Basic geometrical objects such as polygons, circles, spheres, cones, cylinders, pyramids, cuboids and their relationships. Basic geometrical properties of these objects.
Construction of geometrical objects. Scale and its use in everyday situations.
Comparing, estimating and measuring length, area, volume, mass, time and angles using common units of measurement. Measurements using contemporary and older methods.
Symmetry in everyday life, in arts and nature and how symmetry can be constructed.
Methods for determining and estimating circumference and areas of different two-dimensional geometrical gures.
Mathematical formulation of questions based on everyday situations.
Strategies for mathematical problem-solving in everyday situations
Objective: to be able to classify quadrilaterals and triangles based on their properties Properties of Quadrilaterals (video - Khan Academy) Here are some slides on naming triangles, angles, and quadrilaterals. Textbook Pages: 197, Q. 5 198, Q. 6, 7.
Objective: We will look at finding the area and perimeter of polygons.
Using Coordinates
Objective (Teaching Point):
Find a point on a grid
Read and Plot Coordinates
Solve a problem to work out a missing coordinate
Lesson:
Projected coordinate graph on the board. Review the 4 quadrants and the positive and negative values on the axes.
Remember: when plotting or locating a point on a graph its value on the x-axis goes first then the y-axis (x,y).
Students will be asked to locate points being read out loud by the teacher and find missing points to complete shapes. ex/ plot the points for example: (-2, 4), (8, 0), (-3, -2), (0, -9).
Challenge: write the coordinates of the vertices of a triangle with area of 12 units square.
Individual Work in Class:
Page 89 - 91
Extension:
1) The ice cream store wants to locate their new shop halfway between Riverside and Fairview. Riverside is located at (2,4) on the grid shown below. Greenville is located at (12,4).
Where should the shop be located?
2) Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The starting point is at (3,1) and the ending point is at (3,9). At (3,7), there's a water station to make sure the walkers stay hydrated.
Plot the starting point, ending point, and the water station.
How far along will Aidan be in the walk when he reaches the water station?
3) Maya is putting up one of her paintings in her living room. Suppose there were a grid on the wall where each unit measured a foot. The painting is represented by the inner square and the frame is represented by the outer square. Maya places a nail so that it lies halfway across the top of the frame.
On the graph, plot the point where Maya places the nail.
Name the point by filling in the blanks.
4) A map of the local disc golf course shows the holes on a grid similar to the coordinate plane. The tee on the first hole is at the point (1,2), and the hole is at the point (8,2).
Plot the two points representing the tee and the hole.
Find the distance between them.
5) Ying is putting up one of her paintings in her living room. Suppose there were a grid on the wall where each unit measured a foot. The upper-left corner of the frame is at the point (1,8) and the upper-right corner at (7,8). The bottom-left corner is at (1,2) and the bottom-right corner at (7,2).
Plot the four corners of the frame.
What is the width of the painting plus frame?
Conclusion:
On a coordinate grid plot the points (2,10), (-4, -2).
Objective (Teaching Point): Recognize whether a shape has reflection symmetry Know about the symmetry properties of triangles and quadrilaterals Lesson: Can review with this presentation on reflection symmetry. Have the students work on problems in the textbook on pages 250 and 251. When finished with the problems, try this worksheet. They will have to reflect across the mirror line (which we will talk about more next lesson). Support: Students having trouble seeing the lines of symmetry can cut out these various shapes and try folding them to find the lines of symmetry. Extension: Students who finish the class work can symmetrically color-in this rangoli design
Transformations Objective: Review translating and reflecting shapes Reflect a shape on a mirror line that is not the x or y axis Lesson: Hand out this coordinate graph paper (print double-sided). Project the coordinate graph on the board and plot a right triangle with points A (6,6), B (6,12), and C (10,6). Have the students plot the triangle on their graphs. Have them translate (slide) the triangle 16 units left and 2 units down. What are the new coordinates for each point? A (-10,4), B (-10, 10), C (-6, 4). Now draw a mirror line at y = -2 (in Quadrant 3). Have them reflect the new triangle across the mirror line. Make sure they understand that the new points should be exactly the same distance from the mirror line as the old ones. The new points should be A (-10,-8) B (-10,-14) C (-6,-8). Now have them turn the worksheet over to the unused graph. Draw a right triangle with points A (0,0) B (0, 10) and C (5, 0). Explain that we are going to rotate, or turn, the triangle. First, we must choose a direction. clockwise (medsols OR medurs) counter-clockwise (motsols OR moturs) Let them decide the direction, and then rotate it 90 degrees about point A (0,0). Explain that when we rotate about a point, the point will keep the same coordinates, but the other points will change. Rotate another 90 degrees, and then another. Students should see that a 360 degree rotation will land the shape in exactly the same position it started in. Draw a rectangle with points A (0,18) B (0,12) C (4,12) D (4,18). Have the students rotate it 90 degrees counter-clockwise (motsols) about point B. What are the new coordinates? answer: A (-6,12) B (the same) C (0,16) D (-6,16) Support: Draw a circle on the board and label 90, 180, and 270 degrees on the circle so that students can visualize the degree of rotation. Students can also use the cut-out shapes from last week to practice physically rotating shapes on their graphs. Have them rotate the shapes on a point at the origin. Extension: Page 253 - 255 in the textbook. Conclusion: Review the names of the three transformations: translating, reflecting, and rotating.
Lesson: Explain that in the metric system we use, millimetres, centimetres, metres and km’s, see if students know how much each is, ask them what unit would best determine the length of their notebooks? distance to school? distance they walk to their next class? Display this image on the whiteboard and have students copy it into their notebooks. The 2 strategies I’ll use to solve these problems will be either to multiply/divide or to move the decimal point. When multiplying/dividing first find the conversion rate between the unit. If you are going from a larger unit to a smaller unit multiply. If you are going from a smaller unit to a larger unit divide. Present the first part of this video, pause it at: 7:50, and show put these example questions on the whiteboard: 3m = cm? 24cm = mm? 2,5km = m? cm? give students a few minutes to try to work them out on their own, then have a student come up to fill out the answer, model where necessary Present the second part of the video: from 7:50 - the end and put these example questions on the whiteboard. 65mm = cm? 345m = km? 42 800cm =km? Repeat step from above. If you are moving the decimal point, count the number of steps from the unit you are starting to the unit you want to end up at. That is the amount of spaces to move the decimal point. Below are some worksheets that are easier and more difficult. Support: Extension: Conclusion: Have each student solve the following problems. 34 cm = ___ m 561 mm = ___ m 28 m = ___ cm 49 m = ___ km
