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Unit 4 Extending Decimals Grade 5

5E Lesson Plan Math Grade Level: 5th Subject Area: MathLesson Title: Extending Decimals Unit Number: 4 Lesson Length: 6 daysLesson OverviewThis unit bundles student expectations that address foundational understandings of decimals as well as adding and subtracting of decimals through the thousandths place. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.During this unit, students are formally introduced to the thousandths place. Students build upon the idea that our base-ten place value system extends infinitely to very small values as well as very large values, and that each place-value position is one-tenth the value of the place to its left and 10 times the position to the right. Students relate previous representations of decimals to the hundredths with concrete and pictorial models to develop their conceptual knowledge of decimals through the thousandths. Students are expected to use expanded notation and numerals to represent the value of a decimal through the thousandths. Students use comparison symbols to compare and order decimals to the thousandths and round decimals to the tenths or hundredths place. Students continue to estimate solutions and extend addition and subtraction with decimals to include the thousandths place. Numerical expressions are revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.

Unit Objectives:Students will…

Relate previous representations of decimals to the hundredths with concrete and pictorial models to develop their conceptual knowledge of decimals through the thousandths.

Use expanded notation and numerals to represent the value of a decimal through the thousandths.

Use comparison symbols to compare and order decimals to the thousandths and round decimals to the tenths or hundredths place.

Estimate solutions and extend addition and subtraction with decimals to include the thousandths place.

Communicate solution processes and solve problem situations involving decimals using numerical expressions.

Standards addressed:

TEKS:5.1A Apply mathematics to problems arising in everyday life, society, and the workplace.5.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.5.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as

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appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.5.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.5.1E Create and use representations to organize, record, and communicate mathematical ideas.5.1F Analyze mathematical relationships to connect and communicate mathematical ideas.5.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.5.2A Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. Supporting Standard5.2B Compare and order two decimals to thousandths and represent comparisonsusing the symbols >, <, or =. Readiness Standard5.2C Round decimals to tenths or hundredths. Supporting Standard5.3A Estimate to determine solutions to mathematical and real-world problemsinvolving addition, subtraction. Supporting Standard5.3K Add and subtract positive rational numbers fluently. Readiness Standard5.4F Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. Readiness Standard

ELPS:1A use prior knowledge and experiences to understand meanings in English2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency4H read silently with increasing ease and comprehension for longer periods5B write using newly acquired basic vocabulary and content-based grade-level vocabulary5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.

Misconceptions: Some students may think placing zeros at the end of a decimal number always affects

the value of the number rather than being used as a place-holder (e.g., In 0.400 the zeros do not affect the value, but in 0.04 the zero in the tenths place does affect the value.)

Some students may think you can only round certain numbers to a specific place value, rather than being able to round to any given place value (e.g., The decimal number 34.25 can be rounded to the nearest tenths place, ones place, tens place, hundreds place, etc.)

Some students may use the digit in the tenths place to determine how many boxes to shade in on a hundredths grid (e.g., shading in 8 of the 100 boxes for 0.8) rather than determining the value of the number written as hundredths (e.g., shading in 80 of the 100 boxes of 0.80).

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Some students may order decimals incorrectly by trying to relate whole number understandings to decimal understandings (e.g., 0.29 is greater than 0.6 because 29 is greater than 6) rather than using decimal place value understandings (e.g. 0.29 is less than 0.60).

Some students may order decimals based on the number of digits in the number, rather than determining its value. (e.g. 0.123 is greater than 0.45 because 0.123 has three digits and 0.45 only has two digits.)

Vocabulary:

Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value

Compatible numbers – numbers that are slightly adjusted to create groups of numbers that are easy to compute mentally

Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}

Decimal number – a number in the base-10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part

Digit – any numeral from 0 – 9 Estimation – reasoning to determine an approximate value Expanded notation – the representation of a number using place value (e.g.,

985,156,789.782 as 900,000,000 + 80,000,000 + 5,000,000 + 100,000 + 50,000 + 6,000 + 700 + 80 + 9 + 0.7 + 0.08 + 0.002 or 9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) + 5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7(0.1) + 8(0.01) + 2 (0.001) or 9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) +

