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4 FOURTH GRADE MATH CHARTS
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FOURTH GRADEMATH CHARTS
NUMBER AND OPERATIONS: FRACTIONS
GENERATE EQUIVALENT FRACTIONS .............................................................................
COMPARE FRACTIONS ......................................................................................................
ADD FRACTIONS WITH LIKE DENOMINATORS .............................................................
SUBTRACT FRACTIONS WITH LIKE DENOMINATORS ..................................................
ADD MIXED NUMBERS WITH LIKE DENOMINATORS ..................................................
SUBTRACT MIXED NUMBERS WITH LIKE DENOMINATORS ........................................
MULTIPLY A FRACTION BY A WHOLE NUMBER .............................................................
DECIMAL PLACE VALUE .....................................................................................................
COMPARE DECIMALS ........................................................................................................
RELATE FRACTIONS AND DECIMALS ..............................................................................
EQUIVALENT FRACTIONS AND DECIMALS ....................................................................
TABLE OF CONTENTS
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39
41
43
45
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49
51
53
55
57
59
61
63
OPERATIONS AND ALGEBRAIC THINKING
MULTIPLICATIVE COMPARISONS .......................................................................................
FACTORS AND MULTIPLES ..................................................................................................
PRIME AND COMPOSITE ....................................................................................................
INTERPRET THE REMAINDER ............................................................................................
NUMBER AND OPERATIONS IN BASE TEN
PLACE VALUE .......................................................................................................................
COMPARE NUMBERS .........................................................................................................
ROUND WHOLE NUMBERS ..............................................................................................
ESTIMATE SUMS AND DIFFERENCES ..............................................................................
ADDITION: TRADITIONAL ALGORITHM ..........................................................................
SUBTRACTION: TRADITIONAL ALGORITHM ..................................................................
MULTIPLY AND DIVIDE TENS, HUNDREDS AND THOUSANDS ....................................
ESTIMATE PRODUCTS ........................................................................................................
MULTIPLY USING AN AREA MODEL .................................................................................
MULTIPLY USING PARTIAL PRODUCTS ............................................................................
MULTIPLY USING EXPANDED FORM ................................................................................
DIVISION: AREA MODEL ....................................................................................................
DIVISION: PARTITION THE DIVIDEND .............................................................................
DIVISION: MULTIPLY UP .....................................................................................................
DIVISION: PARTIAL QUOTIENTS .......................................................................................
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MEASUREMENT AND DATA
LINE PLOTS WITH FRACTIONAL DATA ............................................................................
ELAPSED TIME .....................................................................................................................
MEASURE AND DRAW ANGLES ........................................................................................
ADJACENT ANGLES ............................................................................................................
AREA .....................................................................................................................................
PERIMETER ..........................................................................................................................
METRIC SYSTEM ..................................................................................................................
U.S. CUSTOMARY SYSTEM .................................................................................................
GEOMETRY
LINES, RAYS AND LINE SEGMENTS ..................................................................................
CLASSIFY ANGLES ..............................................................................................................
LINE SYMMETRY ..................................................................................................................
USER LICENSE .....................................................................................................................
TABLE OF CONTENTS (cont.)
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FACTOR UNKNOWN (number of groups unknown)
It takes Jack 6 minutes to get ready for school and his brother Ben 24 minutes. How many times as long does it take Ben to get ready?
Jack
Ben
t x 6 = 24 4 x 6 = 24 t = 4
It takes Ben 4 times as long to get ready.
FACTOR UNKNOWN (size of each group unknown)
It takes Ben 24 minutes to get ready for school. This is 4 times as long as it takes Jack to get ready for school. How long does it take Jack to get ready for school?
Ben
Jack
4 x j = 24 4 x 6 = 24 j = 6
It takes Jack 6 minutes to get ready for school.
MULTIPLICATIVE COMPARISONS
PRODUCT UNKNOWN It takes Jack 6 minutes to get ready for school. It takes his little brother Ben 4 times as long. How long does it take Ben to get ready for school?
Jack
Ben
4 x 6 = b 4 x 6 = 24 b = 24
It takes Ben 24 minutes to get ready for school.
6
6 6 6 6
?
6
24 min.
24 min.
PREVIEW
FACTOR UNKNOWN (number of groups unknown)
It takes Jack 6 minutes to get ready for school and his brother Ben 24 minutes. How many times as long does it take Ben to get ready?
Jack
Ben
t x 6 = 24 4 x 6 = 24 t = 4
It takes Ben 4 times as long to get ready.
FACTOR UNKNOWN (size of each group unknown)
It takes Ben 24 minutes to get ready for school. This is 4 times as long as it takes Jack to get ready for school. How long does it take Jack to get ready for school?
Ben
Jack
4 x j = 24 4 x 6 = 24 j = 6
It takes Jack 6 minutes to get ready for school.
MULTIPLICATIVE COMPARISONS
PRODUCT UNKNOWN It takes Jack 6 minutes to get ready for school. It takes his little brother Ben 4 times as long. How long does it take Ben to get ready for school?
Jack
Ben
4 x 6 = b 4 x 6 = 24 b = 24
It takes Ben 24 minutes to get ready for school.
