MATH
REGIONAL PRIORITIZED CURRICULUM
GRADE 5
Topic / Standards/Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/ Classroom Ideas / Assessment Ideas / TimeMathematical Reasoning
(Woven throughout curriculum) / 1. 1. 11. 2. 1
1. 3. 1
3. 1. 1A
3. 1. 1B
3. 1. 3
3. 1. 4A
3. 1. 4C
3. 7.1
3. 7. 2 / · What do you need to know to solve this problem?
· Can you explain your answer?
· Is there another way to solve this problem?
· What patterns do you see that can help to solve this problem?
· What relationships, similarities, etc. are there that could help you to solve this problem? / · Apply a variety of reasoning strategies
· Make and evaluate conjectures & arguments using appropriate mathematical language
· Make conclusions based on inductive & deductive reasoning
· Justify conclusions involving simple & compound statements (and/or)
· Valid & invalid arguments
· Basic language of logic (and, or, not)
· Recognize different types of patterns (bilateral, rotating, repeating, growing, etc.) / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Discuss solutions and strategies with peers
· Restate problems in own language
· Identify pertinent and irrelevant info in problems
· Construct physical representations of complex problems
· Solve a simpler version of a problem and relate to more difficult problem
· Use Venn diagrams to demonstrate simple & compound statements / · Journal entries
· Teacher observations
· Individual assessments
· Homework
· Daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics used)
Topic / Standards/
Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/ Classroom Ideas / Assessment Ideas / TimeWhole Numbers
(place value, addition & subtraction, multiplication & division, estimation) / 3. 2. 13. 2. 2
3. 2. 3
3. 3. 1
3. 3. 3
3. 3. 4
3. 6.2
3. 7. 3A
3. 7. 3B
3. 7. 3C
3. 7. 4 / · What is place value?
· How does place value help to read large numbers?
· How does knowledge of our place value system help?
· When will I use addition and subtraction skills?
· When will I need to multiply numbers?
· When will I need to divide numbers? / · Read & write numbers including decimal places from the billions to the thousandths
· Express large numbers, using powers of 10.
· Exponential notation
· Compare values
· Rounding off
· Round numbers to the nearest hundredth and up to 10,000.
· Estimate using rounding off
· Problem solve using algebraic equations
· Apply the associative, commutative, distributive, inverse, and identify properties
· Understand, represent, and use numbers in a variety of equivalent forms
· Add, subtract, multiply, and divide fractions, decimals, and integers.
· Multiply and divide by three-digit numbers.
· Grouping symbols (parentheses) to clarify the intended order of operations.
· Use distributive property to multiply mixed numbers.
· Understand basic characteristics of a variable & use variables to represent relationships
· Know when an estimation is more appropriate than an exact answer / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Demonstrate using a number line how to round off numbers to the billions place
· Reinforce place value concepts by using exponential notation
· Introduce the use of exponential form of powers of 2, 3, 5 and 10 and relate these forms to factoring
· Students show under-standing of place value by holding up the correct digit
· Use the number line to model a variety of numbers
· Use number line for rounding off activities
· Relate rounding skills to estimation.
· Students explain an estimated answer.
· Use a theme for problem solving like restaurant (menu) or banking situations with checkbooks and deposit slips
· Play War with cards laying down 2-3 cards at a time
· Identify patterns in operations
· Write and solve open sentences dealing with inverse operations, using letters as well as frames as placeholders
· Create a problem situation based on a given open sentence, using a single variable
· Review computation skills by describing and extending number patterns and sequences.
· Introduce the conventional rule for order of operations (1-parentheses, 2-exponents, 3-multiplication and division, 4-addition and subtraction) / · Journal entries
· Teacher observations (during activities that require these skills)
· Individual assessments
· Homework
· Daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics)
Topic / Standards/
Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/ Classroom Ideas / Assessment Ideas / TimeWhole Numbers
(con't.)
/ · Solve one step linear equations in one variable
· Functions and relationships with whole numbers / · Determine the effects of addition, subtraction, multiplication, and division on size and order of numbers.
Decimals
/ 3. 2. 13. 2. 4
3. 2. 5
3. 3. 1A
3. 3. 1B / · Where do you find decimals in real life?
· How do you represent fraction amounts as decimals?