5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7 ( ) + 8( ) + 2 ( )) Expression – a mathematical phrase, with no equal sign, that may contain a

number(s), a unknown(s), and/or an operator(s) Fluency – efficient application of procedures with accuracy Front-end method – a type of estimation focusing first on the largest place value in

each of the numbers to be computed and then determining if the next smallest place value(s) when grouped should be

Numeral – a symbol used to name a number Order numbers – to arrange a set of numbers based on their numerical value Order of operations – the rules of which calculations are performed first when

simplifying an expression Parentheses and brackets – symbols to show a group of terms and/or expressions

within a mathematical expression Place value – the value of a digit as determined by its location in a number, such as

ones, tens, hundreds, one thousands, ten thousands, etc.

Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are whole numbers, and b ≠ 0 which includes the subsets of whole

numbers and counting (natural) numbers (e.g., 0, 2, etc.) Rounding – a type of estimation with specific rules for determining the closest value Standard notation – the representation of a number using digits (e.g.,

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985,156,789.782) Trailing zeros – a sequence of zeros in the decimal part of a number that follow the

last non-zero digit, and whether recorded or deleted, does not change the value of the number

Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n} Written notation – the representation of a number using written words (e.g.,

985,156,789.782 as nine hundred eighty-five million, one hundred fifty-six thousand, seven hundred eighty-nine and seven hundred eighty-two thousandths)

Related Vocabulary:

About Greater than (>)

Approximately Less than (<)

Ascending Magnitude

Base-10 place value system Number line

Descending Position

Equal to (=)

Equivalent Estimate Hundredths

Tenths

Thousandths

List of Materials:Materials are listed each day

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Phase: 1 Engage

Day 1 Activity

Materials: Base Ten Blocks

● Provide students with sets of Base Ten Blocks.● Start by modeling whole numbers. Suppose a unit block equals 1.

● What is the value of a rod? (10)● What is the value of a flat? (100)● What is the value of a cube? (1000)

● As each question is asked, allow students time to work with a partner to model the question with their cubes and to discuss their answers before sharing with the class.

● After each question, ask students to explain their reasoning. (i.e., “There are 10 units in a rod, so a rod equals 10.” or “There are 10 flats in a cube and one flat equals 100, so 10 of these equals 1000.”)

● Change the whole. Say: Suppose that a flat represents 1 whole.

● What is the value of a rod? 110

● What is the value of a unit? 1100

● What is the value of a cube? (10)● Again, allow students time to work with a partner to model the question

with their cubes and to discuss their answers before sharing with the class. Students should be asked to explain how they know. (i.e., “There

are 10 rods in a flat, so one rod would be 1

10 of the flat.” Or “There are

10 flats in a cube. If one flat equals 1, then 10 flats would equal 10.”)

What’s the teacher doing?Teacher provides concrete models for students to explore decimals to the thousandths

What are the students doing? Students use the base ten blocks to explore decimals to the tenth, hundredth and thousandth

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Phase 2 ExploreDay 1 Activity:Materials: Dry erase markers and white boardsStudents will represent value of digits in decimal numbers to the thousandths place with standard, expanded and word notation. They will understand that numerals get 10 times larger each time place value moves to the left.

And numerals get 110 smaller each time place value moves to the right:

Students will write numerals in their place value chart by placing the digits in the correct place.Teacher writes three thousand forty seven on the board. On personal white boards, students write this number in standard form and expanded form. Explain that you have written the word form.Tell students: Explain to your partner the purpose of writing this number in these different forms.Student Response: Standard form shows us the digits that we are using to represent that amount. Expanded form shows how much each digit is worth and that the number is a total of those values added together.Explain that there is another form called unit form and unit form helps us see how many of each size units are in the number. Example: 3 thousands, 4 tens, 7 ones.

Give students a place value chart that has decimal place values to the thousandths. Use Teacher resource: Place Value Chart Day 1. Make enough copies for each student. Place in a plastic sleeve or laminate so students can use a dry erase marker to write the numerals. Put students in pairs.

