1. Notes for the 3 rd Grading Period Mrs. Neal 6 th Advanced & 7 th Average

2. Section 5.4 Fractions and Decimals Objective –To write fractions as terminating or repeating decimals and to write decimals as fractions Vocabulary –1. Terminating decimals – decimals that stop- they have an end – have a remainder of zero Ex. ¼ =.253/8 =.375 –2. Repeating decimals – decimals that go on without end repeating the same number or series of numbers. Ex. 1/3 =.333333…6/11 =.54545454…

3. Section 5.4 Fractions and Decimals –3. Bar Notation – a way of writing an abbreviation of a repeating decimal – draw a bar over the first number or set of numbers that repeat. Ex..333333… =.3.54545454… =.54

4. Section 5.4 Fractions and Decimals How to: –Fraction changed to a Decimal Divide the numerator of the fraction by the denominator –Ex numeratornumerator ÷ denominator denominator 33 ÷ 5 = 0.6 or.6 5 66 ÷8 = 0.75 or.75 8

5. Section 5.4 Fractions and Decimals How to –Decimal changed into a Fraction Terminating decimal –The place value of the last digit becomes the value of the denominator of the fraction. The numbers following the decimal point become the numerator. Then simplify to lowest terms. –Ex.56 – the last number is six and it is in the hundredths place so 100 is the denominator and 56 is the numerator.5656 ÷ 2 = 28 ÷ 2 = 14 100 ÷ 2 = 50 ÷ 2 = 25

6. Section 5.4 Fractions and Decimals How to –Decimal changed into a Fraction Repeating decimal –Count the amount of numbers in the set of repeating numbers – that is how many nines (9) are to be used for the denominator. –EX.12121212… =.12 – two numbers are repeating so two nines are used for the denominator the numerator is the numbers that repeat. 12.3333. =.3 = 3 = 1 99 9 3

7. Section 5.5 Fractions and Percents Objective Objective –To write fractions as percents and percents as fractions Vocabulary Vocabulary –1. Ratio – a comparison of two numbers by division – comparison of the numerator to the denominator  Ways to write a ratio – 3 out of 5 people prefer rainy days –3 out of 5 or 3:5 or 3 5 –2. Percent – A ratio in which the numerator is compared to 100 ( 100 is the denominator). Any number over 100 is a percent!

8. Section 5.5 Fractions and Percents How to How to –Fraction changed to a Percent  18 = ?Make an equivalent fraction with a 30 100denominator of 100  18 ?Cross multiply then divide by the 30 100remaining number 30 100remaining number 18 x 100 ÷30 = 60 so 18 = 60 which is 60% 30 100 30 100 2 = 2 = ?= 2 x 100 ÷5 = 40 so 2 = 40% 5 5 100 5 1.1. 2.

9. Section 5.5 Fractions and Percents How to How to –Percents changed to Fractions  Put the percentage over 100 in a fraction then simplify. –40% = 40 ÷ 20 = 2 100 5 100 5 –6% = 6 ÷ 2 = 3 100 50 100 50 –24% = 24 ÷ 4 = 6 100 25 100 25

10. Sections 5.6 Percents and Decimals Objectives To write percents as decimals and to write decimals as percents. How to Change a decimal to a percent – 2 ways 1. multiply the decimal by 100 Ex.45 =.45x 100 = 45 so.45 = 45% 2. move the decimal point two places to the right Ex.45 =.45 = 45 = 45%

11. Sections 5.6 Percents and Decimals How to Change percents into decimals – 2 ways 1. divide the percent by 100 Ex 7% = 7 ÷ 100 =.07 so 7% =.07 2. move the decimal point two places to the left Ex 7% = 7 = (fill in empty space with zero) =.07

12. Section 5.8 Comparing and Ordering Rational Numbers Objective – To compare and order fractions, decimals, and percents Vocabulary  1. Common denominator – a common multiple of the denominators Ex:23 three common denominators 34of 3 and 4 are 12, 24, 36  2. Least Common Denominator – the lowest of the common multiples So 12 would be the LCD of 12, 24, and 36

13. Section 5.8 Comparing and Ordering Rational Numbers 3. Rational Numbers – numbers that can be written as a fraction – made up of whole numbers, integers, terminating and repeating decimals, fractions and percents Remember in order to compare or order rational numbers, they must be in the same form – percent form, decimal form, or fraction form.

