1. Copyright © Allyn and Bacon 2010 Big Ideas 1.Decimal numbers are another way of writing fractions. 2.The base-ten place-value system extends infinitely in both directions. 3.The decimal point is a convention to indicate units position. 4.Percents are hundredths and another way to express fractions and decimals. 5.Addition and subtraction with decimals are a simple extension of whole numbers. 6.Multiplication and division of two numbers will produce the same digits, regardless of the positions of the decimal points.

2. Copyright © Allyn and Bacon 2010 Developing Decimal Number Sense Familiar fractions connected to decimals Approximation with a nice fraction Ordering decimal numbers Other fraction–decimal equivalents

3. Copyright © Allyn and Bacon 2010 Introducing Percents Models and terminology Realistic percent problems Teaching percents 1.Limit the percents to familiar fractions 2.Do not suggest any rules or procedures 3.Use terms part, whole, and percent 4.Require students to use models or drawings 5.Encourage mental computation Estimation

4. Copyright © Allyn and Bacon 2010 Connecting Fractions and Decimals Base-ten fractions — base-ten fraction models — multiple names and formats Extending the place-value system — a two-way relationship — the role of the decimal point — the decimal with measurement and monetary units Fraction–decimal connection

5. Decimals Think about the location of the decimal point and the relationship of one digit to the next. Now decide if the relationship between a digit and the number to the left is the same on both sides of the decimal point.

6. Where Does the Decimal Point Go? 23.408 + 3.6 + 124.052 + 7.75 = 1 5 8 8 1 0 0

7. Where Does the Decimal Point Go? 714.6 − 35.0112 = 6 7 9 5 8 8 8

8. Where Does the Decimal Point Go? 7.8 × 24.35 = 1 8 9 9 3

9. Where Does the Decimal Point Go? 8.432 × 5.75 = 4 8 4 8 4

10. Where Does the Decimal Point Go? 3.326 × 0.32 × 31.5 = 3 3 5 2 6 0 8

11. Where Does the Decimal Point Go? 306.15 ÷ 75.4 = 4 0 6 0 3 4 4 8

12. Measurement

13. Big Ideas 1.Measurement involves a comparison of an attribute of an item or situation with a unit that has the same attribute. 2.Meaningful measurement and estimation of measurements depend on personal familiarity with the unit of measure being used. 3.Estimation of measures and the development of bench-marks help students increase familiarity with units. 4.Measurement instruments are devices that replace the need for actual measurement units. 5.Area and volume formulas provide a method of mea-suring these attributes by using only measures of length. 6.Area, perimeter, and volume are related. Copyright © Allyn and Bacon 2010

14. What do we measure? LengthAreaVolume/ Capacity Weight/ Mass AnglesTimeMoney

15. Time Duration Clock reading—suggested approach 1.Start with a clock that has only the hour hand 2.Discuss what happens to the big hand as the little hand goes from one hour to the next 3.Use two real clocks, one with hour hand only and one with two hands 4.Teach time in 5-minute intervals 5.Predict the reading on a digital clock when shown an analog and vice versa Elapsed time Copyright © Allyn and Bacon 2010

16. Money Coin recognition and values Counting sets of coins Making change Copyright © Allyn and Bacon 2010

17. Developing Formulas for Area and Volume Students’ misconceptions Area of rectangles, parallelograms, triangles, and trapezoids From parallelograms to triangles Circumference and area of circles Volumes of common solid shapes Connections among formulas Copyright © Allyn and Bacon 2010