2-D and 3-D Shapes, Lines and Arrows,

Angles and Protractors,

and Coordinate and Background Grids

by Brandi Crouch

Mittelstädt Elementary

Prep-work:

  • Make sure you have Mult-e-Maths installed. This program is located under All Programs>Cambridge Hitachi> Mult-e-Maths>Mult-e-Maths Toolbox
  • Use RAP in the Control Panel to install Mult-e-Maths if you don’t have it.

Tutorials for Mult-e-Maths:

2-D Shapes Tool: Model and manipulate two-dimensional shapes/plane figures

  1. Open Mult-e-Maths and click on the 2-D ShapesToolbox
  2. The first five shape buttons create circles, semi-circles, ellipses, rectangles, and squares.
  3. Clicking on the shape is just like selecting clip art. It creates handles that can be dragged to resize the shape.
  4. Some of the dimensions on rectangles can be changed by clicking on the Edit Properties button. (The rectangle has to be selected first.)
  5. The Polygon button allows you to create any closed shape with straight sides. Clicking each time will set the corners of the polygon. Clicking on the starting corner closes the shape.
  6. Shape buttons with numbers in them indicate the number of sides a regular polygon will have. These buttons can create: triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, decagons, and dodecagons.
  7. Clicking on any 2-D shape reveals the 2-D Object toolbar.
  8. Clicking on a circle or square reveals an additional toolbar for working with fractions.
  9. The 2-D Object toolbar:

    edit line border fill vert., reflect undo rotate
    properties thickness color color horiz., diag. reflection translate
    mirrors

Reflections:

  1. Select the shape, then click a mirror line button: for a vertical mirror line, for a horizontal mirror line, or for a diagonal mirror line. Then click on the sheet to insert a mirror line in the required position relative to your shape. The mirror line can be repositioned by dragging.
  2. Click your shape and then the Reflect button to reflect the shape about the mirror line. The Clear reflection button clears any reflected shapes from the sheet.

Try this:

  1. Use the Polygon button to draw a 6-sided polygon.
  2. Select the polygon and then change the line thickness to the thickest and border color to green.
  3. Change the fill color to yellow and click on the shape.
  4. Click on the vertical mirror button and place a mirror line under the polygon.
  5. Reflect it.
  6. You should have made something similar to this:

Rotations:

  1. Figures can be rotated automatically at pre-set angles and can be rotatedmanually.
  2. To rotate an object manually, select the shape and click the Rotate button .
  3. Drag the shape to rotate it about its center, which is marked by.
  4. To rotate an object automatically, select the shape and click the Rotate automatically button.
  5. The Rotation bar will appear:
  6. Use the scroll arrows on the rotation bar to set the number of degrees you wish to rotate your shape through. Then, select a clockwise or counterclockwise direction.
  7. The center of rotation can be dragged manually. The Center of rotation button will reset the center of rotation back to the center of the figure.
  8. The Reset button places the shape back in its original orientation.

Co-ordinate Grids Tool: Plotting points, lines and figures on co-ordinate grids.

  1. These tools provide a choice of three co-ordinate grids (Grid I: one quadrant; Grid II: two quadrants; Grid III: four quadrants). Click the appropriate button to insert a co-ordinate grid.
  2. The one quadrant co-ordinate grid can be used to more accurately show translations and rotations.

Translations:

  1. Figures can be translated (slid) automatically or manually.
  2. Set a coordinate grid first. Use Grid I.
  3. Create a shape on the coordinate grid.
  4. Select your shape and then click the (left) Translate manually button to open the Translate dialogue box.
  5. Click the arrows on the box to translate the shape one grid square at a time.
  6. To translate automatically, click the (right) Translate automatically button .
  7. Enter a move in the dialogue box using the scroll arrows to choose the step value and the direction arrows to choose a direction. A sequence of moves can be entered in this way.
  8. Click the Go button to translate the shape according to your instructions. A trace of the shape’s original position will remain so you can compare it with the shape’s new position.
  9. The Reset button returns the shape to its original position without removing the instructions from the dialogue box. The Clear button removes all instructions from the dialogue box without returning the shape to its original position.


