1. Monica Hartman February 7, 2011
TIPM3 4th and 5th Grade
Monica Hartman
February 7, 2011

2. Agenda Lesson Sharing Review of Division Strategies Decimals
Alignment of Text to Common Core
Differentiating Math Instruction

3. Division Methods
Tara 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?

4. Division Methods Using 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 )
Expanded division algorithm (p.210)

5. 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?

6. 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?

7. 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.

8. 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.

9. 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 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.

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

11. Relate Decimals to Money
If 100 pennies = 1 whole 10
100
Then 10 pennies =
or .10 20
100
Then 20 pennies =
or .20
If 10 dimes = 1 whole
What do you notice about
.10 and .1? 1 10
Then 1 dime =
or .1 2 10
Then 2 dimes =
or .2

12. Practice with Special Relationships
1/ / / / / /4
Student volunteer goes to the board and points to a fraction or a decimal. The class reads the number together.

13. 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

14. More Practice with Special Relationships
1/ / / / / /4
Student volunteer points to a decimal number and the class reads the equivalent fraction.

15. Still More Practice with Special Relationships
1/ / / / / /4
Student volunteer points to a fraction and the class reads the decimal.

16. Explain why 3 tenths is the same as 30 hundredths.
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 Explain why this is true.

17. Read these fraction / decimal pairs
Read the number below: 0.28
Why is it read that way?
Read these fraction / decimal pairs
Students close eyes while teacher reads either a decimal or fraction. When they open their eyes, ask which number was read. Of course they cannot tell.
and /100
and /100
and /100

18. 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.

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

20. 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.

21. Compare Decimal Numbers
and
>
and 0.4
= 0.4
0.09 and 0.9
0.09 < 0.9
0.1 and 0.01
0.1 > 0.01
and 0.7
< 0.7
0.3 and
0.3 >
Make these numbers on your decimal place value mats.

22. More Comparing Decimal Numbers
and 0.2
> 0.2
0.8 and 0.9
0.8 < 0.9
0.8 and 0.09
0.8 >
0.08 and 0.6
0.08 < 0.6
and 0.7
<
and 0.5
> 0.5
Make these numbers on your decimal place value mats.
What patterns did you notice to help you compare these decimals?

23. Comparing Decimal Numbers
and
>
and 5.98
> 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 >
and 0.9
< 0.9
Did your patterns work for these decimals?
What new pattern or strategies did you see?

24. Ordering Decimal Numbers
Write these numbers on separate sticky notes. Put them in order from least to greatest: Explain how you did this.

25. Ordering Decimal Numbers
Write these numbers on separate sticky notes. Put them in order from least to greatest: Explain how you did this.

26. Ordering Decimal Numbers
Write these numbers on separate sticky notes. Put them in order from least to greatest: Explain how you did this.

27. Rounding Decimals
Use 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?

28. Rounding Decimals
Use the Decimal Mat to round these decimals to the nearest tenth O
Can you find these numbers on the number line?

29. Rounding Decimals
Use 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?

30. Rounding Decimals
Use the Decimal Mat to round these decimals to the nearest whole number. O
Does it help to think of dollars and cents?

31. AIMS Lessons From Tens to Tenths Dueling Decimals
Multiplying Decimal Patterns
Decimal Detectives

32. Mathematical Practices
1. 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.

33. 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.

34. 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

35. 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

36. 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