· How do you know where to put the decimal point when multiplying or dividing? / · Convert fractions to decimals & visa versa
· Divide numbers with decimal in the dividend
· Place value concepts to thousandths
· Role of place value in decimal fractions
· Add, subtract, multiply, and divide decimals
· Add and subtract decimals to thousandths
· Multiply decimals to hundredths, and divide decimals to hundredths, using whole number divisors
· Round fractional and decimal numbers for estimates in computation / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Measure the area and perimeter of triangles, circles, and irregular polygons, using manipulative materials and informal methods
· Problem solve with money and measurement amounts
· Relate the algorithm of multiplying decimals to fractions
· Use graphic representations to model relationship of fractions and decimals (ex. Record first 100 days of school by shading in 1/100 of pie– that is divided into 100 slices – each day and record it fractionally and with decimals – 1/100=.01, 25/100=1/4=.25, 20/100=1/5=.20, etc.)
· Decimal activities in About Teaching Mathematics: a K-8 Resource pp.227-233
/ · Journal entries
· Teacher observations
· Individual assessments
· Homework
· Daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics used)
Topic / Standards/
Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/ Classroom Ideas / Assessment Ideas / TimeFractions
/ 3. 2. 13. 2. 2
3. 2. 4
3. 3. 1B
3. 3. 1C / · What do fractions represent?
· When do you use fractions?
· What is a prime number?
· How can prime numbers help when working with fractions?
· What do we mean by “simplify”?
· How do you recognize fractions that are of equal value?
· How is adding & subtracting fractions similar to adding & subtracting whole numbers?
· What do you need to know about adding or subtracting fractions with unlike denominators?
· When do you multiply or divide fractions in real life?
· How do you multiply fractions?
· What does division by a fraction look like? / · Recognize, read & write fractions
· Proper fractions, improper fractions, & mixed numbers
· Equivalent fractions
· Simplify fractions
· LCM & GCF
· Simplify using the GCF Prime and composite numbers
· Factoring techniques to determine common denominators
· Represent numbers as prime factors
· Add and subtract mixed numbers
· Multiply & divide common fractions & mixed numbers
· Change improper fractions to mixed numbers and vice versa
· Convert common fractions to decimal form
· Change mixed numerals to an improper fraction
· Divide a whole number by a fraction by dividing up the whole number into parts and by subtracting the fraction from the whole number
· Eratosthenes sieve
· Factor trees / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Identify prime numbers and discover patterns and concepts using a hundreds board.
· Factor trees to identify prime factors
· Use prime numbers to simplify fractions 6/8 = 2. 3/2. 2. 2 = ¾
· Demonstrate multiplying a whole number by a fraction as an addition problem
· Pie graphs to represent fractional parts
· Use graph paper to illustrate a fraction ´ a fraction
· Use with measurement (2/3 of a foot = ___ inches)
· Regroup whole numbers to fraction values of 1, and add to the fraction (5-1/3 = 4-4/3)
· Use manipulatives to demonstrate fractional parts (pattern blocks, fraction bars, fraction circles, etc.),
· Regroup improper fractions to mixed numerals
· Solve problems from real life that use fractions
· Use fractions in measurement – parts of an inch, cups/pints/quarts/gal
· Fraction activities in About Teaching Mathematics: a K-8 Resource pp.212-226 / · Journal entries
· Teacher observations (during activities that require these skills)
· Individual assessments
· Homework
· Daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics used)
Topic / Standards/
Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/Classroom Ideas
/ Assessment Ideas / TimeGraphing/
Statistics/
Probability / 3. 4. 2A
3. 4. 2B
3. 4. 3
3. 5. 6 / · When would graphing data
be useful?
· What are the different ways of graphing data?
· How do you determine how often something will probably happen?
· How can this help predict its frequency of happening?
· What is the best way to organize probability data?
· What kind of conclusion can I reach when I examine data? / · Characteristics & uses of different types of graphs (line, bar, pie, picto-, tables & charts)
· Make predictions based on sample data
· Organize data into a sample space
· Arrangements & combinations
· Understand that when predictions are based on what is known about the past, one must assume hat the conditions stay the same from the past event to the predicted future events
· Determine probabilities of independent events
· Express probabilities as fractions, decimals, or percents for theoretical & experimental situations
· Identify events with a probability equal to zero, events that are certain & events that happen sometimes
· Mean, mode, median, range
· Compute the mean, mode, median & range / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Bring in examples of graphs from a newspaper
· Graph information gathered by or from students (favorite foods, TV shows, where parents work, brands of cars, etc.)