14. Section 5.8 Comparing and Ordering Rational Numbers Ways to compare  1. Put in decimal for and compare the decimal values Ex: Compare 8/9 to 5/6  8/9 =.888… and 5/6 =.8333…  So 8/9 > 5/6  2. Find the common denominator, make equivalent fractions and compare the numerators Ex: Compare 3/5 to 5/8  3/5 = 24/40 and 5/8 = 25/40  So 5/8 > 3/5

15. Section 7.5 Fractions, Decimals, and Percents Objective  To write percents as fractions and vice versa Percents fractions and decimal are all different names that represent the same number. 80% Percent fraction4 0.8 Decimal 5

16. Section 7.5 Fractions, Decimals, and Percents How to  1. Change the fraction into a decimal by dividing the numerator by the denominator  2. Change the decimal to a percent by multiplying the decimal by 100 and add the % sign  FractionDecimalPercent  PercentDecimalFraction

17. Section 6.3 Adding and Subtracting Mixed Numbers  Objective –To add and subtract mixed numbers  2 Ways –1. Turn the mixed number into an improper fraction – find a common denom.- then add or subtract the numerators- then reduce and simplify if necessary  Example 1 419311963 9 39399 9 39399 19+63 = 82 1 99 9 99 9 += Change to improperFind common denom. and rename = Add and reduce change back to mixed # = 2 7 9 ++

18. Section 6.4 Multiplying Fractions and Mixed Numbers Objective Objective To multiply fractions and mixed numbersTo multiply fractions and mixed numbers Review Vocabulary Review Vocabulary GCF – greatest common factor – the greatest of the common factors for two or more numbersGCF – greatest common factor – the greatest of the common factors for two or more numbers Multiplying Fractions – to multiply fractions, multiply the numerators and multiply the denominators Multiplying Fractions – to multiply fractions, multiply the numerators and multiply the denominators aca x c ac3 6 3x6 18 2 bdb x d bd5 9 5x9 45 5 x = = x = ==

19. Section 6.4 Multiplying Fractions and Mixed Numbers Multiplying Mixed Numbers Multiplying Mixed Numbers Change the mixed number into an improper fraction then multiply straight across like before and reduce or change back to a mixed number Example 2 414 456 82 2 414 456 82 3 7 3 721 33 3 7 3 721 33 x 4 == == 2

20. Section 6.6 Dividing Fractions and Mixed Numbers Objective Objective –Divide fractions and mixed numbers To divide by a fraction, multiply by its multiplicative inverse To divide by a fraction, multiply by its multiplicative inverse a c a d a x d ad7 3 7 4 7x4 28 1 b d b c b x c bc8 4 8 3 8x3 24 6 1 ÷= x== ÷=x = ==

21. Section 10.1 Angles Objective –To classify and draw angles Vocabulary –1. Angle – two rays with a common endpoint –2. Degrees – unit used to measured angles –3. Vertex – the point where two rays meet – an endpoint –4. Acute angle – an angle that measures less than 90 degrees

22. Section 10.1 Angles –5. Right Angle – an angle that measures exactly 90 degrees –6. Obtuse angle – an angle that measures more than 90 degrees but less than 180 degrees –7. Straight angle – an angle that measures exactly 180 degrees – a straight line –8. Adjacent angles – two angles that share a common side Symbols –1. - symbol for angle

23. 10.3 Angle Relationships Objective  To identify and apply angle relationships Vocabulary  1. Vertical angles – opposite angles formed by two intersecting lines – they have the same measure  2. Congruent angles – angles with the same measure  3. Supplementary angles – two angles whose measures sum to 180 degrees

24.  4. Complementary angles – two angles whose measures sum to be 90 degrees Symbol  = is congruent to 1 angle 1 and angle 4 are vertical angles 3 2they are congruent to each other 4 angles 2 and 3 are vertical angles and are congruent 140 40 angles 1 and 2 equal 180 so they are supplementary angles 10.3 Angle Relationships

25. Complementary angles the angles sum is 90 55 35

26. 10.4 Triangles Objective Objective To identify and classify triangles To identify and classify triangles Vocabulary Vocabulary 1. Triangle – a figure with three sides and three angles whose sum measures 180 degrees 1. Triangle – a figure with three sides and three angles whose sum measures 180 degrees 2. Acute triangle – a triangle with all acute angles 2. Acute triangle – a triangle with all acute angles (all less than 90 degrees)

27. 10.4 Triangles 3. Right Triangle – a triangle with one right angle 3. Right Triangle – a triangle with one right angle 4. Obtuse Triangle – a triangle with one obtuse angle 4. Obtuse Triangle – a triangle with one obtuse angle 5. Scalene Triangle – a triangle with no congruent sides – all are different lengths 5. Scalene Triangle – a triangle with no congruent sides – all are different lengths 6. Isosceles triangle – a triangle with 2 congruent sides 6. Isosceles triangle – a triangle with 2 congruent sides 7. Equilateral triangle – a triangle with all 3 sides congruent 7. Equilateral triangle – a triangle with all 3 sides congruent Symbol Symbol m 1 - measure of angle 1 m 1 - measure of angle 1

