Overview Continued

Quarter 2 focuses on how numbers are represented, the relationships among fractions/decimals/percents and multiplication/division, patterns in our world, appropriate measurement skills, predictions, estimations, and computation in problem solving. You will develop higher level problem solving skills involving a variety of mathematical relationships, the meanings of mathematical concepts and use them to make sense of your world. You will understand expanded aspects of familiar math concepts as skills and operations from previous grades such as computation, measurements, patterns, whole numbers and parts of numbers, and estimating in problem solving will be taken to higher and more complex levels.

Quarter 3 focuses on more complex patterns, data representation and analysis, estimation in relation to computation to determine reasonableness of answer, and the relationship between the operations. The conceptual understanding of the four computational operations will be explored; how and why the operations work. As fifth graders you will gain a deeper understanding of complex linear patterns and how changing a variable changes the answer or outcome; interpret, analyze, and draw conclusions from a variety of data displays; read, interpret, analyze, and choose appropriate scales on maps, number lines, and graphs; use familiar computations to solve real world problems like pay rates; and learn the importance of estimation in determining the reasonableness and appropriateness of an answer.

Quarter 4  expands your knowledge of computation, data and graphs, and number sense. You will learn to use and explain strategies to add and subtract common fractions with like denominators; use multiplication and division to solve and evaluate the solutions/arguments of math and real world problems for reasonableness; compute money earned using pay rates; construct various displays of data given a data set; review computation of whole numbers and decimals in problem solving situations; represent fractions/decimals/percents and their equivalents; apply order of operations; and review computation of whole numbers without context in all operations.
 

Enduring Understandings are important ideas that students should carry with them years beyond the instruction received this year.

• Real life problems can be solved using the information we have learned about numbers and functions in mathematics. 

• There are relationships between fractions, decimals, and percents, and a fraction of 1/1 and 0 have meaning.

• Recognizing patterns helps us make sense of our world.

• Mathematical operations have inverses (opposite operations).

• We make predictions based on probability and/or statistics.

• Geometry builds our world by using terms to identify attributes (characteristics).

• Estimation and computation are vital skills necessary for communicating mathematical reasoning.

• Graphics are tools used to clarify data.

• Estimation and computation are vital skills necessary for communicating mathematical reasoning.

• There is more than one effective way to solve a problem.

• Commonly-used fractions can be easily added or subtracted with like denominators.
• Multiplication and division are inverse operations and can be used to evaluate solutions for reasonableness.
• Computation with decimals and money/pay rates prepares us for real life.
• Data displays help us make sense of information in our world.
• Order of operations prepares us for higher level mathematics.

Essential Questions are most important “big picture” questions students should be able to answer after completing learning activities.

• How can I solve this problem in other ways?
• How can fractions and decimals help me solve real-world problems?
• How are multiplication and division related? How do they relate to fractions and decimals?
• What are the ways to get information from different data displays?
• Why is order of operations important?

• What are factors, multiples, prime, and composite numbers? What are even, odd, prime and square numbers?

• How are fractions, decimals, and percents related? How do percentages show quantity?

• What are inverse operations?

• How do probability and statistics help us make predictions?  What are the tools and how do we use them?

• What do the probabilities of 1 and 0 mean?

• How do we make a prediction? When is it appropriate to use estimation, and how does using it help determine the reasonableness of solutions?

• How does geometric vocabulary help us describe our world?

• What is the difference between similar and congruent?

• Why is it important to be fluent at computation?

• How are computation skills and techniques used strategically in real-world situations?

• What information is necessary to solve problems?

• What can patterns reveal? How do the many types of patterns help us solve problems?

• How can graphic representations of data help us solve problems?

• Why be fluent at computation? How are computation skills and techniques used strategically in real-world situations?

• How do algorithms work in addition, subtraction, division, and multiplication?

• How does using estimation help determine the reasonableness of solutions?

• What are the inverse operations?

