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# Grade 5 Math Standards Resources

It is recommended that teachers review activities and read the associated directions and/or lesson plan ideas prior to using them with their students. In some cases, the activities are very open-ended and are best used in conjunction with paper/pencil activities or when students are paired and working on a single computer. If the directions and/or lesson plans are not obvious, a link is provided within the description of the resource.

It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.

## 5.1 Number and Operations and Data Analysis: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.

### Use fraction models to represent the addition and subtraction of fractions with unlike denominators. Students use circle graphs to add fractions with unlike denominators.

Note: Students must do paper pencil work to figure out the common denominator for each fraction. The numerator and denominator are labeled which reinforces vocabulary. The explain button gives a good visual of the changed fractions. Fractions-Adding

Students take 2 fractions with different denominators, find a common denominator by clicking on arrows to further divide the pictures, and then use the pictures to make the new fractions for adding.

### Use decimal models, place value, and number properties to add and subtract decimals (to the thousandths). Base Block Decimals

Students use base 10 pieces to add and subtract decimals.

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### Solve problems involving the addition and subtraction of fractions and decimals. Diffy

Students find the difference between pairs of numbers on each side of a square to solve a puzzle. Students choose which kind of numbers to use (whole numbers, integers, fractions, decimals, or money).

### Use ordered pairs on coordinate graphs to specify locations and describe paths. Simple Coordinates Game

Students calculate and enter the coordinates of a randomly placed house. This activity only uses positive numbers. Simple Maze Game

Students enter coordinates to maneuver a robot through a mine field. This activity only uses positive numbers. Good for student practice after using Simple Coordinates Games.

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## 5.2 Number and Operations and Algebra: Develop an understanding of and fluency with division of whole numbers.

### Apply understanding of models for division (e.g., equal-sized groups, arrays, area models, equal intervals on the number line) and the relationship of division to multiplication to solve problems.

Number Line Arithmetic

Students use the number line to understand the effects of dividing numbers.

Note: Activity also supports addition, subtraction, and multiplication. Can be translated into
Spanish. Rectangle Division

Students explore and practice division using a grid and a labeled division problem. The relationship of multiplication to division can be shown by pairing with Rectangle Multiplication.

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## 5.3 Geometry, Measurement, and Algebra: Describe and relate two-dimensional shapes to three-dimensional shapes and analyze their properties, including volume and surface area.

### Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).

Angles

Students work with acute, right and obtuse angles that are formed from two parallel lines and one angled line.

NOTE: If you go into the instructor section it will walk you through a lesson. Congruent Triangles

Students build triangles with line segments; it is useful for developing understanding and reviewing geometric terms to describe figures.

Is is possible to have the example in a link so it's not in the list (or a drop down or PDF)? Classroom Example: Use the line segments to explore and demonstrate understanding of type of angles, intersecting lines and parallel lines. Lines can be manipulated through rotation and translation.

Peter Almeida used some of the following prompts and could see instantly who needed assistance because the screen is visible from across the room. Often other students could help others who were not clear on concepts.

1. Build three sets of intersecting line segments.

2. Identify which angles are obtuse and which are acute.

3. Make three sets of intersecting lines that are perpendicular. How many right angles should you have on your screen if each segment intersects only one other segment?

4. Build three acute angles: one very sharp, one nearly a right angle and one that is between.

5. Build three obtuse angles: one nearly a right angle, one almost a straight angle and one in between.

6. Make three sets of parallel lines: one close, one on opposite sides of the screen and one in between. How can you check if your lines are parallel? (Students discovered that they could grab the lines and drag one over the other to see if they can see only one line.)

After this exploration, students went back to exploring congruent triangles which is the intended purpose for this activity.

Geoboards

Students build, draw, and compare two-dimensional shapes to describe, classify, and understand relationships among types of two-dimensional objects using their defining properties.

NOTE: You can use these boards to do everything you would do with a standard geoboard. It would be best used with teacher guidance first and directed student exploration after.

### Find and justify relationships among the formulas for the areas of triangles and parallelograms. Triangle Explorer

Students calculate the area of a triangle on a grid. "Give Hint" allows the student to see the relationship to a rectangle.

### Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces.

Platonic Solids

Students can manipulate each shape to explore the number of faces, edges, and vertices.

NOTE: Only has cube and triangular-based pyramid included from the standard.

### Recognize volume as an attribute of three-dimensional space. Surface Area and Volume

Teacher can demonstrate the dimensions of a triangular or rectangular prism and how to find the volume of each. There are two different settings for students: explore and compute. In the explore students can adjust the height, base, and depth of the prism and see how the volume changes. The compute allows students to compute the volume of the prisms on their own and then check their answer.

Cubes

Students determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Students can change the width, depth, and height to see boxes of various sizes.

### Determine volume by finding the total number of same-sized units of volume that fill a three-dimensional shape without gaps or overlaps.

Cubes

Students determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Students can change the width, depth, and height to see boxes of various sizes.

### Recognize a cube that is one unit on an edge as the standard unit for measuring volume. Surface Area and Volume

Teacher can demonstrate the dimensions of a triangular or rectangular prism and how to find the surface area and volume of each. There are two different settings for students: explore and compute. In the explore students can adjust the height, base, and depth of the prism and see how the surface area and volume changes. The compute allows students to compute the surface area and volume of the prisms on their own and then check their answer. Isometric Drawing Tool
This site is a interactive tool that allows students to create drawings on isometric dot paper. Draw figures using edges, faces, or cubes. You can shift, rotate, color, decompose, and view in 2_D or 3_D.

The direction section is very clear and easy to use. This is a great place for exploration.

Space Blocks

This activity allows students to build figures with cubes of a given volume or surface area. There are also activities that have students unfolding a cube to determine which "net" would build the cube.

Note: The surface area activity does not allow the shapes to be rotated. One must build from back to front which does not allow students to see the back and bottom of the shape. The unfolding activity allows students to rotate the cube to see all sides.

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### Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms. Surface Area and Volume

Teacher can demonstrate the dimensions of a triangular or rectangular prism and how to find the volume of each. There are two different settings for students: explore and compute. In the explore students can adjust the height, base, and depth of the prism and see how the volume changes. The compute allows students to compute the volume of the prisms on their own and then check their answer.

Cubes

Students determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Students can change the width, depth, and height to see boxes of various sizes.

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