SAU #35 Grade 5 Mathematics
Strand: Numbers, Numeration, Operations, and Number Theory
Broad Goals
Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system. Students will understand the meanings of and relationships between number operations and their properties. Compute accurately and efficiently and make reasonable estimates.

 

Strand: Geometry and Measurement

Broad Goals

Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

Develop spatial reasoning and visualization techniques and skills.

Students will use geometric transformations to analyze situations and solve problems.

Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

 

Strand: Data Analysis, Statistics, and Probability

Broad Goal

Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

 

Strand: Functions, Relations, and Algebra
Broad Goals
Students will recognize and describe patterns. Students will represent, analyze, and model mathematical situations and structures. Students will analyze change in various contexts.

Numbers, Numeration, Operations, and Number Theory

Broad Goal #1: Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
1.1.1 Represent a fraction or decimal, no higher than the thousandths place, using a physical model.

1.1.2 Given a positive rational number, draw and diagram a representation of that number.

1.1.3 Given a set of fractional models, name and write those that represent equivalent fractions.

1.1.4 Given a pair of fractions, determine which is greater by using physical models or illustrations.

1.1.5 Explore order relations for positive rational numbers.

1.1.6 Explore the use of different bases (e.g. base 2 and 5).

1.1.7 Identify multiples and factors of whole numbers.

1.1.8 Apply number theory to the factoring of whole numbers and the equivalency of positive rational numbers.

1.1.9 Read and write positive rational numbers.

1.1.10 Demonstrate the meaning of 10%, 25%, 50%, 75%, and 100% and their fractional and decimal equivalents.

1.1.11 Explore simple ratios.

1.1.12 Demonstrate the relationship of decimals in tenths and hundredths to fractions and vice versa.

1.1.13 Identify numbers that are divisible by 2, 3, 5, 6, 9, and 10.

1.1.14 Read and write whole numbers, including numbers in the millions.

1.1.15 Understand the place value structure of the base 10 number system.

  

 

 


EDM Unit 5

  

 

 

 

 

 

 

 

1/3 is more than 1/4

9/16 is more than 1/2

 

 

 

 

 



.25, 1/4, 25%



number of boys to girls

  

 

 


Hershey Math

 

 

 


Fraction Bars

 

Numbers, Numeration, Operations, and Number Theory

Broad Goal #2: Students will understand the meanings of and relationships between number operations and their properties.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
1.2.1 Develop an understanding of the four basic operations and the relationships among them.

 

1.2.2 Develop the concept of addition and subtraction of fractions with like denominators and decimals to the hundredths, using manipulatives.

1.2.3 Develop the associative and commutative properties for addition and multiplication

 

1.2.4 Explore the distributive property.

1.2.5 Apply the multiplicative and additive properties of zero and the multiplicative property of one.

1.2.6 Demonstrate an understanding that when a number is divided by 1, the quotient is equal to the dividend.

   One model of multiplication is repeated addition, subtraction is the inverse of addition.

 

 



(63+32) + 18 = 63 + (32 + 18)
63 x 18 = 18 x 63


6(3+2) = 6x3 + 6x2

4 + 0 = 4, 6 * 0 = 0 and 1 * 10 = 10


56 divided by 1 = 56

  

Numbers, Numeration, Operations, and Number Theory

Broad Goal #3: Compute accurately and efficiently and make reasonable estimates.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
1.3.1 Demonstrate mastery of multiplication facts with factors less than or equal to 10.

1.3.2 Multiply two-digit whole numbers by two-digit whole numbers.

1.3.3 Divide two-digit whole numbers by one or two-digit whole numbers.

1.3.4 Develop and use algorithms to add and subtract decimals.

1.3.5 Use models to introduce algorithms for multiplication of decimals.

 

1.3.6 Using physical models and illustrations, determine the sum or difference of fractions with like denominators.

1.3.7 Make appropriate estimations relating to quantity and capacity.

 

1.3.8 Use a variety of invented algorithms to solve division problems.

1.3.9 Know about and be able to use a variety of mental computation techniques.

 

1.3.10 Select and use appropriate mental computation and estimation strategies in problem solving situations and to determine the reasonableness of answers.

1.3.11 Explore the concepts behind order of operations.

    

 

 

 

 

 

 




Halves, thirds, fourths, sixths, and eighths


Given a container filled with liquid, approximately how many cups of liquid are present?

 


Using compatible numbers and applying properties of operations.

  

Geometry and Measurement

Broad Goal #1: Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
2.1.1 Identify, describe, and name properties of common two-dimensional objects.

