Mathematics

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The second chapter of the fifth grade math book focuses on adding and subtracting whole numbers and decimals. The standards for chapter 2 are:

Chapter 2

Number Sense: Estimate, round and manipulate very large and very small numbers

Number Sense: Add and subtract, with decimals, and verify the reasonableness of the results

Number Sense: Demonstrate an understanding of, and ability to use standard algorithms for the addition and subtraction of multi-digit numbers

Algebra and functions: Write and solve one-step linear equations in one variable

Algebra and functions: Interpret and evaluate mathematical expressions that now use parentheses

Algebra and functions: Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution

Mathematical reasoning: Students make decisions about how to approach problems

Mathematical reasoning: Indicate the relative advantages of exact and approximate solutions to problems

This chapter connects with previous and future learning in this way:

Looking Back	Right Now   Adding and Subtracting Whole Numbers and Decimals	Looking Ahead
In grade 4, students learned how to add and subtract four-digit numbers. They also learned about expressions and equations with addition and subtraction. Solve: + 6 = 7	In this chapter, students will learn how to add and subtract five-digit whole numbers and decimals. They will also learn to evaluate expressions and to solve equations. Solve: X - 8 = 15	Next year, students will learn how to write and evaluate expressions and write and solve equations with addition and subtraction of decimals. Solve: X - 2.4 = 4.56

The chapter has three sections of problem solving where the students are introduced to new strategies or are asked to apply previously learned concepts in new problems. The strategies for the second chapter are:

Deciding if an estimate is enough pages 48-49

Writing an equation pages 58-59

Using money pages 66-67

Many students have a tough time with problem solving. Often, a student will want to jump to the answer without taking the time to think through and verbalize the steps necessary in solving the problem. Many times, that is fine, but the problem lies in that when the student is challenged with more difficult problems, the thought processes have been shortcircuited and the problem becomes harder. Therefore, I emphasize the explaining of all problems, no matter how simple they seem. By learning with the easier, simpler problems, the correct thinking can developed and then generalized to the more difficult problems.

The textbook emphasizes four steps in problem solving. They are:

Understand~

What is the problem asking?

What facts are given?

What must be found?

How would you restate the problem in your own words?

Plan~

Make a plan for solving the problem. Think of the different strategies that are available to the mathematician. How can the problem be solved? What other strategies might also work?

Draw a picture

Make a model

Work backward

Guess and check

Act out the problem

Write a number sentence

Solve~

How will the problem be solved? What materials should be used: paper and pencil; mental math; calculator; or manipulatives? Use the best materials that are available.

Look Back~

Is the answer correct? Does it make sense and is it a logical solution? Think of a way to check the problem and take the time to do so. Does the selected solution answer the question?

By following these steps in problem solving on a consistent basis, students should become stronger in the application of those steps!

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Let's Practice Some

Online Problem Solving!

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is written on a separate card. Just enough cards are drawn to place a digit in each space available. Many different choices of numbers are possible. What digits would you choose and where would you place them?

Day 1: The sum is less than 500: _ _ _ + _ _ <500

Day 2: The sum is greater than 500: _ _ _ + _ _ _ > 500

Day 3: The sum is the greatest possible: _ _ + _ _ + _ _

Day 4: The difference is less than 100: _ _ _ - _ _ < 100

Day 5: The sum, rounded to the nearest hundred, is 600: _ _ _ + _ _ _

Day 6: The sum is greater than 10: _ ._ _ + _ . _ _

Day 7: The difference is less than 10: _ _ ._ _ - _ ._ _

Day 8: The difference is greater than 50: _ _ ._ - _ ._

Day 9: The sum is closest to 100: _ _._ + _._

Day 10: The sum is 8 when rounded to the nearest whole number: _ . _ _ _ + 0 + _ _ _

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How About Some More Practice?

Palindromes

A palindrome is a number that is read the same backward and forward such as 3,883. Find the following sums only if the addends are both palindromes.

373 + 595 =	1,331 + 4,224 =	8,228 + 646 =
1,991 + 1,234 =	999 + 3,333 =	4,545 + 2,332 =

There are rules for finding palindromes: 1. Write a three digit number: 2. Reverse the digits: 3. Add the two numbers: 4. If the sum is not a palindrome, repeat steps 2 and 3 until it is:

695 596 695 + 596 = 1,291 1,291 + 1,921 = 3,212 3,212 + 2,123 = 5,335 *

Try creating palindromes for decimals too!

