District 11 Division of Operations & Instruction
Mathematics

Grade 5, Quarter 4: Computation and Data

Overview

In Quarter 4 of fifth grade, you will review and expand 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 set of data; 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.

 

Standards

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

  • 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?
  • Why is computational fluency important in life?
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 - 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 fro 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

Read, write, order, locate, and compare positive fractions, and decimal numbers to hundredths (including on a number line).

Read, write and locate on a number line rational numbers with whole number place value to billions and decimal place value to hundredths.

Order and compare negative numbers.

Standard 2: Patterns and Algebra - April

Recognize and continue a geometric and/or numeric pattern (6th grade item).

Translate written words into algebraic form (6th grade item).

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.

Standard 3: Data and Graphs - April

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.

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.

Distinguish between median and mode of a set of data.

Identify mean, median, mode and range of data.

Standard 4: Geometry - April

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 - April

Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem.

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

Standard 6: Computation - April

Review computation of whole numbers without context (addition, subtraction, multiplication, division).

Add and subtract decimals in problem-solving situations (6th grade item).

Use, explain and demonstrate the understanding of addition and subtraction operations in problem solving situations, then justify those results with correct computations. 

Standard 1: Number Sense - May

Represent and use fractions, decimals, and percents in a variety of models and then write the equivalencies for each model (6th grade item).

Read, write, order, locate, and compare positive fractions, and decimal numbers to hundredths (including on a number line).

Read, write and locate on a number line rational numbers with whole number place value to billions and decimal place value to hundredths.

Standard 2: Patterns and Algebra - May

Recognize and continue a geometric and/or numeric pattern (6th grade item).

Translate written words into algebraic form (6th grade item).

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.

Standard 3: Data and Graphs - May

Organize and construct a line graph, bar graph, and frequency table from a set of data (6th grade item).

Identify mean, median, mode and range of data.

Standard 4: Geometry - May

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 - May

Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem.

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

Standard 6: Computation - May

Add and subtract decimals in problem-solving situations (6th grade item).

Apply order of operations (6th grade item).

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.

Add and subtract fractions with unlike denominators.

Sample Units

March/April Unit

April/May Unit

Parents

You can support your fifth grader in mathematics in fun, no-cost ways. Have your child explain their thinking and processing as they work on homework activities. Share your strategies and thinking in solving problems and working multi-digit multiplication and division problems. If you have a short-cut, or strategy that is especially useful to you, ask your child if they would like to learn it. Gone are the days of having students learn only one way to compute or problem solve. Just being interested in your child and available for homework support will go a long way toward making your child feel competent in mathematics. Like most things, attitude and self-perception is everything. You can, if you think you can! Show your child that they absolutely can!
Reading and Math Strategies for Parents - includes the top 10 strategies in each subject.

 

Everyday Mathematics Resources Math Expressions Resources
Everyday Mathematics requires lesson by lesson presentation to preserve the spiral nature of the instruction. The page links provided on the Unit Chart are for comparison only. Teachers are advised to follow the district-determined EDM pacing calendar.
Everyday Math Games for
Fifth Grade
Click the following links to find books and games correlated to units of instruction K - 5th grades.

MX Literature Lists

MX Game Lists

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