|
What is a Tree Diagram?
A tree diagram is simply a way of representing a sequence of events. Tree diagrams are particularly useful in probability since they record all possible outcomes in a clear and uncomplicated manner. Example: Let's take a look at a simple example, flipping a coin and then rolling a die. We might want to know the probability of getting a Head and a 4. If we wanted, we could list all the possible outcomes: (H,1) (H,2) (H,3) (H,4) (H,5) (H,6) (T,1) (T,2) (T,3) (T,4) (T,5) (T,6) Probability of getting a Head and a 4: P(H,4) = 1/12 Calculating probabilities can be hard, sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do ... tree diagrams to the rescue!
https://www.mathsisfun.com/decimals.html
When comparing fractions with the same numerator but different denominators, some students will be confused by the fraction with the greater denominator and mistakenly think it is the greater fraction.
Think about sharing a whole, such as a pizza, by dividing it into equal parts. In which pizza would the parts be larger, one cut into 3 equal parts, or one cut into 5 equal parts --- would you rather have thirds or fifths..... Fractions representing more than one whole can be shown using either an improper fraction or a mixed number.
Students will be relating division to fractions.
They will order fractions on a number line, and read, write and compare and represent the place value of decimals to hundredths. They will explore equivalent decimals as well as practice multiplying and dividing decimal numbers. Similarly, they will explore equivalent fractions and patterns involving fractions. They will also relate fractions with a denominator of 10 or 100 to a decimal. coordinates practice
http://resources.oswego.org/games/BillyBug/bugcoord.html http://www.beaconlearningcenter.com/weblessons/GridGraph/default.htm Shapes can often be put together to make tessellations.
Example 1 Regular octagons (which have eight sides) will not tessellate alone but they can be combined with squares: Example 2 Rectangles and triangles can be combined: Example 3 Parallelograms and triangles can be combined: A figure and its image after a translation, a reflection or a rotation are congruent.
"Rotation" means turning around a center:The distance from the center to any point on the shape stays the same.
Every point makes a circle around the center: https://www.mathsisfun.com/geometry/rotation.html For a ROTATION - the image has a different position and orientation, but the same size and shape.
For a REFLECTION - the image has a different position and orientation, but the same size and shape. For a TRANSLATION - the image has a different position but the same size, shape and orientation. Coordinate Systems
Coordinates can be used to describe locations on a grid. On a map, coordinates refer to a square. On a grid, coordinates refer to a point. Always go ACROSS first then UP. If Across and Up are in alphabetical order, ACROSS comes FIRST - the same is true for HORIZONTAL and VERTICAL. Albert has a rectangular garden with a perimeter of 48m.
The length and width of the garden are whole numbers of metres. What might the dimensions and Area of Albert's garden be? Find all possible answers. Length Width Area 23m 1m 23 sq m 22m 2m 44 sq m 21m 3m 63 sq m 20m 4m 80 sq m 19m 5m 95 sq m 18m 6m 108 sq m 17m 7m 119 sq m 16m 8m 128 sq m 15m 9m 135 sq m 14m 10m 140 sq m 13m 11m 143 sq m 12m 12m 144 sq m May 19th Math Notebooks
I took a peek at the Math notebooks students were brave enough to hand in. I was looking to see who was doing the work, who was keeping a presentable notebook and a peek at how people were doing. The following students have everything to be proud of and nothing to worry about - this does not mean that their math is perfect, but in many cases, it is pretty close, it means that their Math Student Skills are EXEMPLARY: EZ, RR, ML, NP, OO, PPH, BO, GS, AM, AH, JK, RO, RC. The following students need to either pay attention to perseverance or presentation: BD, MK, AD, BR, EH, LN, SJ. The next list are kids that are doing good Math, but I can't find page numbers, dates, question numbers or make sense of their notebooks: AF, RS, CM, MP, PN. The final list are students who need to rethink their efforts - give what you can in class, try. For some of you, the math is doable, and the efforts are not made. For others the presentation is possible but efforts are not made, either way, the work leaves space for improvement: JH, JW, BCP. If you are not named here, well, there is a bigger problem going on...... Make certain you understand these kinds of questions:
Oscar's drawing room measures 12 metres by 16 metres. He wants to put a new carpet in the drawing room that cost $15 per square metre. How much will it cost for Oscar to carpet his drawing room?
