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Apply a variety of appropriate problem-solving strategies
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Apply Polya's four-step guideline for solving problems
Communicate the advantages and disadvantages of different problem-solving strategies
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Identify different sets of numbers in correlation with the number line
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Determine if a given number is counting, whole, integer, rational, and/or real
Identify counting numbers and place them on a number line
Identify whole numbers and place them on a number line
Identify integers and place them on a number line
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Represent place value using different strategies
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Represent decimal numbers using bundled objects
Represent decimal numbers using powers of ten
Represent a decimal number using appropriate rounding techniques
Compare numbers to determine which is largest by using a number line
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Communicate how to use fractions to describe parts of objects, collections, and quantities
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Determine if fractions are equivalent by changing to decimals
Determine if fractions are equivalent by changing denominators
Compare the magnitude of different fractions by converting to decimal numbers
Compare the magnitude of different fractions by using common denominators
Compare the magnitude of different fractions by using common numerators
Compare the magnitude
Express improper fractions as mixed numbers
Express mixed numbers as improper fractions
Reduce fractions to lowest terms
Plot proper fractions, improper fractions, and mixed numbers on a number line
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Communicate how to use percents to describe parts of objects, collections, and quantities
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Interpret the definition of percent
Convert fractions into percents
Convert decimals into percents
Convert percents into fractions
Convert percents into decimals
Solve percent problems for base
Solve percent problems for amount
Solve percent problems for percentage
Translate a verbally stated application involving percentages into an equivalent computation
Determine if a given problem that involves combining percentages can be solved by adding the percentages
Calculate percent increase and percent decrease in several different ways
Calculate quantities from a given percent increase or decrease
Distinguish between percent increase/decrease and percent of
Solve problems involving percent increase or decrease
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Apply different procedures used to add and subtract whole numbers, decimal numbers, and integers
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Apply the regrouping algorithm for adding and subtracting
Show the regrouping algorithm for addition using manipulatives
Show the regrouping algorithm for subtraction using manipulatives
Apply the regrouping algorithm to other bases such as time and weight when adding and subtracting
Use addition or subtraction to translate story problems
Use subtraction when comparing quantities
Use number line to add or subtract
Use manipulatives or a picture diagram to demonstrate part-part-whole problems, take-away problems, or comparison problems
Write story problems that involve addition or subtraction of negative numbers
Change a subtraction problem to a related addition problem involving the additive inverse
Relate subtraction facts to their corresponding addition facts via the four-fact (number-fact) families
Write a story problem for a given addition or subtraction problem
Describe how the associative and commutative properties of addition aid in mental math
Identify where the commutative or associative properties of addition have been used
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Apply different procedures used to add and subtract fractions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Describe how to add and subtract fractions by changing to a common denominator
Demonstrate why fractions must have common denominators in order to add and subtract
Write story problems for adding and subtracting fractions
Use pictures, manipulatives or number lines to explain the logic of writing improper fractions as mixed numbers
Use the regrouping algorithm to borrow when subtracting fractions
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Apply different procedures used to multiply whole numbers
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Use pictures or manipulatives to describe why multiplication applies to a problem exhibiting equal groups
Explain why multiplying by 10 moves each digit one place to the left
Explain why multiplying by powers of 10 moves each digit to the left an equal number of places as the exponent
Explain why we can multiply to find the area of a rectangle by drawing rectangles filled with unit squares
Explain the commutative property of multiplication by subdividing rectangles or arrays of objects in two different ways
Use the commutative property of multiplication to write a related problem
Explain why we can multiply to find the volume of a box by subdividing it into unit cubes
Explain the associative property of multiplication by subdividing boxes or groups of groups of objects in two different ways
Explain the distributive property by illustrating the total number of objects in a subdivided array in two different ways
Use the associative and commutative properties of multiplication in problems
Use the distributive property in problems
Show how the associative, commutative and distributive properties of multiplication can aid in mental math
Use subdivision to demonstrate the logic of the partial-products algorithm
Use partial products to demonstrate the logic of placing a zero in the one's column of the second line in the standard multiplication algorithm and extend this concept to any other lines needed when multiplying by larger numbers
Subdivide arrays containing groups of groups and show that the portions correspond to the lines in the standard multiplication algorithm
Compare how place value is handled in the partial-products and standard algorithms
Validate the partial-products algorithm by writing equations that use expanded forms and the distributive property
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Apply different procedures used to multiply fractions, decimals and negative numbers
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Use pictures and manipulatives to solve story problems involving fraction multiplication
Use simple story problems and pictures to show why we multiply both the numerators and denominators when multiplying fractions
Use estimation to explain where to place the decimal point in a multiplication problem
Show how decimal multiplication is used in area problems
Write story problems for decimal multiplication
Use a story to demonstrate why multiplication by a positive number and a negative number will result in a negative number
Use a story to demonstrate why multiplication by a negative number and a negative number will result in a positive number
Use commutative, associative and distributive properties to explain the rules for multiplying negative numbers
Rewrite numbers using standard and scientific notation
Use scientific notation to solve problems
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Apply different procedures used to divide whole numbers, fractions, decimals and negative numbers
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
Use the "How many groups" interpretation and the "How many in each group" interpretation to write two different story problems for the same division fact
Determine whether a division story problem should be answered exactly or with a decimal, mixed number or whole number/remainder format based on the context of the problem
Explain why division by zero is not defined
Use division to solve problems
Explain how to use the scaffold method to carry out division
Compare the scaffold method to the standard long division algorithm
Explain why zeros are sometimes necessary as place holders in the long division algorithm
Show how long division can be used to create a decimal when dividing two whole numbers
Write a story problem involving division of whole numbers that results in a decimal answer
Describe how a fraction can be represented as a division problem
Explain how long division is used to convert a fraction into a decimal
Explain why a quotient involving a whole number and remainder can be described as a mixed number
Write a story problem that requires converting an improper fraction into a mixed number