Problem 1Represent 1 thousandth and 3 thousandths in standard, expanded, and unit form.Tell students to write one thousandth using digits on their place value chart. Ask: “How many

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ones, tenths, hundredths, and thousandths?”Student response: Zero, zero, zero, one.Teacher’s response: This is the standard form of the decimals for 1 thousandth.We write 1 thousandth as a fraction like this: (write

11000 on the board)

1 thousandth is a single copy of a thousandth. I can write the expanded form using a fraction like this, 1 x

11000

(saying one copy of one thousandth) or using a decimal like this 1 x 0.001 (write on the board)The unit form of this decimal number looks like 1 thousandth (write on the board). We use a numeral (point to the 1) and the unit (point to the thousandth) written as a word.

Tell the students to imagine 3 copies of 1 thousandth. How many thousandths is that?Student response: 3 thousandths(write that in standard form, decimal form, and a fraction)Tell students to write that in their place value chart.3 thousandths is 3 copies of 1 thousandth, turn and talk to your partner about how this would be written in expanded form using a fraction and a decimal.

Students can copy these examples in their math journals along with explanations of expanded form, standard form and unit form.Problem 2Represent 13 thousandths in standard, expanded, and unit form.

T: Write thirteen thousandths in standard form, and

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One thousandth = 0.001 = 1

10001

1000 = 1 x ( 1

1000 )

0.001= 1 x (0.001)

1 thousandth

Three thousandths = 0.003 = 3

1000

31000 = 3 x (

11000 )

0.003 = 3 x (0.001)


expanded form using fractions and then using decimals. Turn and share with your partner.

S: Zero point zero one three is standard form. Expanded forms are

1 x 1

100 + 3 x 1

1000 and 1 x 0.01 + 3 x

0.001

T: Now write this decimal in unit form. S: 1 hundredth, 3 thousandths 13 thousandths.

T: (Circulate and write responses on the board.) I notice that there seems to be more than one way to write this decimal in unit form. Why?S: This is 13 copies of 1 thousandth.

You can write the units separately or write the 1 hundredth as 10 thousandths. You add 10 thousandths and 3 thousandths to get 13 thousandths.

Repeat with 0.273 and 1.608 allowing students to combine units in their unit forms (for example, 2 tenths 73 thousandths; 273 thousandths; 27 hundredths 3 thousandths). Use more or fewer examples as needed reminding students who need it that and indicates the decimal in word form.

Problem 3Represent 25.413 in word, expanded, and unit form.T: (Write on the board.) Write 25.413 in word form on your board. (Students write.)S: Twenty-five and four hundred thirteen thousandths.T: Now, write this decimal in unit form on your board.S: 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths.T: What are other unit forms of this number?Allow students to combine units, e.g., 25 ones 413 thousandths; 254 tenths 13 hundredths;25,413 thousandths.

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Thirteen thousandths = 0.013 = 13

100013

1000=¿0.013 = 1 x 0.01 + 3 x 0.001

1 hundredth 3 thousandths13 thousandths


T: Write it as a mixed number, then in expanded form. Compare your work with your partner’s.

Repeat the sequence with 12.04 and 9.495. Use more or fewer examples as needed.

Problem 4 Exit Ticket:Write the standard, expanded, and unit forms of four hundred four thousandths and four hundred and four thousandths.T: Work with your partner to write these decimals in standard form. (Circulate looking for misconceptions about the use of the word and.)T: Tell the digits you used to write four hundred four thousandths.T: How did you know where to write the decimal in the standard form?S: The word and tells us where the fraction part of the number starts.T: Now work with your partner to write the expanded and unit forms for these numbers.

What’s the teacher doing?Teacher will model how the standard, expanded and unit forms are written.

What are the student’s doing?Students will work with their partners to write the expanded, standard and unit form of several decimal numbers.

Phase __2 Explore___

Day 2 Activity Materials: Nerf Ball, Starting Line-up Cards, Starting Line-up Grid and Data Table, Trash Can, Masking Tape, “Post-it” notes, index cards and scissors

Tell students that today they will be learning about decimals and how to use them.

