1. Be a STAAR Ultimate Survivor!

2. Place Value: Whole Numbers

3. Comparing Whole Numbers

4. Ordering Whole Numbers

5. Expanded Form In expanded form, you display a number as the sum of the value of each digit. Example: 35,406 in expanded form is: 30,000 + 5,000 + 400 + 6

6. Place Value: Decimals

7. Read & Write Decimals

8. Order & Compare Decimals

9. Expanded Form: Decimals Expanded form of decimals is just like expanded form of whole numbers. You display a number as the sum of the value of each digit. Example: 0.478 in expanded form is: 0.4 + 0.07 + 0.008

10. Equivalent Fractions A fraction names part of a whole or part of a group. Sometimes two fractions are written differently but actually name equal parts. These are called equivalent fractions. To create an equivalent fraction, multiply or divide the numerator AND denominator by the same number. To determine if 2 fractions are equivalent, you can use cross multiplication (butterflies).

11. Comparing Fractions * When the denominators are the same, the larger numerator is the larger fraction. * When the numerators are the same... the smaller denominator is the larger fraction. * When neither numerator or denominator is the same, create equivalent fractions with the same denominator and then compare - the larger numerator will be the larger fraction. *** OR... in all cases, you can use cross-multiplication (butterflies).

12. Mixed Numbers & Improper Fractions There are two ways to name a fraction greater than 1. A mixed number includes a whole number and a fraction. For example, 4 1/2 is a mixed number. An improper fraction has a numerator that is greater than or equal to the denominator. For example, 8/3 and 5/2 and are improper fractions. There are two ways to name a fraction greater than 1. A mixed number includes a whole number and a fraction. For example, 4 1/2 is a mixed number. An improper fraction has a numerator that is greater than or equal to the denominator. For example, 8/3 and 5/2 and are improper fractions. How Do You Name a Fraction Greater Than 1?

13. Converting mixed numbers to improper fractions Converting improper fractions to mixed numbers

14. Decimals to Fractions Easy Peasy! If your decimal is in the 10ths place, place it over the denominator of 10. Ex: 0.7 = 7/10 If your decimal is in the 100ths place, place it over the denominator 100. Ex: 0.23 = 23/100 Fractions to Decimals Before you can write a fraction as a decimal, the denominator MUST be a 10, 100, or 1000. If the fraction doesn’t have a denominator of 10, 100, or 1000, you must first create an equivalent fraction that does have a 10, 100, or 1000 and then it may be written as a decimal. 2/5 x 2/2 = 4/10 = 0.4 17/25 x 4/4 = 68/100 = 0.68 Fractions to Decimals Before you can write a fraction as a decimal, the denominator MUST be a 10, 100, or 1000. If the fraction doesn’t have a denominator of 10, 100, or 1000, you must first create an equivalent fraction that does have a 10, 100, or 1000 and then it may be written as a decimal. 2/5 x 2/2 = 4/10 = 0.4 17/25 x 4/4 = 68/100 = 0.68 How Are Fractions Related to Decimals? Decimals are a way to write fractions with denominators of tens and hundreds.

15. Problem Solving Strategies 1. Read the ENTIRE problem 2. Underline the question ~ focus your thinking 3. Circle important information ~ information that helps you solve the problem 4. Cross out extra information ~ info you don’t need to solve the problem 5. Make a plan to solve (one step? more than one step? Need bigger numbers (+ or x)? Need smaller numbers (- or /)?) 6. Show your work!!! All of your work! Be a warrior! 7. Reread the problem... Did you answer the question? Does your answer make sense?

16. Problem Solving Operations When do you add, subtract, multiply or divide?? Add When you need to combine. You will get a bigger number. Subtract When you need to compare two number. When you need to find the difference between two numbers. When you need to take a number away from another number. You will get a smaller number. Multiply When you need to combine equal groups. When you are adding the same number over and over. Often, a word problem will say “per” or “each” to indicate equal groups. Division uses these words too. Divide When you need to separate into equal groups. You may be asked to determine the number in each group or the number of equal groups you can make. Often, a word problem will day “per” or “each to indicate euql groups. Multiplication uses these words too.

17. ALWAYS show work. You are an EPIC WARRIOR. WORK HARD!

18. ALWAYS go back & reread the questions. Did you answer the question they asked?

19. ALWAYS go back & reread the questions. Does your answer make sense?

20. Common Factors Factors shared by two or more numbers are called common factors of those numbers. For example, 5 is a common factor of 10 and 25 because 5 is a factor of 10 and also a factor of 25.

