Multiply using the grid method.

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Transcription:

Multiply using the grid method.

Learning Objective Read and plot coordinates in all quadrants

DEFINITION Grid A pattern of horizontal and vertical lines, usually forming squares.

DEFINITION Coordinate grid a grid used to locate a point by its distances from 2 intersecting straight lines. 6 5 4 3 2 1 0 0 1 2 3 4 5 6

DEFINITION x axis a horizontal number line on a coordinate grid. x 0 1 2 3 4 5 6

HINT x is a cross (across ) x 0 1 2 3 4 5 6

DEFINITION y axis a vertical number line on a coordinate grid. y 6 5 4 3 2 1 0

DEFINITION Coordinates an ordered pair of numbers that give the location of a point on a grid. (3, 4) 6 5 4 3 2 1 0 (3,4) 0 1 2 3 4 5 6

HINT The first number is always the x or first letter in the alphabet. The second number is always the y the second letter in the alphabet. 6 5 4 3 2 1 0 (3,4) 0 1 2 3 4 5 6

HOW TO PLOT ORDERED PAIRS Step 1 Always find the x value first, moving horizontally y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 (2, 3) x

HOW TO PLOT ORDERED PAIRS Step 2 Starting from your new position find the y value by moving vertically (2, 3) y 6 5 4 3 2 1 0 (2,3) 0 1 2 3 4 5 6 x

HOW TO FIND ORDERED PAIRS Step 1 Find how far over horizontally the point is by counting to the right y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 (5, 4) x

HOW TO FIND ORDERED PAIRS Step 2 Now count how far vertically the point is by counting up y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 (5,4) x

WHAT IS THE ORDERED PAIR? (3,5) y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 x

WHAT IS THE ORDERED PAIR? (2,6) y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 x

WHAT IS THE ORDERED PAIR? (4,0) y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 x

WHAT IS THE ORDERED PAIR? (0,5) y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 x

WHAT IS THE ORDERED PAIR? (1,1) y 6 5 4 3 2 1 0 0 1 2 3 4 5 6 x

Learning Objective Read and plot coordinates in all quadrants

* *When the number lines are extended into the negative number lines you add 3 more quadrants to the coordinate grid. y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* * If the x is negative you move to the left of the 0. x = -2 y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* * If the y is negative you move down below the zero. y y = -3 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* * Step 1 - Plot the x number first moving to the left when the number is negative. y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 (-3, -2) x

* * Step 2 - Plot the y number moving from your new position down 2 when the number is negative. (-3, -2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* * When x is positive and y is negative, plot the ordered pair in this manner. (2, -2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* * When x is negative and y is positive, plot the ordered pair in this manner. (-2, 2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* (-3, -3) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* (-1, 2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* (1, -1) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* (2, -2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

* (-3, -2) y 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 x

Coordinates Keywords & Rules Y Axis and positioning vertical ORIGIN SECOND QUADRANT 10 9 8 7 6 5 4 3 2 y 1-10 -9-8 -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 8 9 10 x THIRD QUADRANT -1-2 -3-4 -5-6 -7-8 (4,8) FIRST QUADRANT FOURTH QUADRANT Use brackets (?,?) and remember X first Y next X Axis and positioning horizontal 32-9 -10 Mr D. Pay

YOUR TASK! Whole class investigation: Pairs plot the following coordinates on grids: ( -3, -7), (3,5), (0, -1), (1, 1), (-2, -5), (5,9), (-1, -3), (2,3). Join al l the points, what do you notice? Choose three of the points and add 3 to each of the x coordinates. Chose these three new points to each other using a different coloured pencil. Try subtracting three and drawing the new points from x coordinates. What happens if you subtract three from the y and x coordinates?

d Coordinates in 4 Quadrants. y 10 a -5,9 b 9 8 7 6 5 4 3 2 1-10 -9-8 -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 8 9 10 x a -8,9-10,4 d 6-7,4-6,2 c e c b d -10,-1-6,-1-10,-5 7 d -6,-5-6,-8 c -4,-10-5,6 d 5 a 8-2,6 a b -1,2-3,-5 c -1-2 -3-4 -5-6 -7-8 -9-10 a c b 0,-6-1,-10 d 1,0 2,7 1,4 c 2 4,-3 2,-9 a 4 6,4 b a 7,-1 d b 1 7,-6 6,-9 a c 3 8,10 8,4 b 10,7 b c 10,-6 Mr D. Pay What are the vertex coordinates of each shape? 10,-1 35

Learning Objective Recognise parallel and perpendicular faces and edges on 3.D shapes Rehearse the terms polyhedron, tetrahedron and begin to use dodecahedron.

What is the difference between a 2D shape and 3D shape? Which 3D shapes can you name?

CUBE Can you think of any objects which are the shape of a cube?

CUBOID Can you think of any objects which are the shape of a cuboid?

SPHERE Can you think of any objects which are shape of a sphere?

CONE Can you think of any objects which are the shape of a cone?

CYLINDER Can you think of any objects which are the shape of a cylinder?

SQUARE BASED PYRAMID

TRIANGULAR PRISM

What is a Polyhedron? Polyhedrons Non-Polyhedrons

Do you notice a difference? Polyhedrons Non-Polyhedrons

Polyhedrons A solid that is bounded by polygons with straight meeting faces. There are two main types of solids: Prisms and Pyramids

Face The polygons that make up the sides of a polyhedron

Edge A line segment formed by the intersection of 2 faces

Vertex A point where 3 or more edges meet

Name the Polyhedron and find the number of Faces, Vertices, and Edges a. b. c.

a. b. c. F = 5 V = 5 E = 8 F = 5 V = 6 E = 9 F = 8 V = 12 E = 18

a. b. c. F = 5 V = 5 E = 8 F = 5 V = 6 E = 9 F = 8 V = 12 E = 18 Does anybody see a pattern?

Euler s Theorem F + V = E + 2

Euler s Theorem Example: F + V = E + 2

Euler s Theorem Example: F + V = E + 2 F = 6, V = 8, E = 12

Euler s Theorem Example: F + V = E + 2 F = 6, V = 8, E = 12 6 + 8 = 12 +2

Euler s Theorem Example: F + V = E + 2 F = 6, V = 8, E = 12 6 + 8 = 12 +2 14 = 14

Example: Use Euler s Theorem to find the value of n Faces: 5 Vertices: n Edges: 8

Visualise 3.D shapes from 2.D drawings and identify different nets for a closed cube.

NET 1

NET 2

NET 3

NET 4

NET 5

NET 6

NET 7

NET 8

YOUR TASK! Draw the net of an open cube using five squares. What other arrangements of five squares will also make a net which we can fold to make an open cube? Explore different arrangements. Cut them out to check they do indeed fold to create an open cube.

Nets of cubes Solutions There are 11 in total

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