Mention that decimals are just another way of recording fractions. Ask, “Who likes to play basketball?” Explain that they will be using

basketball to learn about decimals. Ask for a student volunteer. Tell the student to stand on a tapeline

placed 8 feet away from a trashcan. Have the student take 10 shots at the

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Twenty-five and four hundred thirteen thousandths = 25413

1000 =

25.413

25 413

1000= 2 x 10 + 5 x 1 + 4 x 1

10 + 1 x 1

100 + 3 x 1

100025.413= 2 x 10 + 5 x 1 + 4 x 0.1 + 1 x 0.01 + 3 x 0.001


trashcan baskets with a Nerf ball or wadded up piece of paper. Display teacher resource “Trashcan Hoops” on an overhead projector to record the results. Explain how the shots made are recorded as a decimal. Repeat procedure with three more students.

Ask, “Who made the most shots? What does that decimal look like?” Who made the least shots? What does that decimal look like?’

Ask, “Who do you think is the best player in the NBA?” Elicit responses from students. Who do you think is better between Allen Iverson, LeBron James and Shaquille O’Neal? Elicit responses from students. Say, “We are going to look at real data on these three players to help us better

understand decimals.” Display a transparency of Teacher Resource Sheet “Player’s Stats.”

“How do you think that the people that keep the NBA statistics come up with these numbers?” (They divide the number of shots that the player attempts by the number of shots they actually made; just like we did yesterday in our trashcan hoops game.)

Ask, “Can anyone tell me anything they notice about the statistics?” Elicit responses from students. Be sure and have them explain how they made that observation.

What do you notice about these decimals?”(They have three places beyond the decimal point)“Why do you think they did that?”“If we compare Allen Iverson field goal average to LeBron James’ and only look at the decimal to the tenths place what would happen? (They would both have 0.4)“If we continue to look at those same statistics and continue out to the hundredths place what happens? (We have 0.42 and 0.47)“If we keep looking at that third number beyond the decimal point, which is called the thousandths place, then what 2 decimals are we comparing? (0.424 and 0.472)“So, how do you think extending the decimal out to the thousandths place helps us? (It gives us more detail and makes the number more accurate).

If available, illustrate the scenario above using overhead decimal squares so that students have a visual representation of the relative size of the tenths, hundredths and thousandths.

Students can use decimal place value charts to compare the decimals. Continue in this manner comparing other averages to the thousandths

place. Ask probing questions such as, “Who has a better field goal average?

How do you know? Who has a better three point shot average? How do you know? Who has a better free throw average? How do you know?

Write 0.649 on the chalkboard or overhead projector. Say, “We know that decimals are composed of digits and one decimal point. Each

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digit in relation to the decimal point has a particular value. What is the value of 6 in 0.649? What is the value of 4? What is the value of 9? As with all numbers, decimals can be placed on a number line. We can do this to illustrate how close they are to either 0 or 1.Say, “Think about what we know so far about decimals. What would be an example of a digit that a decimal might have in the tenths place that would make it fall very close to 1 on a number line? (List students’ responses.) What would be an example of a digit that a decimal might have in the tenths place that would make it fall in the middle of a number line between 0 and 1? (List students’ responses.) What would be an example of a digit that a decimal might have in the tenths place that would make it fall very close to 0 on the number line?

(List students’ responses.) Write 0.751 and 0.708 on the board. Ask, “What if I have two decimals

that have the same digit in the tenths place how do I know which one goes where on the number line?

Write 0.328 and 0.323 on the board. Ask, “If I have two decimals that have the same digit in the tenths and the hundredths place, how do I know where the numbers are on the number line?

Draw a line on the chalkboard that is at least 6 feet long (If you do not have a chalkboard long enough, you may use a tape line on the wall or the floor). Place Teacher Resource Sheets, “Backboard Benchmark Near 0”, on the far left end of the line, and “Backboard Benchmark Near 1”, on the far right end of the line.

Distribute one 3”X 3” Post-It note and a marker to each student. Instruct students to write a decimal to the thousandths on their post-it using clearly visible digits. Challenge students to try to think of a decimal that no one else will think of and to not let anyone else see their decimal.

Have students trade their post-it with another student. Tell students that they are going to use the number line on the board to

estimate the value of the decimal on their post-its. Have 2-3 students at a time come up and place their decimal on the

number line in relation to being near 0 or near 1. Have each student explain why he or she placed their decimal where they did.