21. Add and Subtract Fractions * When you add or subtract fractions, DO NOT change the denominator! Ex: 2/7 + 3/7 = 5/7 * When subtracting a fractional amount from a whole, convert the whole into a fraction. Ex: Emma made a pan of brownies. Her family ate 5/12 of the brownies. How much of the brownies are left? 12/12 - 5/12 = 7/12 of the brownies are left * To convert a whole into a fraction, you must have the same numerator and denominator. The denominators have to be the same.

22. Estimate Solutions When Should You Estimate an Answer? When you do not need an exact answer to a problem, you can estimate to find an answer that is close to the exact answer. For example, some problems ask “about how many” or “approximately” how much. Use estimation when solving such problems. There are two ways to estimate to solve problems. 1: Rounding 2: Compatible Numbers Rounding Round numbers BEFORE you complete the math problems. Do NOT round single digit numbers. Ex: If Sally spent $27 on dinner and $14 on breakfast, about how much money did she spend on the two meals together? Round $27 to $30 and $14 to $10... $30 = $10 = $40 Sally spent about $40 on the two meals. Compatible Numbers Sometimes you can choose numbers that are close to the actual number that are easy to compute - the numbers are compatible. Ex: If you are asked to separate 47 candies into 8 bags, you could choose a compatible number to replace the 47. Replace 47 with 48 and divide by 8. 48/8=6

23. ALGEBRA

24. Relationships between sets of numbers Don’t get it backwards. Watch for labels... crates/cartons,bottles/boxes. Don’t get ideas backwards... multiplication/division,add/subtract,less/more

25. Prime & Composite Prime Numbers have exactly 2 factors: 1 and itself. Ex: 5 is prime. 5 has only 2 factors. 1x5=5 1 & 5 are the only factors of 5. There are no other whole numbers that are factors of 5. * 2 is the only prime even number. Composite Numbers have MORE THAN 2 factors. Ex: 6 is composite. 6 has 4 factors. 1x6=62x3=6 1, 2, 3, and 6 are factors of 6. * all even numbers OVER 2 are composite.

26. Geometry

27. Angles

28. 2-d shapes Other 2-d shapes to know... Triangles can be classified by the length of their sides or by their largest angle. Length of sides: Equilateral: all sides are congruent Isosceles: 2 sides are congruent Scalene: NO sides are congruent Angle: Right triangle: 1 right angle, 2 acute Obtuse triangle: 1 obtuse angle, 2 acute Acute triangle: 3 acute angles Quadrilaterals: Parallelograms: 2 pair of parallel sides Rectangles: parallelogram with 4 right angles Square: parallelogram with 4 right angles and congruent sides congruent sides Rhombus: parallelogram with congruent sides, no right angles right angles Trapezoid: a quadrilateral with 1 pair of parallel sides parallel sides

29. 3-d shapes You can describe a three-dimensional figure (or solid figure) by counting the number of vertices, edges, and faces the figure has. ● A face is a flat surface in the shape of a two- dimensional figure. ● An edge is a line segment where two faces meet. ● A vertex is a point where three or more edges meet. The plural of vertex is vertices. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A prism is made of 2 congruent shapes attached by rectangles. A pyramid has a polygon at its base and comes to a point.

30. Transformations Transformations are ways of moving a figure in a plane. Three kinds of transformations are translations, reflections, and rotations.

31. Ordered Pairs/Coordinate Grids A coordinate grid or a coordinate plane is a grid used to locate points. A point is located by using an ordered pair of numbers. The two numbers that form the ordered pair are called the point’s coordinates. ● Every coordinate plane has a special point called the origin. The coordinates of the origin are (0, 0). ● The horizontal line is called the x-axis. The first number of an ordered pair tells how many units the point is to the right of the origin. The first number goes right. ● The vertical line is called the y-axis. The second number of an ordered pair tells how many units the point is above the origin. The second number goes up.

32. Measurement

33. Conversions Smaller units to larger units = divide by the number of smaller units in the larger unit (this is found on the mathematics chart!!) Ex: 8 cups = ___________ pints cups are smaller pints are larger smaller units to larger units = divide divide by 2 because there are 2 cups in a pint 8 / 2 = 4 8 cups = 4 pints Larger units to smaller units = multiply by the number of smaller units in the larger unit (this is found on the mathematics chart!!) Ex: 4 yards = ______ feet yards are larger feet are smaller larger units to smaller units = multiply multiply by 3 because there are 3 feet in 1 yard 4 x 3 = 12; 4 yards = 12 feet Multi-step conversions Sometimes you must take baby steps toward a solution... you can do it... you’re a warrior! Ex: 5 yards = _____ inches yards is larger inches are smaller larger to smaller = multiply 5 yards x 3 = 15 feet; 15 feet x 12 = 180 inches

34. Perimeter * Perimeter is the distance around an object. * To find perimeter, add up all the sides. * Perimeter is a distance measurement and is measured in regular units (ft, inches, meters, etc). (ft, inches, meters, etc). * There are special formulas to find the perimeter of rectangles and squares.

