Math ReviewQuarter 1

Base 10 Number System

There are ten digits in our number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

When we use these digits to create a number, we place them in different place value positions.

Each place value position is ten times greater than the place value position to its right.

Example: How do the two “7’s” compare in the number 9,741 and 1,479?”

Read, Write, Say Numbers

Standard form: the form of a number written using digits

Ex. 12, 378Written form: the form of a number using words

instead of digitsEx. Twelve thousand three hundred seventy eightExpanded form: a way of writing a number to show

the value of each of its digitsEx. 10,000 + 2,000 + 300 + 70 + 8

How much is a million?Millions Hundred

ThousandsTen Thousands

Thousands Hundreds Tens Ones

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

So we can see that one million is ten times greater than one hundred thousand.And one hundred thousand is ten times greater than ten thousand. This pattern continues throughout the chart and proves that each place value is ten times greater than the place value to the right of it! Check out this number sentence:

1 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1, 000, 000.

Rounding Numbers

Remember, rounding is only one of the strategies we can use for estimating. Others include convenient numbers and benchmark numbers.

Strategies for rounding include:Using hundreds charts

Using number linesUsing standard rounding rules

Using front end estimation rules

Comparing Numbers

Important Vocabulary: greatest, least, more than, less than, greater than, less than, equal to

Important Symbols: = , < , >

Comparison Strategies: Base 10 Models Number lines with benchmark numbers Place Value Charts Expanded Form

Sample Problems

• How is the 3 in the number 753 similar to and different from the 3 in the number 735?

•  Write the number 328,416 in expanded form and word form.

• Which is greater: 15 thousands or 3 ten thousands? How do you know?

• Round the number 43,987 to the nearest thousand. • Is 9,040 closer to 9,000, or 9,100? How do you

know? Prove your answer using a number line.

Addition with Regrouping

Remember to use graph paper or lined paper to help you align place value columns

Use estimation as a check for reasonableness of your sum

Use expanded form for the addends to help you visualize the regrouping

Example: 21, 378 + 9, 054 = ______

Subtraction with Regrouping

Remember to use graph paper or lined paper to help you align place value columns

Use estimation as a check for reasonableness of your difference

Be cautious as you regroup – especially across zeroes!

Example: 12, 043 – 9,756 = _______

Addition Change Problems

Change Plus Start Unknown: • At the park there were some children in the morning. Then 25 more children came to

play in the afternoon. Now there are 50 children at the park. How many children were at the park in the morning?

• _______ + 25 = 50 Change Plus Change Unknown• At the park there were 35 children in the morning. Then some more children came to

play in the afternoon. Now there are 50 children at the park. How many children came to play in the afternoon?

• 35 + ______ = 50Change Plus End Unknown• At the park there were 35 children in the morning. Then 25 more children came to play

in the afternoon. How many children were at the park altogether? • 35 + 25 = ________

Subtraction Change Problems

• How could we rewrite these same change plus problems and turn them into change minus problems? Keep the context of the word problem the same. 

Change Minus Situations

n – 25 = 35          50 – n = 35 50 – 25 = n     Start                     Change                        EndUnknown               Unknown                 Unknown

AdditionCollection Problems

• Collection with Total (whole) Unknown: At the park there are 73 red leaves and 89 yellow leaves on

the ground. How many leaves are there altogether? 73 + 89 = _______ • Collection with Addend (part) Unknown There are 115 leaves on the ground at the park. 46 are red

and the rest are yellow leaves. How many leaves are yellow? 46 + _______ = 115 *Remember: Subtraction undoes addition!

Addition and SubtractionComparison Problems

• 1. Caroline had 12 pets and Sam had 9 pets. How many more pets did Caroline have than Sam? How many fewer pets did Sam have than Caroline?

• 2. Caroline and Sam had 21 pets.

Sam had 3 fewer pets than Caroline. How many pets did Caroline have?

• 3. Caroline and Sam had 21 pets.

Caroline had 3 more pets than Sam. How many pets did Sam have?

MultiplicationVocabulary

Commutative Property – the order of factors can be changed in a multiplication sentence

Associative Property – the grouping of factors can be changed in a multiplication sentence

Factor – a number multiplied by another number to yield a product

Multiple – the product of a whole number and any other whole number

MultiplicationVocabulary

Prime Number - A prime number has two unique factors. The number one is considered to be neither prime nor composite. A prime number can be represented by only one unique rectangular array

Composite Number -A composite number has two or more factors; composite numbers can be represented by at least two unique rectangular arrays.

Sample Problems Is 89 a multiple of 3? How do you know?

Which number is both a factor of 100 and a multiple of 5? A. 4 B. 40 C. 50 D. 500

There are 24 chairs in the art room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group?

Multiplication StrategiesTwo, Three, Four Digit by One Digit

Base 10 Model - use base 10 drawings and grouping

Area Model – use a rectangular array divided into smaller rectangular arrays to show each of the partial products, then add the partial products together

Expanded Notation – use expanded form to represent the greater factor then multiply each part by the one digit factor, write the partial products then add

Partial Products – write out the partial products for each digit in the greater factor multiplied by the one digit factor then add the partial products together

Multiplication StrategiesTwo Digit, Three Digit by Two Digit

Area Method – remember to use expanded form of factors when labeling the rectangles

Lattice Method – remember to use only the digits for the factors when labeling the rectangle

Sample Problems There are 24 tanks of fish at Patsy’s Pet Place. Each tank

contains 37 goldfish. How many goldfish are in the tanks? Mrs. Smith finds a deal on stickers for her prize box. Each pack

contains 9 stickers. She buys 1, 427 packs of stickers. How many stickers does she have altogether?

There are 43 elephants at the North Carolina Zoo. Each elephant

drinks 17 gallons of water a day. How many gallons of water are consumed by the elephants each day at the zoo?

Multi-StepProblems

There are 84 students in the 4th grade and 93 students in the 5th grade. If each 4th grader reads 15 books and each 5th grader reads 12 books, how many books will they read altogether?

There are about 34 boys and 27 girls in 4th grade that run laps at recess. On average the boys run about 35 laps and the girls run about 31 laps. About how many laps will they run altogether?