• What information is necessary to solve problems?

CSAP Tested Standards  Highest Frequency High Frequency Other Standards and E-Skills Highest Frequency = the timing, intensity and level of accountability is extremely high because mastery of these skills will must be demonstrated at this grade level. High Frequency = the timing, intensity and level of accountability is high because mastery of these skills is expected at this grade level. Other Standards and E-Skills = the timing, intensity, and level of mastery are not urgent. It should be introduced during this time so students can experience the concept and return in future quarters to strive towards mastery.

Standard 1: Number Sense - August
Use appropriate techniques to estimate, determine, and then justify the reasonableness of solutions to problems involving whole numbers.
Recognize and write representative numbers in different formats (i.e., 30 + 6; 20 + 16; 9 x 4 = 36).
Develop, use and explain rules about whole number (associative, commutative) properties to evaluate expressions [i.e., 5 + 3 = 3 + 5, (5 x 6) x 2 = 5 x (6 x 2)].
Use estimation strategies to determine reasonable answers in addition and subtraction.
Read and write whole numbers with whole number place value to billions and decimal place value to hundredths.
Define and understand equality and inequality.
Standard 2: Patterns and Algebra - August
Use, explain and demonstrate an understanding of addition and subtraction patterns in problem solving situations.
Standard 3: Data and Graphs - August
Read data (tables, charts, pictographs, line plots, bar graphs, circle graphs, and line graphs).
Read data from tables, charts, pictographs, line plots, bar graphs, circle and line graphs with categorical (i.e., number of pets) and numerical (i.e., heights of buildings) data.
From a given scenario, choose the correct graph from possible graph representations.
Standard 5: Measurement - August
Estimate the length of common objects.
Estimate the measure of angles (i.e., 90°, less than 90°, greater than 90°).
Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem.
Standard 6: Computation - August
Use, explain, and demonstrate the understanding of the four basic operations in problem-solving situations.
Review computation of whole numbers without context (addition, subtraction, multiplication, division)
Use, explain and demonstrate the understanding of addition and subtraction operations in problem solving situations, then justify those results with correct computations.
Use and explain a variety of estimation techniques to solve problems.
Determine from real-world problems whether an estimate or exact answer is acceptable.
Standard 1: Number Sense - September
Read, write, order, locate, and compare positive fractions, and decimal numbers to hundredths (including on a number line)Recognize pictorial representations of common fractions, decimals and percents.
Use appropriate techniques to estimate, determine, and then justify the reasonableness of solutions to problems involving whole numbers.
Show equivalence of common fractions and percents.
Use estimation strategies to determine reasonable answers in addition and subtraction.
Recognize & write representative numbers in different formats (i.e., 30+ 6; 20+16; 9x4=36).
Compare commonly used proper fractions and terminating decimals.
Define and understand equality and inequality.
Develop, use and explain rules about whole number properties (associative, commutative, distributive).
Use number sense to estimate sums and differences of fractions and decimals (i.e., 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1).
Standard 2: Patterns and Algebra - September
Analyze and describe patterns using words, tables and graphs.
Standard 3: Data and Graphs - September
Organize and construct displays of data including tables, charts, pictographs, line plots, bar graphs, circle graphs and line graphs from a given set of data using appropriate tools including technology and pencil/paper.
Analyze and draw conclusions about tables, charts, line graphs, bar graphs, pictographs, and line plots.
Read data from tables, charts, pictographs, line plots, bar graphs, circle and line graphs with categorical (i.e., number of pets) and numerical (i.e., heights of buildings) data.
Describe how data collections methods affect the nature of a data set.
Distinguish between median and mode of a set of data.
Identify mean, median, mode and range of data.
From a given scenario, choose the correct graph from possible graph representations.
Standard 4: Geometry - September
