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Illustrative Mathematics
Lines of Symmetry for Circles
Further your instruction on geometrical symmetry with an investigation of circles. Fourth graders come to realize that the lines of symmetry of a circle are infinite.
Illustrative Mathematics
Hexagonal Pattern of Beehives
Young geometers and biologists investigate the math of nature in an activity that is just the bee's knees. Participants will study the tessellations of hexagons in a beehive, along with the natural rationale behind the specific shape....
Odell Education
Arc Length and Area of a Sector
What do skateboarding and baked goods have in common with math? You can use them to connect half-pipe ramps and cakes to arcs and sectors. Pupils compare the lengths of three different ramp options of a skate park. They calculate the...
Arizona Department of Education
Area and Perimeter of Regular and Irregular Polygons
Extend young mathematicians' understanding of area with a geometry lesson on trapezoids. Building on their prior knowledge of rectangles and triangles, students learn how to calculate the area of trapezoids and other...
Virginia Department of Education
Exploring 3-D Geometry
Take young mathematicians on an exploration of the world of 3-D geometry with this seven-lesson unit. After first defining the terms perimeter, area, and volume and how they apply to the real world, students continue on...
EngageNY
Fundamental Theorem of Similarity (FTS)
How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...
CK-12 Foundation
Multiplying Polynomials: Binomial Cork Board
Cover the cork board with pictures of the house. The interactive provides pictures of a house to duplicate and cover a given area. The pictures' dimensions are expressed as binomials. Pupils determine the area of the cork board based...
Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the...
Noyce Foundation
Apple Farm Field Trip
Monitor the growth of young mathematicians with a comprehensive addition and subtraction assessment. Using the context of a class field trip to an apple orchard, this series of four story problems allows children to demonstrate their...
Buffalo State
A Five Day Approach to Using Technology and Manipulatives to Explore Area and Perimeter
Young mathematicians build an understanding of area and perimeter with their own two hands in a series of interactive geometry lessons. Through the use of different math manipulatives, children investigate the properties of...
Education Development Center
Language of Algebra
Don't rush into algebra, let learners visualize, guess, and predict their way to a successful math career. The introductory unit incorporates beginner algebraic concepts with shapes instead of variables. Young mathematicians use a...
Bowland
Three of a Kind
One is chance, two is a coincidence, three's a pattern. Scholars must determine similarities and differences of a regular hexagon undergoing dilation. They look at lengths, angles, areas, and symmetry.
Illustrative Mathematics
Right Triangles Inscribed in Circles II
So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...
California Education Partners
Photos
Why do all sizes of pictures not show the same thing? Class members analyze aspect ratios of various sizes of photos. They determine which sizes have equivalent ratios and figure out why some pictures need to be cropped to fit...
EngageNY
Computing Actual Lengths from a Scale Drawing
The original drawing is eight units — how big is the scale drawing? Classmates determine the scale percent between a scale drawing and an object to calculate the length of a portion of the object. They use the percent equation to find...
EngageNY
Sequencing Translations
Investigate the results of multiple translations on an image. Scholars use vectors to perform a sequence of translations in the seventh instructional activity of 18. They examine the results and determine the importance of using a...
Inside Mathematics
Population
Population density, it is not all that it is plotted to be. Pupils analyze a scatter plot of population versus area for some of the states in the US. The class members respond to eight questions about the graph, specific points and...
Inside Mathematics
Conference Tables
Pupils analyze a pattern of conference tables to determine the number of tables needed and the number of people that can be seated for a given size. Individuals develop general formulas for the two growing number patterns and...
EngageNY
Drawing Parallelograms
Construct your young mathematicians' understanding by exploring the properties and dimensions of a parallelogram through constructions. The seventh instructional activity in this 29-part series begins with individuals creating...
EngageNY
Between-Figure and Within-Figure Ratios
Tie the unit together and see concepts click in your young mathematicians' minds. Scholars apply the properties of similar triangles to find heights of objects. They concentrate on the proportions built with known measures and solve to...
Balanced Assessment
Square in Square
Challenge the class to devise a method to determine the dimensions of a rectangle inscribed in another rectangle. Pupils make connections between functions and geometry as they examine the area and perimeter of a square or...
Arizona Department of Education
Introduction to Integers
Welcome to the backward world of negative numbers. This introductory lesson teaches young mathematicians that negative numbers are simply the opposite of positive numbers as they use number lines to plot and compare...
Illustrative Mathematics
Right Triangles Inscribed in Circles I
One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...
Illustrative Mathematics
A Midpoint Miracle
Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...