6
6 6 6 6
?
6
24 min.
24 min.
FACTOR UNKNOWN (number of groups unknown)
It takes Jack 6 minutes to get ready for school and his brother Ben 24 minutes. How many times as long does it take Ben to get ready?
Jack
Ben
t x 6 = 24 4 x 6 = 24 t = 4
It takes Ben 4 times as long to get ready.
FACTOR UNKNOWN (size of each group unknown)
It takes Ben 24 minutes to get ready for school. This is 4 times as long as it takes Jack to get ready for school. How long does it take Jack to get ready for school?
Ben
Jack
4 x j = 24 4 x 6 = 24 j = 6
It takes Jack 6 minutes to get ready for school.
MULTIPLICATIVE COMPARISONS
PRODUCT UNKNOWN It takes Jack 6 minutes to get ready for school. It takes his little brother Ben 4 times as long. How long does it take Ben to get ready for school?
Jack
Ben
4 x 6 = b 4 x 6 = 24 b = 24
It takes Ben 24 minutes to get ready for school.
6
6 6 6 6
?
6
24 min.
24 min.
PREVIEW
INTERPRET THE REMAINDER
ADD ONE Add one to the quotient
There are 33 students in a 4th grade class. Each table in the classroom seats 6 students. How many tables will be needed to seat all students?
33 ÷ 6 = 5 r 3
There is a remainder of 3 students. Add one to the quotient so that all the students have a seat.
6 tables will be needed to seat all 33 students.
IGNOREIgnore the remainder and use only the quotient
Books are on sale for $7 each. Peter has $30.00 in his wallet. How many books can Peter buy?
30 ÷ 7 = 4 r 2
There is a remainder of 2 dollars. Peter cannot buy a book with 2 dollars. Ignore the remainder.
Peter can buy 4 books.
USE ITUse the remainder as the solution
Mary buys a new bookcase with 6 shelves. Each shelf holds 8 books. If Mary has 52 books, how many books will not fit on the bookcase?
52 ÷ 6 = 8 r 4
The remainder is the number of books that will not fit on the bookcase. Use the remainder as the answer.
4 books will not fit on the bookcase.PR
EVIEW
INTERPRET THE REMAINDER
ADD ONE Add one to the quotient
There are 33 students in a 4th grade class. Each table in the classroom seats 6 students. How many tables will be needed to seat all students?
33 ÷ 6 = 5 r 3
There is a remainder of 3 students. Add one to the quotient so that all the students have a seat.
6 tables will be needed to seat all 33 students.
IGNOREIgnore the remainder and use only the quotient
Books are on sale for $7 each. Peter has $30.00 in his wallet. How many books can Peter buy?
30 ÷ 7 = 4 r 2
There is a remainder of 2 dollars. Peter cannot buy a book with 2 dollars. Ignore the remainder.
Peter can buy 4 books.
USE ITUse the remainder as the solution
Mary buys a new bookcase with 6 shelves. Each shelf holds 8 books. If Mary has 52 books, how many books will not fit on the bookcase?
52 ÷ 6 = 8 r 4
The remainder is the number of books that will not fit on the bookcase. Use the remainder as the answer.
4 books will not fit on the bookcase.
INTERPRET THE REMAINDER
ADD ONE Add one to the quotient
There are 33 students in a 4th grade class. Each table in the classroom seats 6 students. How many tables will be needed to seat all students?
33 ÷ 6 = 5 r 3
There is a remainder of 3 students. Add one to the quotient so that all the students have a seat.
6 tables will be needed to seat all 33 students.
IGNOREIgnore the remainder and use only the quotient
Books are on sale for $7 each. Peter has $30.00 in his wallet. How many books can Peter buy?
30 ÷ 7 = 4 r 2
There is a remainder of 2 dollars. Peter cannot buy a book with 2 dollars. Ignore the remainder.
Peter can buy 4 books.
USE ITUse the remainder as the solution
Mary buys a new bookcase with 6 shelves. Each shelf holds 8 books. If Mary has 52 books, how many books will not fit on the bookcase?
52 ÷ 6 = 8 r 4
The remainder is the number of books that will not fit on the bookcase. Use the remainder as the answer.
4 books will not fit on the bookcase.
PREVIEW
PLACE VALUE
STANDARD FORM 1,865,732
one million, eight hundred sixty-five thousand, seven hundred thirty-two
1,000,000 + 800,000 + 60,000 +5,000 + 700 + 30 + 2
WORD FORM
EXPANDED FORM
WRITING NUMBERS IN DIFFERENT FORMS
MILLIONS HUNDREDS TENS ONESTHOUSANDSHUNDREDTHOUSANDSTEN
THOUSANDS1 7 3 2568
PREVIEW
PLACE VALUE
STANDARD FORM 1,865,732
one million, eight hundred sixty-five thousand, seven hundred thirty-two
1,000,000 + 800,000 + 60,000 +5,000 + 700 + 30 + 2
WORD FORM
EXPANDED FORM
WRITING NUMBERS IN DIFFERENT FORMS
MILLIONS HUNDREDS TENS ONESTHOUSANDSHUNDREDTHOUSANDSTEN
THOUSANDS1 7 3 2568
PLACE VALUE
STANDARD FORM 1,865,732
one million, eight hundred sixty-five thousand, seven hundred thirty-two
1,000,000 + 800,000 + 60,000 +5,000 + 700 + 30 + 2
WORD FORM
EXPANDED FORM
WRITING NUMBERS IN DIFFERENT FORMS
MILLIONS HUNDREDS TENS ONESTHOUSANDSHUNDREDTHOUSANDSTEN
THOUSANDS1 7 3 2568
PREVIEW
GENERATE EQUIVALENT FRACTIONSMULTIPLY THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
DIVIDE THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
1 of the region is shaded. 2
If each part is split into 2 equal parts, there are 4 parts. 2 of the region is shaded. 4
Divide the region into groups of 3.
