1. Fractions, Decimals and Percents Mini-course Session Six Connecting Fractions to Decimals

2. 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.

3. Homework Discussion Share your solutions for correcting the errors on Decimal Problems 1.

4. 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.

5. 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!

6. 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?

7. 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.

8. 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?

9. 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?

10. 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????

11. 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.

12. 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.

13. 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.

14. 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?

16. 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?

17. Homework: Bringing Mathematics Home 6 Decimal Problems II Bring your paper strip display back next week! We’ll compare to percentages

18. 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?