28. Section 10.5 Quadrilaterals ObjectiveObjective –To identify and classify quadrilaterals VocabularyVocabulary –1. Quadrilateral – a closed figure with four sides and four angles that equal 360 degrees –2. Parallelogram – quadrilateral with opposite sides parallel and opposite sides congruent –3. Trapezoid – quadrilateral with one pair of parallel sides

29. Section 10.5 Quadrilaterals –4. Rhombus – parallelogram with 4 congruent sides –5. Rectangle – parallelogram with 4 right angles –6. Square – parallelogram with 4 right angles and 4 congruent sides

30. Section 10.5 Quadrilaterals SymbolsSymbols –> - arrows on the sides means they are parallel –/ - slashes on the sides means they are congruent

31. 10.7 Polygons and Tessellations  Objective  To classify polygons and determine which polygons can form a tessellation  Vocabulary  1. Polygon – a simple closed figure formed by three or more straight lines that do not cross.  2. Pentagon-5 sided polygon  3. Hexagon- 6 sided polygon

32. 10.7 Polygons and Tessellations  4. Heptagon - 7 sided polygon  5. Octagon - 8 sided figure  6. Nonagon - 9 sided polygon  7. Decagon - 10 sided polygon  8. Regular Polygon - a polygon that has sides congruent and all angles congruent (the same) – equilateral triangles and squares are examples.

33. 10.7 Polygons and Tessellations  9. Tessellation – a repetitive pattern of polygons that fit together with no overlaps or holes Polygons that tessellate have side numbers or degrees that go evenly into 360 degrees Divide 360 by the number of sides or the number of degrees to see if a figure can tessellate Only regular polygons can tessellate  Example soccer ball, checkerboard blanket  Formula for finding each angle measure in a polygon 180(n-2) n = number of sides n

34. Section 10.8 Translations Objective To graph translations of polygons on a coordinate plane To graph translations of polygons on a coordinate planeVocabulary 1. Transformation – a movement of a figure on a coordinate plane 1. Transformation – a movement of a figure on a coordinate plane 3 types 1.) reflection – flip over an axis 2.) rotation – turn of the figure on the graph 2.) rotation – turn of the figure on the graph 3.) translation – slide of the figure on the graph 3.) translation – slide of the figure on the graph Transformations can occur alone or as a combination

35. Section 10.8 Translations 2. Translation – Sliding motion 2. Translation – Sliding motion If slides up or down – the Y coordinate changes If slides left or right – The X coordinate changes Translations to the right or up – addition occurs Translations to the left or down – subtraction occurs Ex. The coordinates of ABC are A =(2,2) B=(5,2)C=(4,6) Translate the figure 3 units left and 2 units up A=(2-3,2+2)=(-1,4) B=(5-3,2+2)=(2,4) C=(4-3,6+2)=(1,8)

36. Section 10.9 Reflections Objective To identify figures with lines of symmetry and graph reflections on a coordinate plane Vocabulary 1. Line symmetry –a figure that when folded the halves are identical 2. Line of symmetry – a line that divides a figure into two halves that are reflections of each other 3. Reflection – a transformation in which a figure is reflected (flipped) over a line of symmetry – the X or the Y axis

37. Section 10.9 Reflections The reflections are mirror images across the x or y axis. The points should be equally spaced on either side of the axis. If the figure is reflected over the y axis, the x-coordinate changes to positive or negative

38. Section 10.9 Reflections If the figure is reflected over the x-axis the y- coordinate changes to either positive or negative Ex. Quadrilateral ABCD has vertices A(1,2) B(3,5) C(6,5) D(6,2) reflect over y axis ( x coordinate changes) A’(-1,2) B’(-3,5) C’ (-6,5) D’(-6,2)

39. Section 6.8 Geometry: Perimeter and Area  Objective  To find the perimeters and areas of figures  Vocabulary  1. Perimeter – the distance around a geometric figure – add al the side lengths together.  Perimeter of a rectangle  P= l + l + w + w or P = 2l + 2wformula l = lengthw = widthshows the relationship among quantities P= 3+3+5+5 = 16 units 3 3 5