Identify, compare, and analyze two-dimensional shapes by attributes (acute angles, obtuse angles, right angles, parallel lines, perpendicular lines, intersecting lines, congruence, similarity, rays, lines, line segments, etc.)
Standard 5: Measurement - September
Determine the appropriate unit of measure (metric or US customary) when estimating distance, capacity, weight, and temperature.
Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem.
Generate a hypothesis or conjecture and solve measurement problems of appropriate complexity created from real-world problems.
Estimate the measure of angles (i.e., 90°, less than 90°, greater than 90°).
Standard 6: Computation - September
Use, explain, and demonstrate the understanding of the four basic operations in problem-solving situations.
Using number sentences and any of the four basic operations, create and illustrate “real” problems with whole numbers.
Use, explain and demonstrate the understanding of addition and subtraction operations in problem solving situations, then justify those results with correct computations.
Use and explain a variety of estimation techniques to solve problems.
Evaluate math reasoning in written and pictorial forms.
Using concrete materials or pictures, determine commonly-used percentages (i.e., 25%, 50%, etc.) in problem-solving situations.
Determine from real-world problems whether an estimate or exact answer is acceptable.
Determine whether information given in a problem is sufficient, insufficient, or extraneous.
Standard 1: Number Sense - October
Read, write, compare, order & place on a number line common fractions (i.e., ½, 1/3, 1/4/ 1/8, 1/10), decimals and percentages.
Read, write, order, locate, and compare positive fractions, and decimal numbers to hundredths (including on a number line).
Recognize pictorial representations of common fractions, decimals and percents.
Show equivalence of common fractions and percents.
Use estimation strategies to determine reasonable answers in addition and subtraction.
Compare commonly used proper fractions and terminating decimals.
Use number sense to estimate sums and differences of fractions and decimals (i.e., 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1).
Standard 2: Patterns and Algebra - October
Recognize, explain and extend a linear pattern in a problem solving situation.
Analyze and describe patterns using words, tables and graphs.
Standard 3: Data and Graphs - October
Organize and construct displays of data including tables, charts, pictographs, line plots, bar graphs, circle graphs and line graphs from a given set of data using appropriate tools.
Analyze and draw conclusions about tables, charts, line graphs, bar graphs, pictographs, and line plots.
Read data from tables, charts, pictographs, line plots, bar graphs, circle and line graphs with categorical (i.e., number of pets) and numerical (i.e., heights of buildings) data.
Describe how data collections methods affect the nature of a data set.
Distinguish between median and mode of a set of data.
Identify mean, median, mode and range of data.
Standard 4: Geometry - October
Identify, compare, and analyze two-dimensional shapes by attributes (acute angles, obtuse angles, right angles, parallel lines, perpendicular lines, intersecting lines, congruence, similarity, rays, lines, line segments, etc.)
Standard 5: Measurement - October
Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem (i.e., degree of angle, nearest ¼ inch).
Determine the appropriate unit of measure (metric or US customary) when estimating distance, capacity, weight, and temperature.
Generate a hypothesis or conjecture and solve measurement problems of appropriate complexity created from real-world problems.
Standard 6: Computation - October
Using number sentences and any of the four basic operations, create and illustrate “real” problems with whole numbers.
Use, explain, and demonstrate the understanding of the four basic operations in problem-solving situations.
Use and explain a variety of estimation techniques to solve problems.
Using concrete materials or pictures, determine commonly-used percentages (i.e., 25%, 50%, etc.) in problem-solving situations.
Determine whether information given in a problem is sufficient, insufficient, or extraneous.

Standard 1: Number Sense - November

Demonstrate equivalent relationships of common fractions and decimals using hands-on materials or pictures (i.e., ½ = 0.5 = 50%).
Using concrete materials, demonstrate the equivalence of commonly-used fractions, terminating decimals, and percents (i.e., 7/10 = 0.7).
Identify the essential components of mathematical real-world problems, using fractions and decimals.