Try this:

  1. Set out a Grid I coordinate grid.
  2. Use the quadrilateral button to draw an irregular, 4-sided polygon.
  3. Select the polygon, fill it red.
  4. Use the translate automatically button to slide the figure up and to the right.
  5. Your picture should be similar to this:

Lines and Arrows Tools: Modeling lines and rays

  1. Click on one of the lines or arrows buttons to draw lines and rays.
  2. Click on your line or arrow to reveal the line toolbar. Use the pop-up menus on the Line thickness , Line style and Line color buttons to produce the required appearance for your line/arrow.

3-D Shapes Tool: Modeling three-dimensional figures/objects

  1. Click on any of the shape buttons (Cuboid, Cube, Square-based Pyramid, Pentagon-based Pyramid, Hexagon-based Pyramid, Sphere, Hemi-sphere, Cone, Cylinder, Triangular Prism, Pentagonal Prism, Hexagonal Prism, Regular Tetrahedron, Regular Octahedron or Regular Dodecahedron) to create your chosen shape automatically on the sheet.
  2. Clicking on your shape creates handles that can be dragged to resize the shape.
  3. To alter the height-to-width ratio of a cone, pyramid, cylinder, prism or cuboid, select it and click on the Edit Properties button. Type in new dimension values and implement the changes by clicking on OK.
  4. Click on your 3-D shape to reveal the 3-D object toolbar.
  5. Choose a new fill color for an entire shape from the pop-up menu. Then click the shape to change it to your chosen color.
  6. Choose a new fill color for a single faceof a shape from the pop-up menu. Then click a shape’s face to change it to your chosen color.
  7. Click this button and then on a shape. Now drag the shape to rotate it.
  8. Click to show a selected 3-D shape as a ‘skeleton’ shape.

Angles and Protractor Tools: Modeling and measuring angles

  1. Click on the Angles Toolbox
  2. As with clip art, selecting the angle you draw and dragging on the handles will change the length of the “arms” of the angle as well as the angle size.
  3. Clicking on the angle you created will reveal the Angle Toolbar.

  4. Click on the Rotate button to show the size of an angle doesn’t change just because it has been spun around.
  5. Clicking on the red arc of the angle you made and then clicking on the Angle Checker will allow you to estimate the size of the angle. Click on Check to get feedback on your estimate.
  6. To find the exact size of an angle quickly, you can click on the Edit Properties button.
  7. The protractors may be used with both the Angles Toolbox and the 2-D Shape Toolbox.
  8. Use the handles around the protractor to change its size. The protractor may be dragged. It will snap to the vertex of an angle when used with the Angles Toolbox.
  9. The Zoom button is an excellent tool to help students see the protractor more easily.

Co-ordinate Grids Tool: Plotting points, lines and figures on co-ordinate grids.

  1. Click on the Co-ordinate Grids Toolbox.
  2. Elementary students will be using the Grid I (one quadrant only).
  3. Clicking on the coordinate grid will reveal the Co-ordinates Toolbar.

  4. To plot a point, choose the Cross buttonand click any gridline intersection on the grid to mark it with a cross.
  5. To identify the coordinates of a point, choose the Co-ordinates label button and click on a gridline intersection to reveal its coordinates.

Using Background Grids with the other tools:

  1. Click on the Background Toolbox button.
  2. The Background Gridtoolbarwill allow you to choose background grids of squares, triangles, or grid paper.
  3. The three grid buttons toggle on and off when you click them.
  4. There are gridline styles to choose from: solid, dashed, or dotty.
  5. The drop-downsize menu allows you to change the size of the background squares or triangles.
  6. The square grid has and additional toolbar to allow fill color to be selected.
    This is a great feature when working withmultiplication arrays or working on area.

Try this:

  1. Set out the medium-sized square grid.
  2. Use the triangle button to draw an equilateral triangle.
  3. Select the triangle, fill it red.
  4. Use the translate automatically button to slide the figure up and to the right.
  5. Rotate the triangle so the base is lined up with one of the horizontal lines on your grid. Use the handles on the triangle to resize it if necessary.
  6. Drag a protractor over the triangle. Drag the protractor so the zero mark is lined up with the triangle’s base and the crosshairs of the protractor line up with a vertex.
  7. Measure the angle. It should be 60°.
  8. Your picture should be similar to this:

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