TIPM34th and 5th Grade

Monica HartmanFebruary 7, 2011

AgendaLesson Sharing

Review of Division Strategies

Decimals

Alignment of Text to Common Core

Differentiating Math Instruction

Division MethodsTara collected 3 times as many cans as Robert.

If Tara collected 7 cans, how many cans did Robert collect?

Santiago collected 4 times as many cans as Carla. If Carla collected 48 cans, how many cans did Santiago collect?

Division MethodsUsing multiples of 10 (pp.16-17)

The use of place value and the distributive property. (p. 18)

The equal groups model (p.19)

Unknown-side-length problem (pp. 20 - 21)

Expanded division algorithm (p.210)

What To Do With Remainders

There are 86 pencils to be divided equally among 9 students. How many pencils will each student get?

Each car holds 7 people. How many cars will be needed to take 45 students and teachers on a field trip?

At a bakery, muffins are put in packages of 6. There are 50 muffins. After the muffins are put in packages, the workers get to eat any muffins that are left. How many muffins do the workers get?

What To Do With Remainders

Eleven cups of flour must be divided equally into 3 parts. How much flour is in each part?

$11 is to be divided equally among 3 people. How much does each person get?

Quin needs to cut a rope that is 11 feet long into 3 equal pieces. How long should each piece be?

Operations and Algebraic Thinking

4.OA Use the four operations with whole numbers to solve problems.

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparisons, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.3 Solve multistep word problems posed with whole-numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Number and Operations in Base Ten

5.NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

4. NF Number and Operations-Fractions

Understand decimal notation for fractions, and compare decimal fractions.

4.NF.4 Express a fraction with denominator 10 as an equivalent fraction with a denominator 100, and use this technique to add fractions with respective denominators 10 and 100.

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, write 0.62 as 62/100. Locate 0.62 on a number line.

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual model.

5. NBT Number and Operations in Base Ten

Understand the place value system.

5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by the powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths.

a.Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b.Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, < symbols to record the results of the comparisons.

5.NBT.4 Use place value understanding to round decimals to any place.

Relate Decimals to Money

If 100 pennies = 1 wholeThen 10 pennies

= 10

100 or .10

Then 20 pennies =

20

100or .20

If 10 dimes = 1 whole

Then 1 dime = 110

or .1

Then 2 dimes =

210

or .2

What do you notice about .10 and .1?

Practice with Special Relationships

0.25 0.50 0.75 1.25 1.50 1.75

1/4 2/4 3/4 5/4 6/4 7/4

Student volunteer goes to the board and points to a fraction or a decimal. The class reads the number together.

Special Relationships Use the transparency and number line paper to determine the equivalent

decimals for these fractions:

1/2

1/4

3/4

1/5

2/5

3/5

4/5

1/10

3/10

6/10

7/10

More Practice with Special Relationships

0.25 0.50 0.75 1.25 1.50 1.75

1/4 2/4 3/4 5/4 6/4 7/4

Student volunteer points to a decimal number and the class reads the equivalent fraction.

Still More Practice with Special Relationships

0.25 0.50 0.75 1.25 1.50 1.75

1/4 2/4 3/4 5/4 6/4 7/4

Student volunteer points to a fraction and the class reads the decimal.

Look at the two-color meter tape or the meter tape.

Explain why 3 tenths is the same as 30 hundredths.

Notice that the tenths are larger than the hundredths even though 10 is a smaller number than 100. Explain why this is true.

Read the number below:

0.28

Why is it read that way?

Read these fraction / decimal pairs0.37 and 37/100

0.49 and 49/100

0.81 and 81/100

Decimal Secret Code Cards

Model 0.37 with the secret code cards.

Explain how you did this.

Make 0.37 on your place on the decimal place value chart.

Model 0.49 with the cards and on the mat.

What is 0.49 made of?

How do you read this?

Model 0.81 with the cards and the mat.

Practice Reading Decimals 0.7 0.07 0.02 0.2 0.09 0.9 0.56 0.5 0.06 0.50

Compare Decimal Numbers

Zachary and Stephanie are traveling the same distance. Zach traveled 4 tenths of the way. Stephanie traveled 26 hundredths of the way. What decimal numbers could we write to represent the distance each person traveled?