Standard 2: Patterns and Algebra - November
In a pattern, explain how a change in one number results in a change in another number (addition, subtraction, multiplication, division within If/Then statements, In/Out boxes, function tables, rule statements).
Represent, describe and explain patterns, including variables.
Recognize that a variable is used to represent an unknown quantity.
Identify situations involving inverse relationships (i.e., more friends; fewer cookies for each person; the larger the denominator in a unit fraction, the smaller the quantity).

Standard 3: Data and Graphs - November

Using a chance device (number cube or spinner), design and explain in writing why the game is fair or unfair.
Use fractions to represent the probability of events.
Describe events such as likely or unlikely, and explain the degree of likelihood using words such as certain, equally likely, and impossible.

 Standard 4: Geometry - November

Identify, compare, and analyze two-dimensional shapes by attributes using “always” and “never” (i.e., a triangle “always” has 3 sides, but “never” 2 parallel sides).
Use geometric shapes to prove attributes and relationships between geometric shapes.
Show lines of symmetry (including multiple lines of symmetry) for geometric shapes.
Identify and build a three-dimensional shape from its two dimensional parts.
Determine whether figures are congruent or similar.

Standard 5: Measurement - November

Measure the sides of rectangles, squares, and triangles to the nearest ¼ inch and nearest centimeter.
Describe angles as acute, obtuse and right.
Identify the essential components of mathematical and real-world problems using units of measurement.

Standard 6: Computation - November

Using number sentences and any of the four basic operations, create and illustrate “real” problems with whole numbers.
Using concrete materials or pictures, determine commonly-used percentages (i.e., 25%, 50%, etc.) in problem-solving situations.
Select and use an appropriate method to solve single-step problems (i.e., mental math, estimation, paper/pencil, calculator).

Standard 1: Number Sense - December

Demonstrate meaning of square numbers using hands-on material.
Identify evens, odds, primes, composites and factors of numbers.
Describe characteristics of prime, composite, factors, multiples and square numbers (i.e., Is an even number times an even number always an even number?)
Use estimation to round numbers (money) to the nearest dollar (and in decimals) to determine reasonable answers (i.e., use of compatible numbers).

Standard 2: Patterns and Algebra - December

Use inverse relationships (i.e., 8 + _ = 15, 15 x _ = 45; 45 - _ = 15), then choose and apply to solve mathematical and real-world problems.

Standard 3: Data and Graphs - December

Use probability and statistics to identify the essential components of mathematical and real-world problems.
Use zero to represent the probability of an impossible event and one to represent the probability of a certain event.

Standard 4: Geometry - December

Identify, compare, and analyze two-dimensional shapes by attributes using “always” and “never” (i.e., a triangle “always” has 3 sides, but “never” 2 parallel sides).
Identify the essential components of mathematical real-world problems using area, perimeter and symmetry.
Solve problems involving the perimeter of polygons.
Solve problems involving the area of rectangles and squares.

Standard 6: Computation - December
Using number sentences and any of the four basic operations, create and illustrate “real” problems with whole numbers.
Select and use an appropriate method to solve single-step problems (i.e., mental math, estimation, paper/pencil, calculator).
Explain mathematical reasoning in written and pictorial forms.
Recognize the different uses parentheses have in an equation.

Standard 1: Number Sense - January

Locate on a number line, order and compare fractions, decimals (including mixed numbers) and percents.

Convert between fractions, decimals, and percents.

Determine reasonableness of answers in ordering and comparing decimals and fractions in real-world situations.

Standard 2: Patterns and Algebra - January

In a pattern, explain how a change in one number results in a change in another number (addition, subtraction, multiplication, division within If/Then statements, In/Out boxes, function tables, rule statements).

Recognize, explain and extend linear (i.e., ascending or descending pattern) and non-linear (i.e., use the rule of 4+3-2) patterns in a problem solving situation.

Match a description of a situation/pattern with its continuous graph.