40. Section 6.8 Geometry: Perimeter and Area  2. Area – the number of square units of space inside of a geometric figure. Uses two dimensions to calculate – EXPRESSED IN SQUARE UNITS  Area of a rectangle  A = l x wFormula - length x width  Area of a square A = S 2 Formula – s= side- so side x side A = 4 2 or 4 x 4 = 16 units 2 A = 4 2 or 4 x 4 = 16 units 2 4

41. Section 11.4 Area of Parallelograms Objective –To find the area of parallelograms Vocabulary –1. Base – any side parallelogram = b –2. Height – the length of a segment= h perpendicular to the base with endpoints on opposite sides Area = b x h Also expressed in square units base height

42. Section 11.5 Area of Triangles and Trapezoids Objective Objective To find the areas of triangles and trapezoids To find the areas of triangles and trapezoids Vocabulary Vocabulary 1. Trapezoid - quadrilateral with one pair of parallel sides. 1. Trapezoid - quadrilateral with one pair of parallel sides. Area of a triangle = A = 1 x b x h or b x h Area of a triangle = A = 1 x b x h or b x h area =.5 x base x height 22 A =.5x3x7 A = 10.5 cm sq base height 7 cm 3cm

43. Section 11.5 Area of Triangles and Trapezoids Area of a trapezoid Area of a trapezoid expressed in square units A =.5h(b 1 + b 2 ) A =.5h(b 1 + b 2 ) or h (b 1 + b 2 ) 2 A =.5 x 5 (8 + 12 ) A =.5 x 5 ( 20 ) A =.5 x 100 A = 50 in squared h=height Base 1 Base 2 8in 12in 5 in

44. Section 6.9 Circumference of Circles Objective – To find the circumference of circles Vocabulary  1. Circle – a set of points in the same plane that are all equal distance from the center.  2. Diameter – distance across a circle through the center = d  3. Radius – the distance from the center to the side of the circle – half the distance across the circle – half the diameter = r

45. Section 6.9 Circumference of Circles  4. Circumference – the distance around the circle = 2 x 3.14 x r or 3.14 x d C = 3.14 x 8 = 25.12 cm C = 2 x 3.14 x 3 = 18.84 in 8cm 3in

46. Section 11.6 Area of Circles Objective Objective To find the area of circles To find the area of circles Vocabulary Vocabulary 1. Pi – the Greek letter that represents an irrational number – approximately = 3.14 1. Pi – the Greek letter that represents an irrational number – approximately = 3.14 r= radius – half the distance of a circle r

47. Section 11.6 Area of Circles Area of a circle = A = 3.14r 2 Area of a circle = A = 3.14r 2 d = diameter =2r A = 3.14 x 2 2 = 3.14 x 4 = 12.56 ft sq 11/2 = 5.5 A= 3.14 x 5.5 2 = 3.14 x 30.25 = 95 mm 2 d 2 ft 11mm

48. Section 5.7 Least Common Multiple Objective To find the least common multiple of two or more numbers Vocabulary 1. Multiple – the product of a number and any whole number 2. Least Common Multiple (LCM) – the lowest of the common multiples of two or more numbers excluding zero.

49. Section 5.7 Least Common Multiple How to – 2 methods 1. List the multiples of the numbers until a common one is found Ex Find the LCM of 6 and 10 − 6 - 6,12,18,24,3030 is the LCM − 10 – 10,20,30 of 6 and 10 Ex Find the LCM of 3 and 7 − 3 – 3,6,9,12,15,18,2121 is the LCM of 3 − 7 – 7,14,21and 7

50. Section 5.7 Least Common Multiple 2. Write the prime factorization Ex Find the LCM of 12 and 18 1218 6 2 3 6 3 2 So 12 = 3 x2 x 2 and 18 = 3 x 3 x 2 use the multiples that occur the most 2x2 and 3x3 = 2 x 2 x 3 x 3 = 36 so the LCM of 12 and 18 is 36

51. 10.6 Similar Figures Objective To determine whether figures are similar and find the missing length in a pair of similar figures. Vocabulary 1. Similar Figures – figures that have the same shape but not necessarily the same size. The sizes are proportional. The angles are congruent. ~ = similar 10 = 8 = 6 - proportional 5 4 3 sides Congruent angles A B C 10 6 8 E D F 5 3 4

52. 10.6 Similar Figures 2. Indirect Measure – using the length, width or height of figures that are too difficult to measure directly Ex Paul is 5 ft tall, his shadow is 4 ft long. The flagpole’s shadow is 36 ft long, how tall is the flagpole. 5 = x 4 x 9 = 36 so 5 x 9 = x =45 4 36the flagpole is 45 ft tall 6 = 5 = 4? = 12 18 15 ? 18 15 ? 6 5 4