Student Game: Copy Teacher Resource Starting Line-Up cards and cut apart. Copy

Teacher Resource, “Starting Line- Up Grid and Data Table”. Draw a copy of the “Starting Line-Up Grid” from Teacher Resource

“Starting Line-Up Grid and Data Table” on the board. Using your precut “Starting Line-Up Decimal Digit Cards” select 5 random decimals.

Explain to students that the game is played by looking at the cards 1 at a time and estimating where it should go on the grid in relationship to 0 and 1. Tell students that once they place a digit card on the grid they may not change its position, so they must think very carefully about each decimal and its relationship to 0 and 1 before they place it. Play one sample round

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with students having them help you decide on each decimals placement on the grid. Be sure to have them explain why they think each decimal should go where they suggest on the grid.

Demonstrate how the decimals are recorded on the data table. If decimals are all placed correctly in at least to greatest sequence, tell students they will place a star beside that row on their data table. If any decimals are out of order, discuss with students how and why the error occurred. Distribute Teacher Resource, “Starting Line-Up Decimal Digit Cards”

and “Grid and Data Table” to each student. Have students cut the Decimal Digit Cards apart.

Allow time for students to play the game and record their results.

When students have played the game, give them 2 index cards and scissors. Tell them to cut the cards in half and write the symbols for greater than, less than, and equal on each half card. Tell them they have ordered the decimals now we will compare two decimals. Tell them to pick two decimal cards and place them side by side. Talk about the symbols for greater than, less than, and equal. Have them right them down in their math journals with examples and non-examples. Using the cards the students will place the correct symbol between the two decimal numbers.Using place value charts, students will write the two decimals in the correct place value and use the chart to compare.If time allows show the video from Learn Zillion: https://learnzillion.com/lessons/35-compare-and-order-decimals-to-the-thousandths-place. Students may access this video by going to the Learn Zillion website and typing in the access code: LZ35.

For Extra practice use Day 2 Re-teaching Page

What’s the teacher doing?While students are playing the game observe and record. Share with students that you will assess their performance as they play the game. Discuss with students the observable behaviors you will be looking for and establish an evaluation method to assess the criteria. For example,0- Student’s understanding is completely incorrect 1- Student shows minimal or partial understanding 2- Student shows complete understanding

• Collect each student’s completed copy of Student Resource Sheet 3, “Starting Line Up Grid and Data Table.” Analyze for understanding and/or error patterns.

What are the students doing?Students will play the game to demonstrate understanding of ordering and comparing decimals

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https://learnzillion.com/lessons/35-compare-and-order-decimals-to-the-thousandths-place

https://learnzillion.com/lessons/35-compare-and-order-decimals-to-the-thousandths-place


Check for understanding of comparing the two decimal cards.Phase ___Explore/Explain______

Activity: Day 3 Materials: White boards and dry erase markersRounding decimal numbers to the tenths place, and/or the hundredths place. Students will first review rounding whole numbers from 4th grade. If Smart Board technology is available use Day 3: Rounding Decimals to review and to reinforce the concept of rounding. Learn Zillion website can also be used to teach the concept of rounding: https://learnzillion.com/lessons/3094-represent-decimal-numbers-on-a-number-line

Use of a number line is important for students to grasp the concept of which number is closest. In this activity students use number lines drawn on white boards to learn the concept. They will also use Turn and Talk strategy to provide understanding of the concept. Modeling knee-to-knee, eye-to-eye body posture and active listening expectations (Can I restate my partner’s ideas in my own words?) make for successful implementation of this powerful strategy.

First Round to the nearest whole number:T: (Project 8.735.) Say the number.S: 8 and 735 thousandths.T: Draw a vertical number line on your boards

with 2 endpoints and a midpoint.T: Between what two ones is the number 8.735?S: 8 ones and 9 ones.T: What’s the midpoint for 8 and 9?S: 8.5T: Fill in your endpoints and midpoint.T: 8.5 is the same as how many tenths?S: 85 tenths.T: How many tenths are in 8.735?S: 87 tenths.T: (Write 8.735 ≈ _______.) Show 8.735 on your number line and write the number

sentence.S: (Students write 8.735 between 8.5 and 9 on the number line and write 8.735 ≈ 9.)

