5th GradeMath Plans

2nd 9 weeks - 2nd week

Start Unit 3 on Decimal Place Value, Read, Write, and Compare Decimals to Thousandths

The student will:

1) Use models and place-value charts to represent decimals to thousandths.

2) Read and write decimals to thousandths using base ten numerals, number names, and expanded form.

Teacher Notes - In 4th grade CC Standards, students should have been taught:

  • 4.NF.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as0.62 meters; locate 0.62 on a number line diagram.
  • 4.NF.7: Compare two decimals to hundredths by reasoning about theirsize. Recognize that comparisons are valid only when the twodecimals refer to the same whole. Record the results ofcomparisons with the symbols >, =, or <, and justify the conclusions,e.g., by using a visual model.

Vocabulary-

digits

value

standard form

expanded form

word form

Ones,Tens,Hundreds,Thousands,TenThousands,HundredThousands,Millions,TenMillions,HundredMillions,Billions,TenBillions,HundredBillions, Tenths,Hundredths,Thousandths

Monday - Teachers, Use your discretion. If your students are not ready for large numbers, use smaller numbers and move to the larger numbers later. This is a review of whole number place value so use your discretion with the size of numbers. Teacher Choice with review of place value (whole numbers) or use any of the below resources.

Materials:

  • Journals
  • Week 11 - Day 1Daily Spiral Review (Resource Box)
  • Envision Math Textbook Lesson 1-1
  • Day 1 Place Value Flipchart (Resource Box) - this flipchart was used with the old math textbook so the handouts at the end of it are from Houghton Mifflin SC Math. Use whatever parts are helpful.
  • Practice for Determining Place Value (Resource Box) - did not run-off because it is 20 pages long - use if needed
  • Extra Practice Resources (with smaller numbers) if needed are in the Resource Box

In this lesson -

1) Review - Students will write the standard, expanded, and word forms of whole number and identify the value of digits in whole numbers up to billions (Teachers - Use your discretion).

Daily Spiral Review: Complete Week 11 - Day 1Daily Spiral Review (Resource Box).

TeachingStrategies: Teachers - Use smaller numbers to start with if your students are having difficulty with larger numbers.

Lesson 1-1 Envision Math Textbook- There is a Day 1 Place Value Flipchart (Resource Box) - this flipchart was used with the old math textbook so the handouts at the end of it are from Houghton Mifflin SC Math. Use whatever parts are helpful.

1. Open up with Problem-Based Interactive Learning on p.6B.

2. Teachers -use your discretion at this point what to use with students.

  • You have a Visual Learning Example if needed at the top of pages 6-7 in Envision teacher's edition. Teacher directions are found on p. 6 left column 1 Visual Learning.
  • You have Guided Practice on p. 6 (which are problems #1-4 on p.6).
  • You have Independent Practice and Problem Solving (p. 7) - may want to do a few of both sections.
  • You have a Quick Check Master to assess students' understanding. Then at the bottom of p. 7A, you have a Prescription for Differentiated Instruction using the options on the top of p. 7B.

SummarizingStrategy:In your journal, answer the following problem - For the standard form of one million, three hundred fifty thousand, five, Danielle wrote 1,350,500. What error did she make? What is the correct standard form of the number?

Homework: Assign Practice for Determining Place Value (Resource Box) - did not run-off because the document is 20 pages long. Pick and choose what you need.

Extra Practice (Resource Box) for students who need more practice with smaller numbers:

  • Guess My Number #1
  • Guess My Number #2
  • Place Value Cards
  • Representing Number in 4 Ways
  • Word Form, Expanded Form, Standard Form

Tuesday– Review from 4th grade

Materials:

  • Journals
  • Week 11 - Day 2 Daily Spiral Review (Resource Box)
  • PlaceValueSongfor ActivatingStrategy (Resource Box)
  • Envision Lesson 13-7 from 4th grade book Reteaching Master (Resource Box)
  • Place Value Chartand Decimal Grids (Resource Box)

In this lesson -

1) Students will use place value to help them read large numbers and numbers that are less than 1.