35. Perimeter of a Square

36. Perimeter of a Rectangle

37. Area Area is a measure of square units inside a 2-d figure. A=L x W To find the area of a square or rectangle, multiply the length x width.

38. Volume Volume is a measure of cubic units inside a 3-d figure. V = L x W x H Volume = length x width x height If you know the area of an object (L x W), multiply the area by the height to find the volume.

39. Time If given a start time and an end time, use the ‘tic-tac-toe’ method. * Count up to the next hour, count the complete hours, then add the additional minutes. * If you have 60 minutes or more, regroup every 60 minutes as one hour. Ex: Practice started at 7:45 and lasted until 9:30. How long was practice? Ex: Practice started at 7:45 and lasted until 9:30. How long was practice? From 7:45 to 8:00 is 15 minutes From 8:00 to 9:00 is 1 hour From 9:00 to 9:30 is 30 minutes.... now add all the time that passed. 1 hour and 15 minutes plus 30 minutes is 45 minutes. Practice lasted 1 hour and 45 minutes.

40. More Time If given a start time and the amount of time an event lasts, and are asked to find the end time: add the start time and the event time. Regroup as necessary! Ex: Mary’s soccer camp began at 4:25 and lasted 3 hours and 30 minutes. What time was soccer camp over? 4:25 4:25 + 3:30 + 3:30 7:55 7:55 Ex 2: Brenna’s twirling camp began at 8:45 and lasted 3 hours and 30 minutes. What time was twirling camp over? 8:45 8:45 + 3:30 + 3:30 11:75 ** 75 minutes is more than an hour...need to regroup! 11:75 ** 75 minutes is more than an hour...need to regroup! +1:-60 +1:-60 12:15 12:15

41. Even More Time If given the amount of time an event lasts and an end time and must determine the start time, subtract the event time from the end time. * Remember - if you must regroup - 60 minutes = an hour. Ex: Football practice was over at 5:30. It lasted for 1 hour and 45 minutes. What time did practice start? 5:30 4:90 5:30 4:90 -1:45 -1:45 REGROUP AS.......... Took 1 hour away & added 60 min 4:90 4:90-1:45 3:45 Football practice began at 3:45 3:45 Football practice began at 3:45

42. Data & Statistics

43. Probability Probability is the likely hood that an event will happen. Probability can be expressed in words or as a fraction. WordsCertain Most Likely Equally Likely Not Likely/Less Likely Impossible Fraction1/3 1 out of 3 If you have a jar with 3 jellybeans: one red, one pink, & one yellow, the probability of choosing a pink jellybean is 1/3 or one out of three.

44. Predictions You can make predictions about future outcomes based on current outcomes/probabilities. First: determine the current probability Second: create an equivalent fraction using the current probability and the number or chances/trials/attempts given in the problem. *Sometimes you must reduce the fraction representing the current probability before you can create an equivalent fraction with the new number of trials. Ex. Ms. Jannsen makes 4 out of every 5 baskets she attempts. (Haha!) What is the best prediction of the number of baskets she will make on her next 20 attempts? 4/5 is the current probability. 4/5 = ?/20 4/5 = 16/20 Prediction: Ms. Jannsen will make 16 of her next 20 attempts.

45. Possible Outcomes Sometimes it is important to see all the results that might happen in a probability experiment. Making an organized list of all possible outcomes is one way to do this. You could also create a tree diagram. If you only need to know the number of possible outcomes and are given different categories of outcomes, multiply the # of possible outcomes in each category. * If you are choosing 2 items from 1 group: Count down starting with 1 less than the total number of items.

46. Line Graphs Line graphs show a change over time.

47. Mode, Median, Range Mode: The number that occurs most often Median: Put #s in order, the number in the middle Range: The difference between the largest number and the smallest number.

48. Griddables! How Do You Use an Answer Grid? * The answer grid contains four columns, the last of which is a fixed decimal point. * The answers to all the griddable questions will be whole numbers. Suppose the answer to a problem is 108. *First write the number in the blank spaces. *Be sure to use the correct place value. For example, 1 is in the hundreds place, 0 is in the tens place, and 8 is in the ones place. *Then fill in the correct bubble under each digit. *Notice that if there is a zero in the answer, you need to fill in the bubble for the zero. *The grid shows 108 correctly entered. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 If the answer is a 2-digit number, you will not use the first column.

49. YOU ARE An Epic Warrior!

50. Out-THINK! Out-WORK! Out-SCORE!

51. Be an Ultimate Survivor!