Objective 1: Demonstrate multiple ways to represent whole numbers and decimals, from hundredths to one million, and fractions.
a. Read and write numbers in standard and expanded form.b. Demonstrate multiple ways to represent whole numbers and decimals by using models and symbolic representations (e.g., 36 is the same as the square of six, three dozen, or 9 x 4).
Objective 3: Model and illustrate meanings of multiplication and division of whole numbers and the addition and subtraction of fractions.
a. Model multiplication (e.g., equal-sized groups, rectangular arrays, area models, equal intervals on the number line), place value, and properties of operations to represent multiplication of a one- or two-digit factor by a two-digit factor and connect the representation to an algorithm.
b. Use rectangular arrays to interpret factoring (e.g., find all rectangular arrays of 36 tiles and relate the dimensions of the arrays to factors of 36).
c. Demonstrate the mathematical relationship between multiplication and division (e.g., 3 x ~ = 12 is the same as 12 ÷ 3 ~ and ~ 4) and use that relationship to explain that division by zero is not possible.
d. Represent division of a three-digit dividend by a one-digit divisor, including whole number remainders, using a variety of methods (e.g., rectangular arrays, manipulatives, pictures), and connect the representation to an algorithm.
e. Use models to add and subtract simple fractions where one single-digit denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4; 3/4 - 1/8).
Objective 4: Solve problems involving multiplication and division of whole numbers and addition and subtraction of simple fractions and decimals.
a. Use estimation, mental math, paper and pencil, and calculators to perform mathematical
calculations and identify when to use each one appropriately.
b. Select appropriate methods to solve a single operation problem and estimate computational
results or calculate them directly, depending on the context and numbers involved in a
problem.
c. Write a story problem that relates to a given multiplication or division equation, and select
and write a number sentence to solve a problem related to the environment.
d. Solve problems involving simple fractions and interpret the meaning of the solution (e.g., A
pie has been divided into six pieces and one piece is already gone. How much of the whole
pie is there when Mary comes in? If Mary takes two pieces, how much of the whole pie has
she taken? How much of the pie is left?)
Objective 5: Compute problems involving multiplication and division of whole numbers
and addition and subtraction of simple fractions and decimals.
a. Demonstrate quick recall of basic multiplication and division facts.
b. Multiply up to a three- digit factor by a two-digit factor with fluency, using efficient
procedures.
c. Divide up to a three-digit dividend by a one-digit divisor with fluency, using efficient
procedures.
d. Add and subtract decimals and simple fractions where one single-digit denominator is 1, 2, or
3 times the other (e.g., 2/4 + 1/4
a. Read and write numbers in standard and expanded form.b. Demonstrate multiple ways to represent whole numbers and decimals by using models and symbolic representations (e.g., 36 is the same as the square of six, three dozen, or 9 x 4).
- Square Numbers
- dozen
- equations
c. Identify the place and the value of a given digit in a six-digit numeral, including decimals to hundredths, and round to the nearest tenth.d. Divide regions, lengths, and sets of objects into equal parts using a variety of models and illustrations.
e. Name and write a fraction to represent a portion of a unit whole, length, or set for halves,thirds, fourths, fifths, sixths, eighths, and tenths.
f. Identify and represent square numbers using models and symbols.
Objective 2: Analyze relationships among whole numbers, commonly used fractions, and decimals to hundredths.
a. Compare the relative size of numbers (e.g., 475 is comparable to 500; 475 is small compared to 10,000 but large compared to 98).
b. Order whole numbers up to six digits, simple fractions, and decimals using a variety ofmethods (e.g., number line, fraction pieces) and use the symbols <, >, and = to record the relationships.
c.Identify a number that is between two given numbers (e.g., 3.2 is between 3 and 4; find a number between 0.1 and 0.2).
d. Identify equivalences between fractions and decimals by connecting models to symbols.
e. Generate equivalent fractions and simplify fractions using models, pictures, and symbols.
Objective 3: Model and illustrate meanings of multiplication and division of whole numbers and the addition and subtraction of fractions.
a. Model multiplication (e.g., equal-sized groups, rectangular arrays, area models, equal intervals on the number line), place value, and properties of operations to represent multiplication of a one- or two-digit factor by a two-digit factor and connect the representation to an algorithm.
b. Use rectangular arrays to interpret factoring (e.g., find all rectangular arrays of 36 tiles and relate the dimensions of the arrays to factors of 36).
c. Demonstrate the mathematical relationship between multiplication and division (e.g., 3 x ~ = 12 is the same as 12 ÷ 3 ~ and ~ 4) and use that relationship to explain that division by zero is not possible.
d. Represent division of a three-digit dividend by a one-digit divisor, including whole number remainders, using a variety of methods (e.g., rectangular arrays, manipulatives, pictures), and connect the representation to an algorithm.
e. Use models to add and subtract simple fractions where one single-digit denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4; 3/4 - 1/8).
Objective 4: Solve problems involving multiplication and division of whole numbers and addition and subtraction of simple fractions and decimals.
a. Use estimation, mental math, paper and pencil, and calculators to perform mathematical
calculations and identify when to use each one appropriately.
b. Select appropriate methods to solve a single operation problem and estimate computational
results or calculate them directly, depending on the context and numbers involved in a
problem.
c. Write a story problem that relates to a given multiplication or division equation, and select
and write a number sentence to solve a problem related to the environment.
d. Solve problems involving simple fractions and interpret the meaning of the solution (e.g., A
pie has been divided into six pieces and one piece is already gone. How much of the whole
pie is there when Mary comes in? If Mary takes two pieces, how much of the whole pie has
she taken? How much of the pie is left?)
Objective 5: Compute problems involving multiplication and division of whole numbers
and addition and subtraction of simple fractions and decimals.
a. Demonstrate quick recall of basic multiplication and division facts.
b. Multiply up to a three- digit factor by a two-digit factor with fluency, using efficient
procedures.
c. Divide up to a three-digit dividend by a one-digit divisor with fluency, using efficient
procedures.
d. Add and subtract decimals and simple fractions where one single-digit denominator is 1, 2, or
3 times the other (e.g., 2/4 + 1/4
3/4; 1/3 – 1/6
1/6).