2) Students will use models and place-value charts to represent decimals to hundredths.

3) Students will read and write decimals to hundredths using base-ten numerals, number names, and expanded form.

Daily Spiral Review: Complete Week 11 - Day 2 Daily Spiral Review (Resource Box).

Teaching Strategies:Using Place Value Chart to Review Decimals

  1. Teachers may want to open up with the Place Value Song (Resource Box).
  2. Put up the following decimal 892.15 and ask students if they would be happy if someone gave them this much money.

Arrange the decimal892.15on the place value chart (Resource Box). Arrange the digits in a place value chart as shown below.

From the chart above, we see that:
the value of 8 is 8 × 100= 800

the value of 9 is 9 × 10 =90

the value of 2 is2 × 1 = 2

(tenths are the dimes)

(hundredths are the pennies)

  1. Why are the tenths how many dimes you have? (Because 10 dimes make a dollar so 1 dime is a 1/10 of a dollar.) – Students may not have thought of this before so go slow with this.
  1. Why are the hundredths how many pennies you have? (Because 100 pennies make a dollar so 5 pennies is 5/100 of a dollar.)
  1. Give students other examples if needed: $4.57, $10.29, $1567.30, etc.
  1. Now move to a visual representation of the decimal part. Let’s start with what 0.2 looks like in a model. First you must identify one whole. That will be our hundred grid (There is decimal grid paperin the resource box for students to use). How many columns do we have? (10) 10 columns can represent tenths because 10/10 is the same as 1 whole. Teachers – Students could also say the tenths go horizontally (rows). It does not matter.

Ex: 0.2 is the same as 2 tenths so let’s shade in 2 tenths.

1/10 1/10

0.2 is the same as 2 one-tenths so 0.2 = 2 x (1/10) = 2/10 or two-tenths.

  1. Try some more problems with tenths. Ex: 0.5, 0.7, etc.
  1. Now let’s try a problem with hundredths (pennies) like 0.08or 8 cents. (Teachers - Lead students to see that 1 penny or 1/100 or 1 hundredth is one of these squares so you need to shade in 8 squares.)

0.08 is the same as 8 one-hundredths so 0.08 = 8 x (1/100) = 8/100 or eight hundredths.

  1. Try some more problems with hundredths. Ex: 0.05, 0.07, etc.
  1. Now move to a decimal with a numeral beside zero in the tenths and hundredths place.

Ex: 0.15 which is the same thing as 15 cents or 1 dime (1/10) and 5 pennies (5/100).

0.15 = 1 tenth 5 hundredths or 1 x (1/10) = 5 x (1/100)

which is the expanded form of this decimal.

IMPORTANT – What is another way to pronounce this beside the above? fifteen hundredths

  1. Try some other problems like 0.27, 0.89, etc.

Base-Ten Numeral Number Name Expanded Form

0.27 = twenty-seven hundredths 2 x (1/10) + 7 x (1/100)

0.89 = eighty-nine hundredths 8 x (1/10) + 9 x (1/100)

Summarizing Strategy: In your journal, solve the following problem -

Andrew found 85 cents in the parking lot at school. He drew a model of what that looks like on a grid. Explain if Andrew’s thinking is correct or not and why.

Homework: Use grade 4 (since we are going back to cover what students have not had yet) Envision Math Textbook Lesson 13-7 Reteaching Master (Resource Box).

Wednesday -

Materials:

  • Journals
  • Week 11 - Day 3 Daily Spiral Review (Resource Box)
  • Decimal Grid Paper (Resource Box)
  • Relating Mixed Numbers and Decimals worksheet (problems 1-3 on one page, 19-21 only on other page)
  • Practice or Enrichment Master from gr. 4 Envision (Resource Box)

In this lesson -

1) Students will use place value to help them read large numbers and numbers that are less than 1 (include whole numbers with the decimals).

2) Students will use models and place-value charts to represent decimals to hundredths. They will read and write decimals in expanded, standard, and word form.

Daily Spiral Review: Complete Week 11 - Day 3Daily Spiral Review.

