal strip, line it up against the fraction family strips and find all the common decimal equivalents or approximates.

Example: Using your fraction strip, find ½ and show that it equals 0.5 on your decimal strip.

Do same for ¼ and 0.25.

Challenge your partner• Let one person name a fraction

found on your strips.

• Ask the partner to name the equivalent decimal name.

• Repeat, taking turns.

This method is a reasonable way to find decimal fractions, but not

completely precise. Why?

Remember the cookie activity?

• If you have 3 cookies to share among 4 people, how much of a cookie does each person get?

• How can we write the answer as a decimal?

Long Division

• A more precise method: LONG DIVISION

• Use long division to find the decimals of 3/20, 2/3 and 2/11

• Hmmm, what’s taking so long??Remember that technology standard? Shall we use a calculator????

Long Division & Calculator Activity

• Now use the calculator to find the decimal for the same fractions. 3/20, 2/3 and 2/11

• Find 5/6 with your calculator.

• A repeating pattern is called an recurring decimal.

Fraction Family Cards• List all Fractions within a

family e.g 1/6, 2/6, 3/6,4/6, 5/6

• Reduce all fractions not in lowest form (Imposters!)

• Use the calculator to change true fractions to decimals.

• Make a poster of all the family members for your assigned family card.

NCTM Reasoning and Proof Standard

Instructional programs from P-12 should enable all students to:

•Make and investigate mathematical conjectures.

•Develop and evaluate mathematical arguments and proof.

Family Card Posters

Look at all the family card posters:

•What traits did you notice within each family?

•What traits are similar between fractions?

•Which families might be relatives?

•What do all terminating or repeating families have in common?

Reflection

• How is this like / unlike the experiences you remember from your previous math classes?

• What value do you see I making or testing conjectures?

• How does it make you feel?

Homework:•Bringing Mathematics Home 6•Decimal Problems II• Bring your

paper strip display back next week!

• We’ll compare to percentages

NO class next week!• UWSP is on Spring Break!

• We will meet next on

Tues. March 25 which we realize is Spring Break

for local schools.

• What fraction of classes are left?