Repeat the process for the tenths place and hundredths place. Follow the same process and procedure for 7.458.

Next, project the following problem on the board:Organic, whole-wheat flour sells in bags weighing 2.915 kilograms. How much flour is this rounded to the nearest tenth? How much flour is this rounded to the nearest one? What is the difference of the two answers? Use a place value chart and number line to explain your

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https://learnzillion.com/lessons/3094-represent-decimal-numbers-on-a-number-line


thinking.Allow students to complete the activity with a partner. Give students place value charts and number lines to complete the activity.

Next tell students to round 49.67 to the nearest ten.

T: Turn and talk to your partner about the different ways 49.67 could be decomposed using place value disks. Show the decomposition that you think will be most helpful in rounding to the nearest ten.

T: Which one of these decompositions did you decide was the most helpful?

S: The decomposition with more tens is most helpful, because it helps me identify the two rounding choices: 4 tens or 5 tens.

T: Draw and label a number line and circle the rounded value. Explain your reasoning.

Repeat this sequence with rounding 49.67 to the nearest ones, and then tenths.

Problem 2Decompose 9.949 and round to the nearest tenth and hundredth. Show your work on a number line.

T: What decomposition of 9.949 best helps to round this number to the nearest tenth?

S: The one using the most tenths to name the decimal fraction. I knew I would round to either 99 tenths or 100 tenths. I looked at the hundredths. Nine hundredths is past the midpoint, so I rounded to the next tenth, 100 tenths. One hundred tenths is the same as 10.

T: Which digit made no difference when you rounded to the nearest tenth? Explain your thinking.

S: The thousandths, because the hundredths decided which direction to round. As long as I had 5 hundredths, I was past the halfway point so I rounded to the next number.

Repeat the process rounding to the nearest hundredth.

Problem 3

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90 tenths

100 tenths = 10

5 tens or 50

45.67

4 tens or 40

99 tenths = 9.99 ones 9 tenths 4 hundredths 9 thousandths

99 tenths 4 hundredths 9 thousandths

994 hundredths 9 thousandths

26

272627

26.5


A decimal number has 1 digit to the right of the decimal point. If we round this number to the nearest whole number, the result is 27. What are the maximum and minimum possible values of these two numbers? Use a number line to show your reasoning. Include the midpoint on the number line.

T: (Draw a vertical number line with 3 points.)T: What do we know about the unknown number?S: It has a number in the tenths place, but nothing else past the decimal point. We know

that is has been rounded to 27.T: (Write 27 at the bottom point on the number line and circle it.) Why did I place 27 as

the lesser rounded value?S: We are looking for the largest number that will round down to 27. That number will be

greater than 27, but less than the midpoint between 27 and 28. T: What is the midpoint between 27 and 28?

S: 27.5T: (Place 27.5 on the number line.)T: If we look at numbers that have exactly 1 digit to the right of the decimal point,

what is the greatest one that will round down to 27?S: 27.4. If we go to 27.5, that would round up to 28.

Repeat the same process to find the minimum value.

To find maximum To find minimum

27.5

As an exit ticket have students round several numbers to the nearest ten, whole number, tenth and hundredth.

What’s the teacher doing?Monitor partners and give feedback during the exploration of the word problems.

What are the students doing?Students are working in pairs to work the problem.

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27

27.4

28


Phase: Explore/Explain

Activity: Day 4

Materials: Take out Menus, Grocery Ads

Estimate decimal numbers to add and subtract. If technology is available use the website: https://learnzillion.com/lessons/545-estimate-the-addition-and-subtraction-of-decimals-using-smart-rounding for concept development.

Students use estimation to solve addition and subtraction problems. Teacher will give students real world problems involving decimal numbers to solve. Using ads from grocery stores or department stores, students can “purchase” items to buy with a specified amount of money to spend. They must find the total cost of items purchased and how much money they have left. They must use estimation and actual cost of items to solve the problem.

Students could also use menus from various restaurants and “play” restaurant with students being customers, waiters, cashiers, etc. Included in resources is an optional Day 4 Menu Math Binder to print and use.