Zach traveled .4 of the distance.

Stephanie traveled .26 of the distance.

Who traveled further? Explain.

Compare Decimal Numbers

0.6 and 0.06 0.6 > 0.06 0.40 and 0.4 0.40 = 0.4 0.09 and 0.9 0.09 < 0.9 0.1 and 0.01 0.1 > 0.01 0.07 and 0.7 0.07 < 0.7 0.3 and 0.03 0.3 > 0.03

Make these numbers on your decimal place value

mats.

More Comparing Decimal Numbers

0.4 and 0.2 0.4 > 0.2 0.8 and 0.9 0.8 < 0.9 0.8 and 0.09 0.8 > 0.09 0.08 and 0.6 0.08 < 0.6 0.07 and 0.7 0.05 < 0.19 0.61 and 0.5 0.61 > 0.5

Make these numbers on your decimal place value

mats. What patterns did you notice

to help you compare these

decimals?

Comparing Decimal Numbers

27.5 and 8.37 27.5 > 8.37 6.04 and 5.98 6.04 > 5.98 7.36 and 7.38 7.36 < 7.38 36.9 and 37.8 36.9 < 37.8 0.5 and 0.26 0.5 > 0.26 0.09 and 0.9 0.09 < 0.9

Did your patterns work

for these decimals?

What new pattern or

strategies did you see?

Ordering Decimal Numbers

Write these numbers on separate sticky notes.

Put them in order from least to greatest:

3.126 7.4 0.75 3.068 0.482

0.482 0.75 3.0683.126 7.4

Explain how you did this.

Ordering Decimal Numbers

Write these numbers on separate sticky notes.

Put them in order from least to greatest:

1.45 4.5 1.045 4.145 0.445

0.445 1.045 1.45 4.145 4.5

Explain how you did this.

Ordering Decimal Numbers

Write these numbers on separate sticky notes.

Put them in order from least to greatest:

3.4 2.172 0.33 0.033 2.089

0.033 0.33 2.089 2.172 3.4

Explain how you did this.

Rounding DecimalsUse the Decimal Mat to round these decimals to

the nearest tenth

O.72

0.35

0.91

2.09

• Can you find these numbers on the number line?

Rounding DecimalsUse the Decimal Mat to round these decimals to

the nearest tenth

O.72 0.7

0.35 0.4

0.91 0.9

2.09 2.1

Can you find these numbers on the number line?

Rounding DecimalsUse the Decimal Mat to round these decimals to

the nearest whole number.

O.72

0.35

0.91

2.09

Can you find these numbers on the number line?

Rounding DecimalsUse the Decimal Mat to round these decimals to

the nearest whole number.

O.72 1

1.53 2

3.91 4

2.09 2

Does it help to think of dollars and cents?

AIMS LessonsFrom Tens to Tenths

Dueling Decimals

Multiplying Decimal Patterns

Decimal Detectives

Mathematical Practices1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

The Eight Mathematical Practices

Webinar: A Closer Look at the Common Core State Standards in Mathematics

Start the webinar at the 18:01 mark. The webinar will walk you through matching the mathematical practices with the standards. There are eight examples. The last one ends at the 46:29 mark. It is important to listen to at least the first 3 examples. The third one ends at the 28:43 mark.

http://educationnorthwest.org/event/1346

Aligning Text to Common Core

Number and Operations – Fractions (4.NF)

Understand decimal notation for fractions, and compare decimal fractions

4.NF.5 4.NF.5 4.NF.7

Operations and Algebraic Thinking (4.OA)

Use the four operations with whole numbers to solve problems.

4.OA.1 4.OA.2 4.OA.3

Number and Operations in Base Ten (4.NBT)

Use place value understanding and properties of operations to perform multi-digit arithmetic

4.NBT.4 4.NBT.5

Aligning Text to Common Core

Number and Operations in Base Ten (5.NBT)

Understand the place value system

5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5 5.NBT.6 5.NBT.7

Differentiating Math Instruction

Read and discuss article in small groups

Think about your next lesson. How can you change the lesson to accommodate the differences in your students?

Work with someone who will be teahcing