Step #1 What is the question? What is the cost of the carpet? Step #2 we can find the area of the drawing room (how much carpet is needed) by using the formula Area = 12m x 16m = 192 metres squared Step #3 Find the cost of the carpet Total cost = Area of the drawing room x cost per square metre Total cost = 192 x $15 = $2 880 Answer is cost of the carpet $2880. Ways to calculate the Area of the grass in the backyard:
TOTAL BACKYARD LxW = unit squared AREA of each item _+_+_ = unit squared Total backyard - 3 items = grass Total grass ____ unit squared BONUS (Can you convert that final number to a different metric measurement?) Yesterday students checked each other's project designs. Corrections were assigned. Today students are asked to determine the area of the grass (not the garden, patio or pool).
Although they had great difficulty getting started, students outlined the perimeter of their fictional backyard.
Using rectangles, they then designed a backyard including: a pool a garden a patio They decided on a scale for a legend. And they calculated and recorded the dimensions, perimeter and area of each region. We use linear dimensions to find the perimeter and area. To find the perimeter of a figure, you measure its side lengths, then add them. If you want to find the perimeter of a rectangle, you can use a formula such as (length x width) x2. Area tells you how much space is inside a figure. Area is measured in square units. A fast way to find the area of a rectangle is to multiply its length times its width. LOOK FORS - accurate lengths, sections - accurate communication - neat presentation (rulers) _http://www.mathplayground.com/area_perimeter.html
The area equal to a square that is 1 centimeter on each side.
Used for measuring small areas such as on drawings. The symbol is cm2 Example: An A4 sheet is 29.7 cm by 21 cm, so has an area of 623.7 cm2 You are ready to DIVIDE by 10, 100 and 1000
http://www.bbc.co.uk/bitesize/ks3/maths/number/decimals/revision/5/ Move the decimal point to the left. Multiplying Decimals by 10 and 100
There is a similar shortcut for multiplying decimal numbers by numbers such as 10, 100, and 1000: Move the decimal point to the right as many places as there are zeros in the factor. Move the decimal point one step to the right (10 has one zero). http://www.homeschoolmath.net/teaching/d/multiply_divide_by_10_100_1000.php What is ROUNDING?
Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate but easier to use. Comparing and Ordering Decimals
https://ca.ixl.com/math/grade-5/put-decimal-numbers-in-order Equivalent Decimals
https://ca.ixl.com/math/grade-5/equivalent-decimals Equivalent decimals name the same amount. 7 tenths on a hundredths grid is 7 rows and 70 hundredths on a hundredths grid is 70 small squares, which is the same as 7 rows. Try at Home: Money Madness
A game for 2 or 3 players Materials • play money • one die The first player rolls the die and takes the number of pennies equal to the number on the die. After the player has made sure that he or she cannot 'trade up' (e.g., trade ten pennies for one dime), the player hands the die to the next player. That player does the same. If a player has ten pennies but hands the die to the next player without trading them up for a dime, the other player can call 'Money Madness' and take the ten pennies (which he or she will then trade for a dime). The game continues until a player gets to $1.00. We will shift soon into decimals and fractions.
A decimal number is just another way to write a fraction. Decimals are read in the same way as fractions are read. The decimal point separates the whole number part and the fraction part of a decimal number. For a decimal less than 1, a 0 is written in the ones place. The decimal point comes after the ones in a decimal number. It shows where the whole number part ends and the fraction part begins. Try these:
1. Mrs. Foster earns a weekly salary of $800. She saves $250, spends $370, and divides the remaining amount equally among her 3 children. How much does each child receive? 2. A florist sold 24 red roses and twice as many pink roses on Saturday. He sold 36 pink roses and half as many red roses on Sunday. How many roses did the florist sell altogether? Try these:
Math Problem Solving orange duotangs:
We did some EXCELLENT work in Math class today! Students really seemed to get a grip on the idea that making mistakes when you are trying can bring you closer to the solution!
Work these out at home, with a friend or family member - practice, practice, practice http://www.mathstories.com/strategies.htm Today's Problem Solving included:
Partitive Division - problems for which the number of sets (quotient) is known and the total (dividend) is known but how many are in each set (divisor) is not known Quotitive Division - are problems for which the number in each set (divisor) is known and the total (dividend) is known but how many sets there are (quotient) is not known Problem Solving in Math
Possible strategies include: Patterning: Keep up with your Math - practice Lesson 1 - #2, #7 Lesson 2 - #3, #5 Lesson 3 - #3, #4 Lesson 4 - #2, #6 When there is a pattern in the input numbers, there is also a pattern in the output numbers.
