5th Grade
Common Core Math

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Operations and Algebraic Thinking

 

 

Write and interpret numerical expressions.

1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

 

  1. Super Maths World   This is a highly visual game.  Students will be totally engaged.  You will log on as a Guest and then choose where to go.  Most of the lesson is locked down unless you sign up  4 Star
  2. Fundamentals of Algebra   You will use this  Smart Board assignment to illustrate the basic steps in Algebra.  SB Created: by Dan Hoffman
  3. Algebraic Reasoning   Learn how to think algebraically with these clever weighing scales. Levels 1 and 2 contain two scales. Level 3 is more difficult and has three scales. Your goal is to determine the weight of one or more of the objects  4 Star
  4. Algebra Puzzle Find the value of each of the three objects presented in the puzzle. The numbers given represent the sum of the objects in each row or column. Sometimes, only one object will appear in a row or column. That makes the puzzle easier to solve. Other times, you will have to look for relationships among the objects.  4 Star
  5. Problem Solving    This lesson will require quite a bit of thought
  6. Algebra Solving with weights 
Analyze patterns and relationships

3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

 

  1. Power Numbers 1  This site will allow the student to use mathematical reasoning 4 star
  2. Power Numbers 2  This site will allow the student to use mathematical reasoning. This site requires password obtained from site 1   4 star
  3. Power Numbers 3  This site will allow the student to use mathematical reasoning.  This site requires password obtained from site 2  4 star
  4. Whole Number Cruncher Similar to the original "Function Machine" but lists input and output in a table and will not let the user attempt to guess the rule on without at least having two data points.
  5. Find the Rule Game  This Cyberchase game has the player create the rule for each set of numbers.
  6. Function Machine  This online tool has you put in a number, and then it spits out a result. Your goal is to determine what the function machine is doing to the number. You can choose the type of function it uses or let it be random.
  7. Mr. Anker- 1 Number Patterns  Great site for number patterns.
  8. Mr. Anker- 2 Number Patterns  Great site for number patterns.
 

Gizmos are fun, easy to use, and flexible enough to support many different teaching styles and contexts. 

You will present to your students a visual animated manipulative allowing for an easier and faster teaching pedagogy.

You will discover this tool strategically located throughout the website.

 

Number and Operations -Base Ten

 

Understand the place value system.

1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

3. Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4. Use place value understanding to round decimals to any place.

 

 

 

  1. Glossary   This site will allow you to look up not only Place but other terms.
  2. Understanding Place Value    You will discover a website that will assist in learning place value
  3. Place Value Learning    You will again discover a website that will assist in learning place value.
  4. Mr. Anker Tests-1 on Place Value  Very good site
  5. Mr. Anker Tests-2 on Place Value  Very good site
  6. Mr. Anker Tests-3 on Place Value  Very good site
  7. Multiplying by 10 
  8. Comparing Decimals  Flash video showing how to do this.
  9. Mr. Anker writing decimals  to 10
  10. Mr. Anker writing decimals  to 100
  11. Mr. Anker writing decimals  to 1000
  12. Comparing decimals  Drag to the correct order.
  13. Comparing the order of decimals
  14. Mr. Anker which decimal has the greater value?
  15. Order and Rounding of Decimals  Choose the operation on the left.
  16. Place Value Millionaire   Play Billionaire A game for one or two people
  17. Place Value Charts  Use the place value chart to make a number.
  18. Mystery Number game

 

 Perform operations with multi-digit whole numbers and with decimals to hundredths.

 

5. Fluently multiply multi-digit whole numbers using the standard algorithm.

6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

 

  1. Divide Decimals by whole numbers What is the quotient?
  2. Add Subtract Multiply Divide Decimals
  3. Addition and subtraction with Decimals
  4. Dividing decimals by whole number  -  This lesson will explain how to divide using decimals and numbers.
 

Number and Operations-Fractions

 

Use equivalent fractions as a strategy to add and subtract fractions.

