Decimals and Fractions

Topic / Page
Decimal Place Value / Decimal Place Value PaperDemonstration
Concrete and Pictorial Using Models to Relate Decimals
to Fractions
IMN-foldable including standard form, word form, and expanded form
IMN-student copy
Decimal Place Value Guided Practice
Printables / 1-6
7-9
10
11
12-15
16

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Decimal Place Value Paper Demonstration

TEKS: 5.2 Number and operations. The student applies mathematical process to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to:

(A) represent the value of the digit in decimals through the thousandths using expanded notation and numerals;(S)

Materials: Teacher place value chart (pp. 2-3), decimal models (pp. 4-6). For no page numbers print from printable section at the end of the lesson.

Vocabulary: place value chart, tens, hundreds, thousands, tenths, hundredths, thousandths, decimal, decimal point, whole

Assembly:

Cut apart the place value name strips (pp.2-3) and tape them end-to-end in this order to create a large place value chart: Hundreds, Tens, Ones, tenths, hundredths, and thousandths.

How to use the model:

1. Lay theplace value strip down folded so only the ones place is showing and the other place values are folded under.
2. Discuss the following questions:
3. What could be a possible number of sheets I could place in the ones place? ( 0-9)
4. What could be the smallest number of sheets I could place in the column, other than zero? (one)
5. Unfold the “tens” and “tenths” place values so that “ones”, “tens”, and “tenths” are all showing. Place 10 pieces of paper above the “tens” place.
6. Show the students the paper that is cut into 10 equal pieces (p.6). Cut off one tenth and place it above the tenths place value.
• What do these two new sections have in common? How are they different?” (The place values both have the word tenin them. Ten means 10 wholes and tenths mean one-tenth of a whole).
1. Discuss how the numbers to the left of the decimal are whole numbers and the numbers to the right of the decimal are a part of a whole.
2. Discuss that the small strip of paper is “one out of ten equal pieces”. Label the place value chart with .
3. Ask students the name of the next place value. (hundreds and hundredths) . Lay 100 sheets of paper above the hundreds place.
4. Take the hundredths grid (p4) and cut off one piece. Place it above the hundredths place. Label it .
• What do these two new place values have in common? What makes them different?”
1. Continue the questioning with the thousands and the thousandths place. Use two reams of paper to make 1000 sheets and cut one rectangle

off of the grid on p. 5 to show one thousandth of a sheet of paper.

1. Ask students to turn to a partner and explain how the decimal and whole numbers are alike and how they are different.
2. How are tenths, hundredths, and thousandths related to each other?
• When one is divided into 10 equal parts, one tenth is one of those parts.
• When one tenth is divided into 10 equal parts, one hundredth is one of those parts.
• When one hundredth is divided into 10 equal parts, one thousandth is one of those parts.

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Property of Cy-Fair ISD Elementary Math (5th Grade) 2014-2015

Concrete and Pictorial Using Models to Relate Decimals to Fractions

TEKS: 5.2 Number and operations. The student applies mathematical process to represent, compare, and order positive rational numbers and understand relationships as related to place value. The student is expected to:

(B) represent the value of the digit in decimals through the thousandths using expanded notation and numerals;(S)

Concrete Materials: decimal manipulatives (concrete or virtual), dry erase boards, markers, guided practice problems, paper model of decimal manipulatives (printables section at the end of lesson)

Vocabulary: decimal, decimal point, tenths, hundredths, thousandths, whole

1.Refer students to their whole decimal manipulative. Discuss the concept of 1 whole by relating it to a whole pizza, whole cake, etc. Ask for other examples of 1 whole. Discuss how we represent 1 whole with numbers. (1 or 1.0)

2.Review the concept of fractions by discussing cutting the whole into equal parts. Decimals are another representation of fractions that have 10 equal parts, 100 equal parts, or 1,000 equal parts.

3.While keeping the "whole" on their student tableas the mat, place a "tenths" piece on top of it. Shade in 1 tenth on the paper model. Discuss what fraction this would represent. ( because it is 1 of ten equal parts.) Discuss how we would write this decimal. (0.1)

= = 0.1

4.Repeat the above process while introducing 2 tenths, 3 tenths, etc. Have students practice building models and writing the fraction and decimal also.

5. Place a "hundredths" piece on top of the "whole" mat to show models of hundredths. Shade in 1 hundredth on the paper model. Discuss what fraction this would represent. (, because it is 1 of 100 equal parts.)

Discuss how we would write this decimal (0.01). Create a decimal place value chart. Discuss and write the names of the decimal place values so far.

ones

(wholes) tenths hundredths

6.Practice naming and building hundredths such as two hundredths, nine hundredths, sixteen hundredths, forty-two hundredths, etc. Students use manipulatives and dry erase boards to practice writing as fractions and decimals.