To develop your number sense, choose the best estimate for each of these differences:

492 - 226 = A) 200 B) 300 C) 400	1,785 - 321 = A) 400 B) 1,400 C) 1,500
8,430 - 3,995 = A) 4,000 B) 5,000 C) 6,000	2,382 -927 = A) 1,300 B) 1,400 C) 1,500

$ 7.83 + 2.25	$ 4.35 + 3.12
$ 12.15 + 14.88	$ 3.47 + 2.25
$ 7.76 + 9.68	$ 17.25 + 23.49

Place the numbers 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 in the following grid so that the sum is 1.5 along each row, column and diagonal.

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Estimation

Use your estimation skills to estimate the answers to the following problems. Then, use a calculator and see how accurate you are. Is there a difference between front-end and rounding?

3.829 + 1.246 =	6.745 + 0.982 =
0.487 + 0.512 =	7.13 + 5.931 =

For a bit more challenge:

Write the numbers 2-10 so that the sum of each row and diagonal is 18.	Miguel has one dollar in change. He has twice as many nickels as dimes. He has 14 more pennies than quarters. What coins does he have?
Find the missing addends in this addition table:  +      16        14        11    17        27    41    87      100	In a word game, a = 2 points, b= 4 points, c = 6 points, and so on. How many points is each of the following words worth? quiz math addend

to math sites!

Adding and Subtracting Links

Mental Math Addition	Mental Math Subtraction	Estimating Sums
Relationship between + and -	Relationship between - and +	Estimating Differences
Adding Money	Subtracting Money	Estimating with decimals
Properties of Addition	Math is our friend!	Four Basic Math Operations

Decimal Links for
Adding and Subtracting

How do you add decimals?	How do you subtract decimals?
Adding Decimals	Subtracting Decimals
Adding Decimals-Money	Subtracting Decimals-Money
Adding & Subtracting Decimals Tutorial	Subtraction Basketball-Decimals
Adding and Subtracting Workout- tutorial and practice	Interactive Quiz

Algebra Links

Practice Addition with one-digit numbers	Working with Variables
Practice Addition with two-digit numbers	Solving Equations 1
Practice Addition with three-digit numbers	Solving Equations 2
Practice Subtraction with one-digit numbers	Solving Equations 3
Practice Subtraction with two-digit numbers	Solving Equations 4
Practice Subtraction with three-digit numbers	Algebra is fun!

Time to Exercise the Brain~

Grade Five Problems	Who Wants to Win $1,000,000 ?	Puzzler Archive
Coin Flipping	Brain Teasers from Houghton Mifflin	Online Mankala

from the previous chapter

Place Value Sites~

Place Value Chart	Play the Place Value Game	Match the Number to the Word
Place Value Number Quiz	Write the Number on the Check	Write the Number- Math Basketball Game
Place Value Word Quiz	Place Value Pirates	Name the Number on the Check

Sites from aaamath.com

Identifying Place Values

Finding Place Values

Place Values-Expanded Form

Comparing 4-digit Numbers

Ordering 4-digit Numbers

Comparing 5-digit Numbers

Ordering 5-digit Numbers

Place Values of 6-digit numbers

Comparing 6-digit Numbers

Ordering 6-digit Numbers

Place Values of 7-digit numbers

Comparing Numbers through Millions

Ordering 7-digit Numbers

How about some algebra!

Working with Variables

Solving Equations 1

Solving Equations 2

Decimal Sites ~

Finding Place Values	Thousandths Place Value	Online Flashcard Practice- say the numbers
Tenths Place Value	Decimals to Ten-Thousandths	Tons of Decimal Help from Math League
Hundredths Place Value	Comparing Decimals	Make Change from Funbrain

Rounding Sites~

Basketball Rounding	Match Game- decimals/whole numbers	Flashcards-tenths
Rounding Riddles #1	Flashcards- decimals/whole numbers	Concentration-tenths
Rounding Riddles #2	Concentration- decimals/whole numbers	Rounding to Tenths
Match Game-tenths	Estimating and Rounding	Rounding to Hundredths

Fun Math Sites to Visit~ 

Great Help for Most of Chapter 1	Need help? Ask Dr. Math
Practice rounding with online flashcards	Math Dictionary for Kids
Online Flashcards-all operations	Tons of chances for practice-worksheets
Totally Tessellated	A+ Math Games
Multiplication Practice-you set the problems!	Late Delivery-Great Algebra Practice
Mystery Math-How do they do that?	Order of Operations
Puzzler	Math Baseball
Multiplication tips by kids	Exponent Basketball
The Fruit Game	Math Playground