Teaching Strategies:

  1. Open up with a view from the last few days. Stress using models and place-value charts to represent decimals to hundredths. Also reading and writing decimals in expanded, standard, and word form (an example is on the next page).

Base-ten numeral Expanded Form Number Name

0.75 7 x (1/10) + 5 x (1/100) seventy-five hundredths

7/10 + 5/100

  1. Today include whole numbers in front of the decimal point. However, we will use small numbers in the ones place because of space.
  1. Ask students to model on the grid paper what 2.75 may look like. Remember that one grid is one whole so they should shade in 2 whole grids and 75 out of 100 of the third grid.

Base-ten numeral Expanded Form Number Name

2.75 2 x 1 + 7 x (1/10) + 5 x (1/100) Two and seventy-five hundredths

STRESS that the decimal point is pronounced and. Have students use the place value chart is they are having trouble writing the expanded form or saying the number name.

  1. Have students do a few more with you.

Classwork: Have students practice a few problems from the Relating Mixed Numbers and Decimals worksheet (problems 1-3 on Relating Mixed Numbers page, 19-21 only on Understanding Decimals through Hundredths page).

Homework: Teacher choice or assign gr. 4 Envision 13-7 Practice or Enrichment Master (Resource Box).

Start 5th grade Standards

The student will:

1) Use models and place-value charts to represent decimals to thousandths.

2) Read and write decimals to thousandths using base ten numerals, number names, and expanded form.

5th grade Math Standards

5.NBT.1 - Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to the right and 1/10 of what it represents in the place to its left.

5.NBT.3a - Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) +

2 x (1/1000) and is pronounced three hundred forty-seven and three hundred ninety-two thousandths.

Thursday -

Materials:

  • Journals
  • Week 11 - Day 4 Daily Spiral Review (Resource Box)
  • Envision 5th Grade Textbook Lesson 1-2

In this lesson -

1) Students will review representing decimals (tenths and hundredths) as fractions. Students also represent fractions with denominators of 10 and 100 as decimals.

Daily Spiral Review: Complete Week 11 - Day 4 Daily Spiral Review (Resource Box).

Important TeachingNotes -

Key to understanding place value is the following:

As you move left on the place value chart, the value is 10 times greater each place you move to the left so a hundred is 10 times ten. A ten is 10 times one. A one is 10 times one-tenth (1/10) and a tenth is 10 times one-hundredth (1/100).

As you move right on the place value chart, the value is 1/10 of the place to the right so a ten is (1/10) of a hundred. A one is 1/10 of a ten. A tenth is 1/10 of one. A hundredth is 1/10 of a tenth.

Hundreds / Tens / Ones / Decimal Point / Tenths / Hundredths
5 / 5 / 5 / . / 5 / 5

Example: 555.55

500 is 10 times 50 (hundreds place is 10 times the value of the tens place).

50 is 10 times 5 (tens place is 10 times the value of the ones place).

5 is 10 times 5/10 (ones place is 10 times the value of the tenths place).

5/10 is 10 times 5/100 (tenths place is 10 times the value of the hundredths place).

50 is 1/10 of 500 (the place to the left of it).

5 is 1/10 of 50 (the place to the left of it).

0.5 is 1/10 of 5 (the place to the left of it).

0.05 is 1/10 of 0.5 (the place to the left of it).

When we do multiplying fractions and decimals, we will review this again.

TeachingStrategies:Lesson 1-2 Envision Math Textbook 5th grade book - Remember that it is important to define what the whole is first. Also you do not have to use problems with fractions that have a different denominators beside 10 or 100.

1. Teachers -use your discretion at this point what to use with students.

  • You have the Problem-Based Interactive Learning Example on p. 8B. Make sure that students realize the whole on this one is 10 squares instead of the hundred grid being the one whole.
  • You have a Visual Learning Example if needed at the top of pages 8-9 in Envision teacher's edition. Teacher directions are found on p. 8 left column 1 Visual Learning.
  • You have Guided Practice on p. 8 (which are problems #1-7 on p.8).
  • You have Independent Practice and Problem Solving (pp. 9-10) - may want to do a few of both sections.
  • You have a Quick Check Master to assess students' understanding. Then at the bottom of p. 11A, you have a Prescription for Differentiated Instruction using the options on the top of p. 11B.