· Use in connection with social studies, science, and projects:
- Graph social studies information from books or almanacs (population of cities, rainfall, temperature of different cities, etc.)
- Graph science information (plant growth, temperature change, etc.)
· Estimate probability of events
· Conduct probability experiments
· Examine data for highest and lowest clusters of numbers
· Probability & statistics activities in About Teaching Mathematics: a K-8 Resource pp.59-78 / · Homework
· Daily Work
· Teacher observations (during activities that require these skills)
· Student projects to gather information and graph appropriately
Topic / Standards/
Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/Classroom Ideas
/ Assessment Ideas / TimeRatios/
Proportion / 3. 2. 2
3. 4. 5A
3. 6. 2
3. 6. 6
3. 6. 8
3. 7. 7 / · What is a ration?
· Where are ratios used in real life?
· How do you use ratios? / · Find examples of ratios
· Problem solve using ratios
· Finding missing value in a proportion in which 3 of the numbers are given
· Characteristics of proportional relationships / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts / · Journal entries
· Teacher observations (during activities that require these skills)
· Individual assessments
· Homework
· Daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics used)
Measurement / 3. 5. 2
3. 5.4A
3. 5.4B
3. 5. 4C / · When, where and why would you use metric and US measurement? / · Measure length, weight, and volume using metric and US measurement
· Convert one value to another using metric charts and rations
· Add and subtract measures
· Add, subtract, and calculate elapsed time / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Use the metric chart to learn the values of the prefixes
· Create mnemonics to remember the metric system / · Journal entries
· Teacher observations (during activities that require these skills)
· Individual assessments
· Homework/daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics)
Topic / Standards/ Key Ideas/ Benchmarks / Guiding Questions /
Essential Knowledge/Skills
/ Activities / Assessment Ideas / TimeGeometry,
Coordinate Geometry,
Motion Geometry / 3. 4. 1
3. 4. 3
3. 4. 5B
3. 4. 5C
3. 5. 3
3. 7. 6
3. 7. 7A
3. 7. 7B
3. 7. 7C / · How do you organize different shapes into like groups?
· What does an angle measure?
· What do area, perimeter, and volume mean?
· How does a grid system work?
· What is the difference between the x-axis & y-axis?What is a line of symmetry?
· How do you know if a figure is similar or congruent?
· What kind of movements can you make with this figure, but not change the figure? / · Basic geometric language for describing & naming shapes
· Properties & characteristics of 2- and 3-dimensional shapes
- 2- or3- dimensionality
- symmetry
- number of faces
- types of angles (acute, obtuse, right)
· Characteristics of lines & angles
· Using a protractor to measure angles
· Scale
· Characteristics & features of rectangular coordinate system
· Visualize, represent, & transform 2- & 3-dimensional shapes
· Use of rulers, compasses & protractors to draw & measure plane geometric shapes
· Relationship between area & perimeter of various shapes / · Students use written language/illustrations to describe how solved problems
· Utilize children’s literature for motivation, introduction and problem solving of skills/concepts
· Use graph paper and blocks to demonstrate and solve area, perimeter, volume problems
· Use coordinates to find intersection points on a grid to create pictures
· Work with shapes that perform the motions of slides, flips and rotations
· Examine figures for lines of symmetry; for being congruent and similar
· Make maps & scale drawings to represent real objects or places using centimeter grids to relate scale to ratio
· Use geometric ideas to solve problems
· Use concrete & artistic activities to explore the concept of symmetry
· Use reflections, turns & slides to explore symmetry
· Explore use of protractors to measure angles / · Journal entries
· Teacher observations (during activities that require these skills)
· Individual assessments
· Homework/daily Work
· Quizzes/tests
(Should incorporate open-ended problem-solving situations, requiring students to show work and/or explain mathematics)
Integers / · How do we represent amounts less than zero? / · Horizontal number line / · Reading thermometers with temperatures that are less than zero
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