Students will create a list of at least five items to purchase and complete an estimation and actual cost of the items. They will determine, given a certain amount of money, if they will have enough to pay the total bill and how much they either need or will receive as change.Students will use various methods of estimation as explained in the examples below.

EX: Front End Rounding

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https://learnzillion.com/lessons/545-estimate-the-addition-and-subtraction-of-decimals-using-smart-rounding

https://learnzillion.com/lessons/545-estimate-the-addition-and-subtraction-of-decimals-using-smart-rounding


EX: Rounding to the nearest place value and then solving the problem.

EX: Using compatible numbers and then solving the problem.

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What’s the teacher doing?

Monitor students’ progress and offer support and feedback.Check for understanding of concepts of estimation.

What are the students doing?

Students will use ads to “purchase” items and compute the cost using estimation and actual computations to find the total cost and amount of change received.

Students will complete an estimation and actual cost of at least five items and determine if they have enough money to pay for the items.

Phase: ElaborateActivity Day 5 Materials: Chart paper, scissors, glue sticks, menus and/or ads and markers

Students will continue with the menu/ads theme from yesterday. Students use menus or store ads and create word problems that involve addition and subtraction of decimal numbers. Place students in groups of 3 or 4. Give menus and/or ads to each group of students. Explain to students that they will be creating their own word problems that involve addition and subtractions of decimal numbers. They must create word problems that involve both operations.Students will be given a piece of chart paper, scissors, glue sticks and markers. Tell students to write their problems on the chart paper and cut out pictures from the menus and/or ads to help tell the story. They will then write the expression used to solve the problem. Students must detail how they solved the problems on the chart paper. The solution to the problems must be written in sentences.Student groups will then present their problems to the class.

What’s the teacher doing?Teacher will be walking around monitoring student groups. Giving feedback and asking questions as the groups create word problems.

What are the students doing?Students are working in groups to create word problems from menus and/or store ads.

They will present their problems to the class.

Phase: EvaluateActivity: Day 6Performance Assessment:Analyze the problem situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each solution process.

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Humboldt Paper Company sells different thicknesses of paper for different types of projects.

1) The paper company wants to create a brochure that describes the products they sell. They would like to order the types of papers from thinnest to thickest paper so that it is easy for their customers to find the paper they want.

a) Represent the value of each of the thicknesses using numerals and expanded notation.

b) Create a table that orders the paper names and their thicknesses from thickest to thinnest.

c) Write a comparison statement using the symbols >, <, or = to compare the thickness of two of the paper types.

2) The company looks at the table and wonders if rounding all of the thicknesses to a common place-value might be easier for their customers to read. Before they round them all, they want to make sure it doesn’t change the order of the papers from thinnest to thickest.

a) Explain how to round each of the thicknesses. Then, predict if it would change the order of the different types of paper.

b) Round each of the paper thicknesses to the tenths place-value.

c) Write a comparison statements using symbols >, <, or = to explain any changes that may occur in the original order of thinnest to thickest.

d) Round each of the paper thicknesses to the hundredths place-value.

e) Write a comparison statements using symbols >, <, or = to explain any changes that may occur in the original order of thinnest to thickest.

f) Compare and contrast the effects of rounding the paper thicknesses to the tenths place versus rounding the paper thicknesses to the hundredths place. Explain why there would be changes to the order.

3) Another company who makes party invitations decides to purchase some of the paper to

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create wedding invitations. Each invitation will have one layer of Vellum paper with a different layer of paper on top. The envelope for the invitation can hold thicknesses up to 0.505 mm.

a) Write an expression that can be used to determine the maximum paper thickness that can be paired with the sheet of vellum to create the invitation.

b) Estimate the thickness of paper that can be paired with the sheet of vellum to create the initiation.

c) Simplify the expression and identify which paper type(s) can be paired with the vellum to create the invitation.

Standard(s): 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.2A, 5.2B, 5.3A, 5.3C, 5.3K, 5.4F

What is teacher doing?Monitor and check for understanding.

What is student doing?Student will complete the steps to the problem.

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Documents

Copy of 5E model example blank document_for Web view5E Lesson Plan Math . Grade ... decimal numbers to the thousandths place with standard, expanded and word ... point to the 1) and