SummarizingStrategy:In your journal, answer the following problem - Daniel says that is the same as 3.

Homework: Teacher Choice - Could use Reteach (only use #4-8), Practice (only use #1-10, 15) or Enrichment Master on p. 11B (Only use problems with 10 or 100 as denominators).

Friday -

Materials:

  • Journals
  • Week 11 - Weekly Assessment (Resource Box)
  • Representing Thousandths Lesson Plan (Resource Box)
  • Base Ten Blocks (need cubes, flats, rods, units) or use pictures of blocks in Resource Box
  • Model for Thousandths - laminated if possible or may use two pages of the 10 x 10 grids (6 to a page - you only need 10 grids for the whole so run-off two pages for each student, but cut-out the 2 extra grids)- this is found in the Representing Thousandths Lesson Plan (Resource Box)
  • Dry-erase markers for thousandths model if laminated
  • Representing Decimals with Base 10 Blocks (Resource Box)

In this lesson -

1) Students will develop an understanding of what a thousandth is using base ten blocks or drawings.

2) Students will represent decimals (thousandths) as fractions and fractions with denominators of 1,000 as decimals.

Weekly Assessment for Week 11: Complete Week 11 Weekly Assessment.

Teacher Notes: It is hard to visualize thousandths. You may use the cubes to represent ones, the flats to represent tenths (because there are 10 flats in a cube and there are 10/10 in one whole), the rods for hundredths, and the units for thousandths. Please take your time with this for students to investigate and discover things.

TeachingStrategies:Teachers - Use the Representing Thousandths Lesson Plan in the Resource Box (pp.1-2, 5-6) to introduce using base ten blocks to help students visualize what a thousandth is or use the following steps:

1. Display a 10 x 10 grid (Resource Box). Explain that the grid represents one whole (always need to define the whole first) and ask students to point to sections of the grid that represent different quantities of tenths and hundredths (e.g., 1 tenth, 7 tenths, 20 hundredths, 92 hundredths).

2. Next, ask students to imagine what one thousandth of the grid would look like. Discuss how a thousandth is one-tenth of a hundredth (a small square. Help students to understand this idea by dividing a small square into ten sections. Discuss how one thousandth is a small quantity compared to the whole grid.

3. Have students work in pairs or groups of 4. Then move toward a cube (which is a 10 x 10 x 10 or 1000 units) as the whole. Have a cube and 10 flats for each group of students to play with to discover that each flat is a tenth of the cube (whole).

4. Next have the groups take a flat and some rods. How many rods make a flat (10 rods)? So a rod is 1/10 of 1/10 or a hundredth.

5. Have students guess what the unit is? It is hard to use a thousand of these units to make a cube so a picture will be easier.

One Whole

One-tenth

One-hundredth One-thousandth

6. Use the Model for Thousandths (Resource Box) for students to visualize what a cube looks like flat (from a 3D version to a 2D version). If this can be laminated, then students can use dry-erase markers to identify certain decimals. Teachers may also use two pages of the 10 x 10 grids (6 to a page - you only need 10 grids for the whole so run-off two pages for each student, but cut-out the 2 extra grids).

7. Stress to students again this time the cube is 1 whole so these 10 flats are a cube (one whole).

How would they find a tenth? a hundredth? a thousandth?

8. What does 1/10 (0.1) look like? (Review several tenths like 3/10, 7/10 )

9. What does 1/100 (0.01) look like? (Review several hundredths like 9/100, 15/100, 87/100).

10. What does 1/1000 (0.001) look like? (Review several thousandths like 5/1000, 17/1000, 250/1000). Are students coming up with quicker ways to identify these larger thousandths?

Classwork: Use the Representing Decimals with Base 10 Blocks (Resource Box). Pair students up with some base 10 blocks.

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