1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

 

  1. Adding fractions 
  2. Fractions - Add and Subtract   This interactive mathematics lesson shows students how to add and subtract common fractions, improper fractions, and mixed numbers. The concepts of equivalent fractions and lowest common denominator are explained. This lesson also includes math problems and a math game.
  3. Simplifying Complex Fractions
  4. Fractions   Many examples are provided
  5. Fractions Percents and decimals  Great Smart Board example in real life.  SB   4 Star
  6. Fractions and Equivalent Fractions  This interactive mathematics lesson reviews concepts such as numerators, denominators, common fractions, mixed numbers, equivalent fractions, and improper fractions. The lesson also includes several math problems that are based on real-life applications of fractions. This interactive mathematics lesson reviews concepts such as numerators, denominators, common fractions, mixed numbers, equivalent fractions.
  7. Fraction Bars Learn about fractions using fraction bars. Virtual Manipulate
  8. Fraction PiecesWork with parts and wholes to learn about fractions. Virtual Manipulate
  9. Fractions - Adding Illustrates what it means to find a common denominator and combine. Virtual Manipulate
  10. Fractions - Comparing Judge the size of fractions and plot them on a number line. Virtual Manipulate
  11. Fractions - Equivalent Illustrates relationships between equivalent fractions.  Virtual Manipulate
  12. Fractions - Visualizing Illustrate a fraction by dividing a shape and highlighting the appropriate parts. Virtual Manipulate
  13. Comparing and Ordering Fractions   This lesson teaches students how to compare and order proper fractions. It also examines the relationship between various fractions. The lesson includes parent notes, teacher notes, an assessment task, an activity sheet, and a glossary. This lesson teaches students how to compare and order proper fractions. It also examines the relationship between various fractions.
  14. Fractions Lesson   In this lesson, students work with fractions (halves, thirds, fourths, fifths and tenths) as part of a region and part of a set. They must identify the fraction shown by a diagram of a region or a set, and create a region or a set to illustrate a given fraction. They must also be able to distinguish between the numerator and the denominator of a fraction. In this lesson, students work with fractions (halves, thirds, fourths, fifths and tenths) as part of a region and part of a set.
  15. Proper Fractions  This lesson teaches students about the elements of a proper fraction and the relationship between numerator and denominator.
  16. Equivalent Fractions This lesson teaches students about equivalent fractions through a comparison of pictorial and symbolic representations.
  17.  

 

 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5. Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b =(n×a)/(n×b) to the effect of multiplying a/b by 1.

6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

 

 

 

 

  1. Surface Area and Volume In this online activity students manipulate dimensions of rectangular or triangular prisms, and watch how the surface area and volume change.
  2. 3-D Boxes  Calculate how many cubes you need to make the different 3D shapes shown with this Flash activity
  3. Making Measurements  Finalist in the 2000 STEM Project awards. Four interactive mathematical challenges inspired by the Weighing and Measuring Gallery at the Science Museum of London.
  4. Measuring the Area and Perimeter of Rectangles  Amy and her brother, Ben, explain how to find the area and perimeter of rectangles and show you how changing the perimeter of a rectangle affects its area. After the lesson, you have an opportunity to measure the length and width of a variety of rectangles and calculate the area and perimeter of each. 4 Star
  5. Triangle Explorer  In this online activity students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid.
  6. Interactive Area and Perimeter Activity Students find perimeter and area for various rectangles and discover there can be more than one correct answer
  7. Area of a Triangle This interactive web site shows how the area formula for a triangle is only dependant upon the base and height. You can alter the vertex, height, and width to see the effect on the area.
  8. Tables and Chairs  Explore rectangular and straight-line arrangements of tables, calculating the number of chairs needed to surround different arrangements. This models the concept of finding the perimeter. Be sure to click the "Help" tab to get instructions.
    (Requires Java)
  9. Mr. Anker Fractions & Decimals - 1
  10. Mr. Anker Fractions & Decimals - 2
 

Measurement and Data

 

Convert like measurement units within a given measurement system.

1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

 

  1. Measurement   This video will help student understand Measurements distance first Measurements Units and rations.

Represent and interpret data.

2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

 

 

 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

3. Recognize

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

 

  1. Mr.  Anker Tests             Measurement & Geometry 1.2 Estimate or determine the area and volume of solid ... attributes of plane and solid geometric figures and use their understanding to ... 2.0 Students use strategies, skills, and concepts in finding solutions: 2.1 Use ...
  2. Platonic Solids - Virtual Manipulative This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
  3. Prisms, Pyramids, Cones, and Cylinders This web site uses pictures and clear explanations to teach about Prisms, Pyramids, Cones, and Cylinders. When done with the review, students can take an interactive quiz over what they learned.
  4. Three Dimensional Review This web site provides a good introduction (or review) of what a three-dimensional object is. After the review, students can take an interactive quiz where they distinguish between two- and three-dimensional objects.
  5. Smart board Game Genius Geometry game
  6. Smart Board Lesson - 4 Star
  7. Super Maths World This is a highly visual game. Students will be totally engaged. 4 Star
   


Geometry

 

 Graph points on the coordinate plane to solve real-world and mathematical problems.