If each part is split into 3 equal parts, there are 6 parts. 3 of the region is shaded. 6
1 is equivalent to 2 and 3 2 4 6
6 is equivalent to 2 12 4
6 of the region is shaded. 12
2 is shaded. 4
Rename 1 as an equivalent fraction. 2
Rename 6 as an equivalent fraction. 12
1 = 2 2 4
1 = 3 2 6
1 = 2 = 3 2 4 6
6 = 2 12 4
1 x 2 = 2 2 x 2 4
1 x 3 = 3 2 x 3 6
6 = 6 ÷ 3 = 2 12 12 ÷ 3 4PREVIEW
GENERATE EQUIVALENT FRACTIONSMULTIPLY THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
DIVIDE THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
1 of the region is shaded. 2
If each part is split into 2 equal parts, there are 4 parts. 2 of the region is shaded. 4
Divide the region into groups of 3.
If each part is split into 3 equal parts, there are 6 parts. 3 of the region is shaded. 6
1 is equivalent to 2 and 3 2 4 6
6 of the region is shaded. 12
2 is shaded. 4
Rename 1 as an equivalent fraction. 2
Rename 6 as an equivalent fraction. 12
1 = 2 2 4
1 = 3 2 6
1 = 2 = 3 2 4 6
1 x 2 = 2 2 x 2 4
1 x 3 = 3 2 x 3 6
6 is equivalent to 2 12 4
6 = 2 12 4
6 = 6 ÷ 3 = 2 12 12 ÷ 3 4
GENERATE EQUIVALENT FRACTIONSMULTIPLY THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
DIVIDE THE NUMERATOR AND DENOMINATOR BY THE SAME NUMBER
1 of the region is shaded. 2
If each part is split into 2 equal parts, there are 4 parts. 2 of the region is shaded. 4
Divide the region into groups of 3.
If each part is split into 3 equal parts, there are 6 parts. 3 of the region is shaded. 6
1 is equivalent to 2 and 3 2 4 6
6 of the region is shaded. 12
2 is shaded. 4
Rename 1 as an equivalent fraction. 2
Rename 6 as an equivalent fraction. 12
1 = 2 2 4
1 = 3 2 6
1 = 2 = 3 2 4 6
1 x 2 = 2 2 x 2 4
1 x 3 = 3 2 x 3 6
6 is equivalent to 2 12 4
6 = 2 12 4
6 = 6 ÷ 3 = 2 12 12 ÷ 3 4
PREVIEW
MULTIPLY A FRACTION BY A WHOLE NUMBER
DRAW AN AREA MODEL USE A NUMBER LINE
PREVIEW
MULTIPLY A FRACTION BY A WHOLE NUMBER
DRAW AN AREA MODEL USE A NUMBER LINE
MULTIPLY A FRACTION BY A WHOLE NUMBER
DRAW AN AREA MODEL USE A NUMBER LINE
PREVIEW
LINE SYMMETRYA geometric figure has line symmetry if it can be folded in half so that the two halves match exactly.
The number of lines of symmetry in a regular polygon is equal to the number of sides.
3 lines of symmetry 4 lines of symmetry 5 lines of symmetry 6 lines of symmetry 8 lines of symmetry
LINES OF SYMMETRY
HorizontalDiagonal
Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Octagon
Vertical
A line of symmetry divides a shape into two parts that are congruent.
PREVIEW
LINE SYMMETRYA geometric figure has line symmetry if it can be folded in half so that the two halves match exactly.
The number of lines of symmetry in a regular polygon is equal to the number of sides.
3 lines of symmetry 4 lines of symmetry 5 lines of symmetry 6 lines of symmetry 8 lines of symmetry
LINES OF SYMMETRY
HorizontalDiagonal
Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Octagon
Vertical
A line of symmetry divides a shape into two parts that are congruent.
LINE SYMMETRYA geometric figure has line symmetry if it can be folded in half so that the two halves match exactly.
The number of lines of symmetry in a regular polygon is equal to the number of sides.
3 lines of symmetry 4 lines of symmetry 5 lines of symmetry 6 lines of symmetry 8 lines of symmetry
LINES OF SYMMETRY
HorizontalDiagonal
Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Octagon
Vertical
A line of symmetry divides a shape into two parts that are congruent.PREVIEW