Sometimes the best way to solve a problem is GUESS & CHECK. 439 X 10 439 X 100 439 X 1000
4390 43900 439000 We use a base 10 number system. Multiplying by 10 moves the digits 1 place to the left, and we add a zero as a place holder.
How can you find 439 X 20 without a calculator? Math Review:
Challenge:
Is a rhombus a regular polygon? How do you know? Sometimes. A rhombus has all sides equal, pairs of parallel sides, and opposite angles equal. A square is a rhombus; it is a regular polygon because it has all sides and all angles equal. Any rhombus that is not a square is not a regular polygon. Is it possible to draw a quadrilateral with 3 obtuse angles? The text book says yes. I said that I would post this question as a bonus question in our test. The text book says that a quadrilateral can have these interior angles: 120degrees, 110degrees, 100degrees, 30degrees - can you construct it? Properties of Quadrilaterals practice:
http://teams.lacoe.edu/documentation/classrooms/amy/geometry/6-8/activities/quad_quest/quad_quest.html Today's Challenge:
A net for a cube has 6 congruent squares. How many different ways can you arrange 6 squares to form a net for a cube? Record each way on grid paper. If needed, or if you are up for an extra challenge, make the cube to show your work and confirm each arrangement forms a net. Interactive Sites to investigate nets
http://www.learner.org/interactives/geometry/3d_prisms.html https://ca.ixl.com/math/grade-5/nets-of-3-dimensional-figures Triangle Constructions
Fashion designers, builders, architects and engineers use accurate constructions (or diagrams) to communicate their ideas to others. We are learning about some of the basic constructions used in geometry. Constructing a Triangle given Two Sides and the Angle between them Step 1: Draw a line, AB, 9 cm long. Step 2: Mark an angle of 70º by placing the centre of the protractor at the point A. Step 3: Join the 70º mark and the point A. Extend the arm AC until it is 7 cm long. Step 4: Join the points B and C to obtain the required triangle ABC. We can sort and name triangles by angle measure.
An ACUTE triangle has all angles less than 90degrees. A RIGHT triangle has one 90degree angle. An OBTUSE triangle has one angle greater than 90degrees. Useful ANGLES Links with Important HELP Reminders
http://www.abcya.com/measuring_angles.htm Protractor Practice: http://www.mathplayground.com/measuringangles.html How to make a proper angle: https://www.mathsisfun.com/geometry/protractor-using.html Geometry will continue:
Videos:
Geometry: https://youtu.be/U-ANBNn_D_A Triangles: https://youtu.be/rdNfOmEiNzs Attribute Games:
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SHAP&lesson=html/object_interactives/shape_classification/use_it.html https://www.ixl.com/math/geometry/classify-triangles http://www.math-play.com/Polygon-Game.html
Taking a break from multiplication and division - but we will return to it in January - Practice your TIMES TABLES!
Geometry: 1st - Polygons can be named by the number of sides and by side length. - Polygons can be named by their vertices. - Triangles can be named by the number of equal sides. Math Help - place value is key
Interactive Multiplication Practice Multiplying 2 digit numbers by 2 digit numbers http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/mult5.shtml "check this box for help" https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-mult-div-topic/cc-4th-multiplication/v/multiplying-2-digit-numbers http://www.math-play.com/multiplication-games.html Using Mental Math to Multiply
197 X 3 = 200 X 3 = 600 3 X 3 = -9 197 X 3 = 591 5 X 45 = 5 X 40 = 200 We were suppose to add 5 forty-five times. We only added 5 forty times. We need to add 5 five more times. 5 x 5 = 25 200 +25 5 x 45 = 225 12 x 45 10 X 45 = 450 plus 2 X 45 = 90 12 X 45 = 540 GOAL: recall multiplication/division facts up to 12x12 = 144
Different strategies and patterns can be used to master basic multiplication and division facts. Most multiplication facts have a related multiplication fact and two related division facts. What are some multiples of 10? (50, 200, 70, 8000) How can you tell if a number is a multiple of 10, 100, and 1000? (The ones digit of any multiple of 10 is 0.) Is any multiple of 100 also a multiple of 10? Hint: Underline the digits in the related basic multiplication fact. For example: 5 x 6000 = 30 000 5 x 6 = 30 5 x 6 000 = 30 000 |