7.Discuss how "sixteen hundredths" is equal to 1 tenth and six hundredths. Show with manipulatives. Practice with other numbers such as 0.32, 0.78, etc.

8.Place a "thousandths" piece on top of the "whole" mat to show models of thousandths. Discuss how small these pieces would be in real life. Show examples of thousandths such as 1 paper clip from a box of 1,000 or 1 colored toothpick with 999 natural wood toothpicks.

9.Shade in 1 thousandth on the paper model and discuss how to write this as a fraction and decimal.

(, and 0.001)

10.Add "thousandths" to the chart of decimal place value names.

Ones

(wholes) tenths hundredths thousandths

11.Practice building and naming other numbers such as 1.303, 0.317, 1.271, etc. Students use manipulatives to build numbers and record fraction and decimals on dry erase boards.

12.Complete IMN foldable for reinforcement and then review standard form, word form, and expanded form.

13. Make connections for students using the Guided Practice Part 1 (pg. 12). Explain to students that the relationship of a digit in different place-value positions is the same with decimals as it is with whole numbers. You can use your understanding of place-value patterns and a place-value chart to write decimals that are 10 times as much as or of any given decimal. Guided Practice #1 and #2 shown below:

Ones / Tenths / Hundredths / Thousandths
0 / 0 / 6
• 0.6 is 10 times as much as 0.06.
• 0.006 is of 0.06.

How did you write a decimal that was 10 times as much as 0.06?

How is finding a decimal that is of a number different from finding one that is 10 times as much as a number?

(Students should recognize that as you move from one decimal place-value position to a lesser decimal place-value position, the number of zeros between the digit and the decimal point increases. The reverse is true when you move froma lesser to a greater decimal.)

IMN: ½ sheetconstruction paper foldable with small paper decimal models. See picture below. Please note that you will need to instruct students to cut the hundredths square into 10 equal parts to shade one piece to show thousandths.

Review Standard Form, Word Form, and Expanded Form using the IMN foldable. Let students repeat with dry erase board practice using dice or number tiles to create numbers to write word form and expanded form.

Example: Standard Form-2.345

Word Form- two and three hundred forty five thousandths

Expanded Form- 2+ 0.3 + 0.04 + 0.005

Guided Practice-Decimal Place Value

Part I

Ones / Tenths / Hundredths / Thousandths
0 / 0 / 6
Ones / Tenths / Hundredths / Thousandths
0 / 0 / 6

1. 0.06 isof ______.

2. 2. 0.06 is 10 times as much as ______.

3. Use the place value chart to complete the table.

Decimal / 10 times as much as / of
0.04
0.8
0.02

Describe the pattern:______

Use place-value patterns to describe the relationship two ways between the decimals.

4. 0.06 and 0.6 ______

______

5. 0.9 and 9.0 ______
______

Guided Practice Decimal Place Value

1. Michael wants to build a tree house. He needs to cut a piece ofwood that is 1.7 meters long. Build a model to represent this number. Write this number as a fraction.

2.According to the 2005 Department of Transportation there were an estimated 247,421,120 registered passenger vehicles in the United States. How is this number written in words?

1. Two hundred forty-seven billion, four hundred twenty-one million, one hundred twenty.

B. Two hundred forty-seven million, four hundred twenty-one thousand, one hundred twenty.

C. Two forty-seven million, four twenty-one thousand, one hundred twenty.

D. Two hundred forty-seven million, four hundred twenty-one, one twenty.

3.Stacy's dad is cutting pipe for a project. The first pipe he cuts is 1 yards long. Build a model to represent this number. Write this number as a decimal.

4.Janet's picture in her bedroom needs a new frame. She must cut one piece of wood 1.032 feet long and the other piece of wood .753 feet long. Build a model to represent each of these numbers. Write these numbers as fractions and in expanded form.

5.Each piece of tile in the kitchen is a square that measures 2.15 cm long. Build this number with decimal manipulatives. Write this number as a fraction and in expanded form.

6.Jack found a piece of string that measureddm long. Build this number with decimal manipulatives and write as a decimal and in expanded form.

7. How is the numeral 34.018 written in words?

1. Thirty-four thousand, eighteen
2. Thirty-four and eighteen thousandths
3. Thirty-four and eighteen hundredths

D. Thirty-four and eighteen

8. What is the relationship between 1.0 and 0.1?

1. 0.1 is 10 times as much as 1.0
2. 1.0 is of 0.1
3. 0.1 is of 1.0
4. 1.0 is equal to 0.1

9. Write the number 0.654 in expanded form.

Property of Cy-Fair ISD Elementary Math 5th 2014-2015

Property of Cy-Fair ISD Elementary Math 5th 2014-2015

Property of Cy-Fair ISD Elementary Math 5th 2014-2015