1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

 

 

  1. Critical Math Series  Geometry   -    This website will explain quite a bit for students.
  2. About Graphing Lines
  3. Plot Negative and positive numbers  We will use  smart board software to present this lesson.  You will also find a video to assist with this lesson.  SB    Michelle Yee is the author of this this Tutorial  4 Star
      a. 
    Video 
    Excellent Lesson  4 Star
  4. General Coordinates Game  Students investigate the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted
  5. Maze Game   Students investigate the Cartesian coordinate system by directing a robot through a mine field laid out on the plane
  6. 2-Dimensional Animation In this animation, students are shown examples of regular and irregular polygons including triangles, quadrilaterals, pentagons, hexagons and octagons...
  7. 2-Dimensional Shapes Activity-1 In this activity, students must correctly match the names of several polygons with their pictures.
  8. 2-Dimensional Shapes Activity-2 In this activity, students must correctly sort a group of regular and irregular polygons according to the number of sides.
  9. 2-Dimensional Shapes Activity-3 In this activity, students must correctly label a group of polygons according to the type of polygon.
  10. 2-Dimensional Shapes Activity-4 In this activity, students must complete sentences that describe the number of sides for each type of polygon presented.
  11. 3-D Objects and 2-D Shapes Lesson Activity-5 In this lesson, students sort 2-D shapes according to the number of sides and describe 3-D objects according to the number of faces, edges and vertices.
  12.  3-D Objects and 2-D Shapes-Explorer Activity-6 in this explorer, students must complete a variety of tasks dealing with 3-D objects and 2-D shapes, in the context of a rocket ship in outer space.
  13. 3-D Shapes Activity 1 Activity-7 In this activity, students must correctly match the names of several 3-D objects with their pictures.
  14. 3-D Shapes Activity 2 Activity-8 In this activity, students must correctly label a face, edge and vertex on a cube.
  15. 3-D Shapes Activity 3 Activity-9 In this activity, students must determine the number of faces on a cube, triangular prism and pyramid.
  16. 3-D Shapes Activity 4 Activity-10 In this activity, students must determine the number of edges on a cube, triangular prism and pyramid.
  17. 3-D Shapes Activity 5 Activity-11 In this activity, students must determine the number of vertices on a cube, triangular prism and pyramid.
  18. 3-D Shapes Animation 1 In this animation, students are shown examples of 3-D objects including a cube, prism, pyramid, cylinder, cone and sphere.
  19. 3-D Shapes Animation 2 In this animation, students are shown examples of a face, edge and vertex on a cube, prism and pyramid.
  20. 3-D Shapes Animation 3 FACES In this animation, students are shown how to count all the faces on a cube, prism or pyramid (as chosen by the student).
  21. 3-D Shapes Animation 4 EDGES In this animation, students are shown how to count all the edges on a cube, prism or pyramid (as chosen by the student).
  22. 3-D Shapes Animation 5 VERTICES In this animation, students are shown how to count all of the vertices on a cube, prism or pyramid (as chosen by the student).
  23. Game for Math shapes This site will allow the student to determine the shape of an item. Great for LCD projectors
  24. Quiz online This online quiz will allow the student to learn about different shapes and provide them with the correct answer. Great for class using an LCD projector 4 Stars
  25. Chinese Tangrams Create your own tangrams using drag and drop shapes - just like Grandfather Tang's story. You may view a gallery of samples or just create on your own!
  26. Chinese Tangrams II Recreate the tangram using shapes. Make a square, swan, cat, dinosaur, duck, phoenix, or rabbit
  27. Dots and Squares Click on the grid to draw one side of a square. Play against the computer. The object of the game is to be the player to complete the most squares
  28. Attribute Blocks – Learn color and shape concepts by sorting blocks.
  29. Platonic Solids - Virtual Manipulative This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
    (Requires Java)
    Outstanding site. You must view this prior to your students. Hold down the sift key and the color and then the side to illustrate. This is a must if you wish to use concrete and abstract instruction.
  30. Shape Game What can you make? This website will allow students to move shapes around and create using their imagination. 4 Star
  31.  

Classify two-dimensional figures into categories based on their properties.

3. Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.

For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

4. Classify two-dimensional figures in a hierarchy based on properties.

 

 

  1.   XP Math  -  You must click on Geometry to go to a section on two dimensional figures.
  2. 2D and 3D Shapes

    Platonic Solids - Virtual Manipulative This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
    (Requires Java)
    Outstanding site. You must view this prior to your students. Hold down the sift key and the color and then the side to illustrate. This is a must if you wish to use concrete and abstract instruction.