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  • Quadrilaterals
28 and It's Upward and Onward
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In this open-ended investigation, students use visualizing skill and work systematically to explore surface area. Learners use linking cubes to build three-dimensional objects with exactly 28 faces exposed. Ideas for implementation, extension and support are included.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
12/05/2009
Area and Perimeter
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This activity reinforces the concepts of area and perimeter and their independent relationship. Students analyze and compose shapes made from unit squares that satisfy area and perimeter specifications. Ideas for implementation, extension and support are included along with printable sheets and shape cards.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
04/05/2011
Chain of Changes
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This activity gives students practice naming and using shape and color attributes to create patterned sequences. The first challenge asks students to use attribute differences to extend a sequence. A second, more open-ended challenge asks students to maximize the length of their sequences under a further constraint. An interactive applet is provided as an alternative to physical manipulatives. The Teachers' Notes page includes suggestions for implementation and discussion questions.

Subject:
Mathematics
Material Type:
Activity/Lab
Interactive
Provider:
NRICH
Date Added:
06/05/2009
A Chain of Eight Polyhedra
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This activity gives students a chance to relate some common three-dimensional solids to their polygonal faces. The object is to put solids in a sequence in which adjacent solids have a polygonal face in common. Ideas for implementation, extension, hints and support are included along with printable cards of the polyhedra.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
06/05/2004
Data Shapes
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This activity asks students to recognize differences in shapes and sort them. They are given a set of 15 shape cards that they can sort by the criteria of color, size and shape. Ideas for implementation, extension and support are included along with a printable sheet of the cards.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
10/05/2011
The Development of Spatial and Geometric Thinking: the Importance of Instruction.
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This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.

Subject:
Mathematics
Provider:
NRICH
Author:
Jenni Way
Date Added:
11/05/2007
Fence It
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This series of problems requires students to apply their knowledge of area and perimeter to find the optimal area given a specified amount of fencing. The problems progress in difficulty as new elements are added to the situation, therefore changing the outcome. This page includes tips for getting started, solution, teachers resource page, and a printable problem page.

Subject:
Mathematics
Material Type:
Lecture Notes
Provider:
NRICH
Author:
Millenium Mathematics Project
Date Added:
11/05/2014
Fitted
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This activity gives students the chance to explore area and perimeter in a problem solving setting. Nine differently-sized squares need to be tiled into a rectangular frame of unknown proportions. Three prompts of solving strategies are provided. Ideas for implementation, extension and support are included along with a printable sheet of the problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
11/05/2011
A Flying Holiday
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In this problem students study motion along a path and the properties of a parallelogram. Students must navigate back to a starting point after traveling three legs in cardinal directions on a compass. Ideas for implementation, extension and support are included.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
05/05/2009
Fractional Triangles
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This problem helps develop an understanding of the relationship between the part and the whole. Given a square figure divided into smaller triangles, students are asked to use the pattern to divide the square into two halves, three thirds, six sixths, and nine ninths. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of of the problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
04/05/2002
Going for Games
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This article highlights a number of mathematical strategy games that are available on the NRICH website. Most have interactive versions but also can be played offline. The author explains their value in the classroom, offers suggestions for implementation and extension, and provides links to the games and to other related articles.

Subject:
Mathematics
Material Type:
Activity/Lab
Game
Teaching/Learning Strategy
Provider:
NRICH
Author:
Liz Woodham
Millennium Mathematics Project
Date Added:
11/05/2014
Halving
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This exploratory problem provides students a way to consolidate their understanding of halving and halves and gives students experience of mathematical proof. The students are given multiple images of squares split in half. The goal is to prove how they are correctly halved and to think of other ways to split a square into two halves. The Teachers' Notes page offers rationale, suggestions for implementation along with a PowerPoint presentation, discussion questions, ideas for extension and support, and printable (pdf) worksheets of the problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
09/05/2009
Leonardo of Pisa and the Golden Rectangle
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This brief article describes the number sequence of Leonardo of Pisa (Fibonacci), and its connecton to the golden ratio and rectangle. Links to related topics and a link to a printable page are included.

Subject:
Mathematics
Material Type:
Diagram/Illustration
Provider:
NRICH
Author:
NRICH team
Date Added:
11/05/2012
Let's Reflect
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This activity allows students to investigate line symmetry and reflections. Using a mirror, students locate the lines of symmetry. in a square and then proceed to find other shapes by reflecting parts of the square. Ideas for implementation, extension and support are included along with a printable worksheet of squares (.doc)

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
08/05/2003
Light Blue - Dark Blue
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This problem provides students the opportunity to explore fractions in a practical context as well as identify and explain patterns and justify their ideas. Solvers are shown a sequence of five squares shaded light blue and dark blue and are asked to find what fraction of the total area of each square is covered by light blue. They are also asked to work out what the next two squares would look like if they followed the pattern. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
NRICH
Date Added:
04/05/2003
Lines of Symmetry For Quadrilaterals
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This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Subject:
Elementary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
11/11/2012
Math Shapes with iPad - 2nd - Tri Quad Pent Hex Cube
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This lesson is focused toward 2nd Grade Math - Shapes - using iPad App Keynote. It includes triangles, quadrilaterals, pentagons, hexagons, and cubes. Time frame - 2 hours - can be expanded or reduced, taught and explored over 4 or 5 short lessonsFormat - Planned for face to face - adaptable to virtual environment - Math Talk would need to be face to face or a syncronous lessoniPad App Needed:  Keynote

Subject:
Elementary Mathematics
Material Type:
Activity/Lab
Lesson Plan
Author:
Bambi Gibson
Date Added:
12/23/2021
Maths Venn: Properties of Quadrilaterals
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How well do your students understand the properties of quadrilaterals and the vocabulary that is used to describe them? Use these Venn diagrams as a way for students to prove which quadrilateral is being described.

Subject:
Mathematics
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Provider:
Maths Venn
Author:
Craig Barton
Date Added:
10/24/2022
A Midpoint Miracle
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This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012