Standard 3: Data and Graphs - January

Interpret, analyze, draw conclusions, and make convincing arguments from tables, charts, line graphs, circle graphs, bar graphs, pictographs and line plots.

Use fractions to represent the probability of events that are neither certain nor impossible.

Solve problems using strategies from finding all possible combinations and arrangements.

Choose and apply a strategy to solve real-world problems using probability.

Evaluate the solutions/arguments of real-world problems for reasonableness in probability.

Standard 4: Geometry - January

Given a coordinate graph, read coordinate pairs in quadrant one.

Create geometric shapes with given attributes within a coordinate plane.

Choose the coordinate graph, which represents a given data set.

Use maps and grids to locate points, create paths, and measure distances within a coordinate system.

Standard 5: Measurement – January

Read, interpret, and use/apply scales on number lines, graphs, and maps.

Select the appropriate scale (i.e., using the appropriate scale when setting up a graph).

Find the perimeter and area of rectangles and squares, using the appropriate units.

Identify the essential components of mathematical real-world problems using area, perimeter and symmetry.

Choose and apply a strategy to solve real-world problems using measurement techniques.

Standard 6: Computation - January

Demonstrate the conceptual meaning of the four basic arithmetic operations using whole numbers and decimals (including money).

Compute money earned using pay rates.

Multiply a number by two- and three-digit number using whole numbers and decimals.

Divide a three-digit number by a one-digit number, and by a two-digit number using decimals and whole numbers.

Select and use an appropriate method to solve single-step and multi-step problems (mental math, estimation, paper/pencil, diagram, calculator)

Use estimation strategies to determine reasonable answers in addition, subtraction, multiplication and division.

Use, explain, draw a non-linguistic representation, and demonstrate the understanding of the four basic operations in problem-solving situations.

Explain mathematical reasoning in written and pictorial forms.

Standard 1: Number Sense - February

Locate on a number line, order and compare fractions, decimals (including mixed numbers) and percents.

Convert between fractions, decimals, and percents.

Determine reasonableness of answers in ordering and comparing decimals and fractions in real-world situations.

Explain clearly the strategy used for ordering and comparing fractions and decimals.

Standard 2: Patterns and Algebra - February

Recognize, explain and extend linear (i.e., ascending or descending pattern) and non-linear (i.e., use the rule of 4+3-2) patterns in a problem solving situation.

In a pattern, explain how a change in one number results in a change in another number (addition, subtraction, multiplication, division within If/Then statements, In/Out boxes, function tables, rule statements).

Match a description of a situation/pattern with its continuous graph.

Standard 3: Data and Graphs - February

Interpret, analyze, draw conclusions, and make convincing arguments from tables, charts, line graphs, circle graphs, bar graphs, pictographs and line plots.

Use fractions to represent the probability of events that are neither certain nor impossible.

Solve problems using strategies from finding all possible combinations and arrangements.

Choose and apply a strategy to solve real-world problems using probability, then evaluate for reasonableness.

Standard 4: Geometry - February

Predict and describe the results of a flip (reflection), a slide (translation), or a turn (rotation) of a two-dimensional shape.

Given a coordinate graph, read coordinate pairs in quadrant one.

Create geometric shapes with given attributes within a coordinate plane.

Choose and apply a strategy to solve mathematical and real-world problems involving maps, grids, and the coordinate system.

Standard 5: Measurement - February

Read, interpret, and use/apply scales on number lines, graphs, and maps.

Select the appropriate scale (i.e., using the appropriate scale when setting up a graph).

Create simple scale drawings to demonstrate how changing one of the dimensions of a rectangle affects its perimeter and/or area.

Find the perimeter and area of rectangles and squares, using the appropriate units.

Choose and apply a strategy to solve real-world problems using measurement.

Standard 6: Computation - February

Use and explain strategies to add and subtract commonly-used fractions with like denominators (i.e., ¼, ½, 1/3).

Using multiplication and division to solve and evaluate the solutions/arguments of mathematical and real-world problems for reasonableness.

