Geometry & Measurement K-6

K.3.1.1 squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres.K.3.1.2 Sort objects using characteristics such as shape, size, color and thickness.K.3.1.3 Use basic shapes and spatial reasoning to model objects in thereal-world. For example: A cylinder can be used to model a can of soup.Another example: Find as many rectangles as you can in your classroom.Record the rectangles you found by making drawings.

K.3.2.1 Use words to compare objects according to length, size,weight and position.For example: Use same, lighter, longer, above, between and next to.Another example: Identify objects that are near your desk and objects thatare in front of it. Explain why there may be some objects in both groups.K.3.2.2 Order 2 or 3 objects using measurable attributes, such aslength and weight.

1.3.1.1 Describe characteristics of two- and three-dimensionalobjects, such as triangles, squares, rectangles, circles,rectangular prisms, cylinders, cones and spheres. For example: Triangles have three sides and cubes have eight vertices(corners).1.3.1.2 Compose (combine) and decompose (take apart) two- andthree-dimensional figures such as triangles, squares,rectangles, circles, rectangular prisms and cylinders.For example: Decompose a regular hexagon into 6 equilateral triangles;build prisms by stacking layers of cubes; compose an ice cream cone bycombining a cone and half of a sphere.Another example: Use a drawing program to find shapes that can be madewith a rectangle and a triangle.

1.3.2.1 Measure the length of an object in terms of multiple copies of another objectFor example: Measure a table by placing paper clips end-to-end and counting

1.3.2.2 Tell time to the hour and half-hour.1.3.2.3 Identify pennies, nickels and dimes; find the value of a group these coins, up to one dollar.

2.3.1.1 Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).2.3.1.2 Identify and name basic two- and three-dimensional shapes,such as squares, circles, triangles, rectangles, trapezoids,hexagons, cubes, rectangular prisms, cones, cylinders and spheres.For example: Use a drawing program to show several ways that a rectangle can be decomposed into exactly three triangles.

2.3.2.1 Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.For example: It will take more paper clips than whiteboard markers tomeasure the length of a table.2.3.2.2 Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch.For example: Draw a line segment that is 3 inches long.

2.3.3.1 Tell time to the quarter-hour and distinguish between a.m. and p.m.2.3.3.2 Identify pennies, nickels, dimes and quarters. Find the valueof a group of coins and determine combinations of coins thatequal a given amount.For example: 50 cents can be made up of 2 quarters, or 4 dimes and 2nickels, or many other combinations.

3.3.1.1 Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such asright triangles, rectangles, parallelograms and trapezoids.3.3.1.2 Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons.

3.3.2.1 Use half units when measuring distances.For example: Measure a person's height to the nearest half inch.3.3.2.2 Find the perimeter of a polygon by adding the lengths of the sides 3.3.2.3 Measure distances around objects.For example: Measure the distance around a classroom, or measure a person's wrist size. .

3.3.3.1 Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.For example: Your trip began at 9:50 a.m. and ended at 3:10 p.m. How longwere you traveling?3.3.3.2 Know relationships among units of time.For example: Know the number of minutes in an hour, days in a week and months in a year.3.3.3.3 Make change up to one dollar in several different ways,including with as few coins as possible.For example: A chocolate bar costs $1.84. You pay for it with $2. Give two possible ways to make change. 3.3.3.4 Use an analog thermometer to determine temperature to thenearest degree in Fahrenheit and Celsius. For example: Read the temperature in a room with a thermometer that hasboth Fahrenheit and Celsius scales. Use the thermometer to compareCelsius and Fahrenheit readings.

6.3.1.1 Calculate the surface area and volume of prisms and useappropriate units, such as cm2 and cm3. Justify the formulas used. Justification may involve decomposition, nets or other modelsFor example: The surface area of a triangular prism can be found bydecomposing the surface into two triangles and three rectangles.6.3.1.2 Calculate the area of quadrilaterals. Quadrilaterals includesquares, rectangles, rhombuses, parallelograms, trapezoidsand kites. When formulas are used, be able to explain why they are valid.For example: The area of a kite is one-half the product of the lengths of thediagonals, and this can be justified by decomposing the kite into two triangles6.3.1.3 Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm2.

6.3.2.1 Solve problems using the relationships between the anglesformed by intersecting lines.For example: If two streets cross, forming four corners such that one of thecorners forms an angle of 120 ̊, determine the measures of the remaining three anglesAnother example: Recognize that pairs of interior and exterior angles inpolygons have measures that sum to 180 ̊.6.3.2.2 Determine missing angle measures in a triangle using the factthat the sum of the interior angles of a triangle is 180 ̊. Usemodels of triangles to illustrate this fact.For example: Cut a triangle out of paper, tear off the corners and rearrangethese corners to form a straight line.Another example: Recognize that the measures of the two acute angles in aright triangle sum to 90 ̊.6.3.2.3 Develop and use formulas for the sums of the interior anglesof polygons by decomposing them into triangles.

6.3.3.1 Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times withinmeasurement systems using appropriate units.6.3.3.2 Estimate weights, capacities and geometric measurementsusing benchmarks in measurement systems with appropriate units.For example: Estimate the height of a house by comparing to a 6-foot man standing nearby.

5.3.1.1 Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.5.3.1.2 Recognize and draw a net for a three-dimensional figure.

5.3.2.1 Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.5.3.2.2 Use various tools and strategies to measure the volume andsurface area of objects that are shaped like rectangular prisms. For example: Use a net or decompose the surface into rectangles.Another example: Measure the volume of a cereal box by using a ruler tomeasure its height, width and length, or by filling it with cereal and thenemptying the cereal into containers of known volume.5.3.2.3 Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.For example: Use cubes to find the volume of a small box.5.3.2.4 Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.

4.3.1.1 Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. 4.3.1.2 Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.

4.3.2.1 Measure angles in geometric figures and real-world objects with a protractor or angle ruler. 4.3.2.2 Compare angles according to size. Classify angles as acute,right and obtuse.For example: Compare different hockey sticks according to the anglebetween the blade and the shaft. 4.3.2.3 Understand that the area of a two-dimensional figure can befound by counting the total number of same size square unitsthat cover a shape without gaps or overlaps. Justify whylength and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squaresand viewing these as grouped into rows and columns.For example: How many copies of a square sheet of paper are needed tocover the classroom door? Measure the length and width of the door to thenearest inch and compute the area of the door. 4.3.2.4 Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.

4.3.3.1 Apply translations (slides) to figures.4.3.3.2 Apply reflections (flips) to figures by reflecting over verticalor horizontal lines and relate reflections to lines of symmetry.4.3.3.3 Apply rotations (turns) of 90 ̊ clockwise or counterclockwise.4.3.3.4 Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent.

These are two resources that I have found useful for students and parents. Sometimes it's difficult for parents to help with math homework if they haven't used some of the terms and concepts since school themselves. Both parents and students can use these resources to help them practice and learn about any math concept easily.

There are hundreds of math resources out on the web. These are a few of my favorite resources for manipulatives. Using manipulatives is a constructivist approach to learning math and most student benefit from hands-on learning.