2.1.2 Identify and describe common three-dimensional objects.

2.1.3 Draw congruent figures, using graph paper.

2.1.4 Recognize shapes that have rotation symmetry.

2.1.5 Recognize and create shapes that have reflection symmetry.

2.1.6 Identify similar figures.

2.1.7 Describe and apply the relationship among the angle and side lengths in congruent figures.

2.1.8 Define and classify angles as right, acute, obtuse, and straight.

      

 

 

 


Daily Analogies

Geometry and Measurement

Broad Goal #2: Develop spatial reasoning and visualization techniques and skills.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
2.2.1 Build and draw common two- and three- dimensional objects using manipulatives.

2.2.2 Create and describe mental images of objects and patterns.

2.2.3 Describe and build simple three-dimensional objects from two-dimensional representations.

      

Geometry and Measurement

Broad Goal #3: Students will use geometric transformations to analyze situations and solve problems.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
2.3.1 Describe the results of flips, slides, and turns on two-dimensional.

2.3.2 Recognize dilations (enlargements and shrinking).

2.3.3 Create tessellations using geometric shapes.

    


Similar figures (2 x 3 and 4 x6)

 Daily Analogies

 

Geometry and Measurement

Broad Goal #4: Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
2.4.1 Recognize, compare and apply standard and non-standard units of measurements.

2.4.2 Use a protractor to measure angles with measurements ending in 0 or 5.

2.4.3 Investigate formulas, techniques, or tools to determine the perimeter of common two-dimensional objects.

2.4.4 Select and use estimation strategies for finding areas and volumes.

2.4.5 Choose appropriate units of linear measure and convert between like units.

 

 

2.4.6 Create scale drawings keeping sides in proportion.

    

 

 

 

 

 

 

Feet and yard, within English and metric systems.



Scale factor to be kept to a small whole number.

  

Geometry and Measurement

Broad Goal #5: Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

5th Grades
Student Outcomes Alignment Examples Resources/Activities
2.5.1 Compare standard and non-standard units of measurement for weight.

2.5.2 Estimate the attributes of capacity using standards units of measure.

2.5.3 Measure weights, times, and temperatures using appropriate units.

2.5.4 Create simple maps and timelines.

2.5.5 Identify hour and half-hour intervals including movement from A.M. to P.M.

 

2.5.6 Determine how much time has passed in a given hour or half-hour intervals, including both A.M. and P.M

2.5.7 Investigate using time zones on maps.

    

 

 

 

 

 

 

 

How much time has passed from 9:30 A.M. to 2:00 P.M.

  

Data Analysis, Statistics, and Probability

Broad Goal #1: Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
3.1.1 Construct and interpret line plots.

3.1.2 Introduce frequency distributions.

3.1.3 Select appropriate data to solve simulations and real world problems.

3.1.4 Demonstrate an understanding of median, mode, and range.

3.1.5 Given a set of two-digit numbers, calculate the mean.

3.1.6 Make predictions, inferences, and decisions based on the interpretation of data.

 

3.1.7 Introduce representing the likelihood of an event by a number.

    

 

 

 

 

 

 

 



2 times more likely

  

Functions, Relations, and Algebra

Broad Goal #1: Students will recognize and describe patterns.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
4.1.1 Recognize, describe, extend, generalize, and create a wide variety of patterns, using models, tables, and simple rules.

4.1.2 Use calculators and computers to create patterns.

      

Functions, Relations, and Algebra

Broad Goal #2: Students will represent, analyze, and model mathematical situations and structures.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
4.2.1 Introduce situations, number patterns, and inequalities with standard algebraic notations.

4.2.2 Introduce the notion of a variable as an unknown quantity represented by a letter or symbol.

4.2.3 Plot positive whole numbers on a coordinate system.

4.2.4 Analyze simple linear equations with one variable using concrete materials.

4.2.5 Use reasoning and intuition to solve simple linear equations with one variable.

      

Functions, Relations, and Algebra

Broad Goal #3: Students will analyze change in various contexts.

5th Grade
Student Outcomes Alignment Examples Resources/Activities
4.3.1 Demonstrate an understanding of how a change in the length of a side will affect the perimeter and area of a polygon.

4.3.2 Quantify and interpret rates of change in discrete settings.

 

 

 		   

 

Cost per unit – If someone gets $7.00 allowance every 2 weeks, and another gets $4.00 per week, how much will each have at the end of 5 weeks, 10 weeks, etc.?