Standards

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

• 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.

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

• 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 can patterns reveal?

• 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?

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 in multiple test items on CSAP at this grade level. High Frequency = the timing, intensity and level of accountability is high because mastery of these skills will be tested 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 - 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.

October/November Unit
November/December Unit

In addition to providing homework space and time to work, you can support your fifth grader’s quarter 2 math work by encouraging your child to explain his/her math work. The concepts in quarter 2 are more sophisticated and build on what has been learned so far in elementary mathematics, so let your child take the lead in the discussion. If your child is reluctant to engage in mathematical discussion at first, have them give you a problem to solve, then check your thinking with your child. This will open up the pathways for communicating in mathematics which will prepare them for the written expression of their thinking and processing on the CSAP math test. Reading and Math Strategies for Parents - includes the top 10 strategies in each subject.