Compute money earned using pay rates.

Demonstrate the conceptual meaning of the four basic arithmetic operations using whole numbers and decimals (including money).

Compute money earned using pay rates.

Multiply a number by two- and three-digit number using whole numbers and decimals.

Divide a three-digit number by a one-digit number, and by a two-digit number using decimals and whole numbers.

Select and use an appropriate method to solve single-step and multi-step problems.

Use estimation strategies to determine reasonable answers in addition, subtraction, multiplication and division.

Use, explain, draw a non-linguistic representation, and demonstrate the understanding of the four basic operations in problem-solving situations.

Explain mathematical reasoning in written and pictorial forms.

Standard 1: Number Sense - March

Locate on a number line, order and compare fractions, decimals (including mixed numbers) and percents.

Convert between fractions, decimals, and percents.

Determine reasonableness of answers in ordering and comparing decimals and fractions in real-world situations.

Order and compare negative numbers.

Explain clearly the strategy used for ordering and comparing fractions and decimals.

Standard 2: Patterns and Algebra - March

Recognize, explain and extend linear (i.e., ascending or descending pattern) and non-linear (i.e., use the rule of 4+3-2) patterns in a problem solving situation.

Analyze and describe patterns using words, tables and graphs.

Recognize that a variable is used to represent an unknown quantity.

In a pattern, explain how a change in one number results in a change in another number (addition, subtraction, multiplication, division within If/Then statements, In/Out boxes, function tables, rule statements).

Match a description of a situation/pattern with its continuous graph.

Standard 3: Data and Graphs - March

Interpret, analyze, draw conclusions, and make convincing arguments from tables, charts, line graphs, circle graphs, bar graphs, pictographs and line plots.

Use fractions to represent the probability of events that are neither certain nor impossible.

Solve problems using strategies from finding all possible combinations and arrangements.

Choose and apply a strategy to solve real-world problems using probability, then evaluate for reasonableness.

Standard 4: Geometry - March

Given a coordinate graph, read coordinate pairs in quadrant one.

Create geometric shapes with given attributes within a coordinate plane.

Predict and describe the results of a flip (reflection), a slide (translation), or a turn (rotation) of a two-dimensional shape.

Choose the coordinate graph, which represents a given data set.

Choose and apply a strategy to solve mathematical and real-world problems involving maps, grids, and the coordinate system.

Standard 5: Measurement - March

Read, interpret, and use/apply scales on number lines, graphs, and maps.

Select the appropriate scale (i.e., using the appropriate scale when setting up a graph).

Create simple scale drawings to demonstrate how changing one of the dimensions of a rectangle affects its perimeter and/or area.

Find the perimeter and area of rectangles and squares, using the appropriate units.

Determine the finish time if the start time and duration are given.

Choose and apply a strategy to solve real-world problems using measurement techniques.

Standard 6: Computation - March

Use and explain strategies to add and subtract commonly-used fractions with like denominators (i.e., ¼, ½, 1/3).

Using multiplication and division to solve and evaluate the solutions/arguments of mathematical and real-world problems for reasonableness.

Compute money earned using pay rates.

Demonstrate the conceptual meaning of the four basic arithmetic operations using whole numbers and decimals (including money).

Compute money earned using pay rates.

Multiply a number by two- and three-digit number using whole numbers and decimals.

Divide a three-digit number by a one-digit number, and by a two-digit number using decimals and whole numbers.

Select and use an appropriate method to solve single-step and multi-step problems.

Use estimation strategies to determine reasonable answers in addition, subtraction, multiplication and division.

Use, explain, draw a non-linguistic representation, and demonstrate the understanding of the four basic operations in problem-solving situations.

Explain mathematical reasoning in written and pictorial forms.

Standard 1: Number Sense - April

Resources:

National Virtual Library of Manipulatives (NVLM) - K-12 math support for Number & Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability