The HOT List of Math Vocabulary and Knowledge

1. The HOT List of Math Vocabulary and Knowledge “Words and other stuff you should know…” Created by: Melissa Williams

2. This is stuff a 7th grader should know how to do: • Compare and order rational numbers • Convert between forms of rational numbers • Represent squares and square roots • Know what multiplication and division of fractions and decimals look like in models • Add, subtract, multiply and divide fractions and decimals • Model integers • Find unit rates (best buy) and work with other ratios • Use the order of operations • Know HOW and WHEN to add, subtract, multiply or divide to solve a problem (whole numbers, fractions, decimals) • Know if an answer is reasonable • Solve percent problems

3. Solve proportions of any type, especially with similar figures, scales, unit costs, measurements • Make measurement conversions • Graph data to demonstrate relationships • Use words and symbols to describe terms in a sequence (nth term, rules, input/output tables) • Solve equations with models • Select an appropriate equation for a problem situation • Find complementary and supplementary angles • Classify triangles and quadrilaterals • Classify pyramids, prisms, cones, and cylinders • Understand and apply the definition of “similar” • Use ordered pairs on a coordinate graph • Graph reflections across the x or y axis • Graph translations

4. Identify 3-d views from different perspectives • Recognize nets for 3-d figures • Solve problems using your knowledge of geometry • Find perimeter, circumference and area • Find volume of prisms and cylinders • Select a sample space for simple/composite experiments • Find the probability of independent events • Understand how to use, read, and interpret different types of graphs • Draw conclusions from graphs and data • Find mean, median, mode, and range • USE ALL THESE SKILLS TOGETHER TO SOLVE PROBLEMS • Grid an answer correctly using place value

5. But…that’s a lot of stuff! • Yes, it is. STAAR emphasizes some skills more than others. • Here’s what I know about the 7th grade STAAR test:

6. 54 questions • 13 – Rational numbers and operations • 13 – Proportional and algebraic thinking • 10 - Geometry and spatial reasoning • 8 - Measurement • 10 - Probability and statistics • 4 of these are griddables • If it’s longer than this, some are “field” questions

7. Rational numbers • Convert between fractions, decimals, percents, and whole numbers • Use addition, subtraction, multiplication, and division to solve problems (including fractions and decimals) • Select and use appropriate operations to solve problems and justify solutions

8. Proportional/algebraic thinking • Solve percent problems • Solve problems involving proportions (similarity, scales, unit costs, and related measurement units) • Select a problem situations when given a simple equation OR formulate an equation when given a problem situation

9. Geometry • Understand and use the definition of similar figures • Graph reflections across the horizontal or vertical axis • Graph translations on a coordinate plane

10. Measurement • Solve problems involving perimeter and circumference • Solve problems involving area of polygons and other shapes • Solve problems involving volume of prisms (rectangular and triangular) and cylinders

11. Probability/Statistics • Make inferences and convincing arguments based on data analysis (graphs and charts) • Choose among mean, median, mode, or range to describe a set of data

12. Reviewing some of the basics… Do you remember?

13. To convert a fraction into a decimal: 5 TI BO Top in, Bottom out

14. To convert a decimal into a fraction: • Write it how you would say it, then simplify if necessary. • 0.6 = six tenths = ÷ 2 ÷ 2

15. To convert a fraction into a percent: • Rewrite it using 100 as a denominator • 15% • Convert it into a decimal, then move the decimal TWICE to the right OR… X 5 = 15% X 5 20

16. Comparing and Ordering • When comparing a mix of fractions, decimals, and percents it is best to convert them into the same form! Read carefully! • Least to greatest? • Greatest to least? • Use a number line or picture to help.

17. Order of Operations • PEMDAS • Parentheses • Exponents • Multiply/Divide • Add/Subtract Remember, always work left to right following the rules! AS MD E • P

18. Integer Rule Rhyme + - Scoreboard to add, Subtract use S.O.O (same, opposite, opposite) Multiply/divide use tic-tac-toe… + - - - + - - - +

19. Integer models • Remember, integer “chips” can be used to represent problem situations Vocabulary: Positive Negative “Zero” or neutral pairs What is the value of this picture? Find a key or read the problem to identify the “positive” and “negative” integer chips.

20. Equation Models Make sure you know what is “positive” and what is “negative”! x • Keep it “fair and balanced.” What happens on one side MUST be done to the other side. You may: • Remove objects • Add objects • Put objects into equal groups x

21. Squares and square roots x2 12 = 1 x 1 = 1 22 = 2 x 2 = 4 32 = 3 x 3 = 9 And so on… A number, that when multiplied by itself, equals a given product. 1 4 9 A square root can be represented as being the SIDE LENGTH of a square. 5 25 A perfect square can be represented as the AREA of a square.

22. Models of Multiplying Fractions Remember, the answer is shaded with BOTH patterns.

23. Proportions • Used to make comparisons • Used in similar figures • Used to make measurement conversions • Used to find unit rates • Used to work with percents • Can be written different ways, as long as the cross-products are the same!

24. Setting up Proportions Melissa paid $9 for 4 tickets to the school play. How much would she pay for 14 tickets? When reading a word problem, look for what is being compared, then create a proportion box with labels. ALWAYS be sure the labels match! You can’t switch from hours to minutes without a conversion…

25. Percent words: • Discount – savings; the money you save when something is on sale (gets subtracted) • Tax – the money you pay when you buy something (gets added) • Tip – the money you leave a waiter or waitress (gets added) • Sale price – a reduced price These problems require CAREFUL reading! Common sense is good too!

26. Similar Figures: • Figures that have Congruent Angles and Proportional Sides (CAPS) • A scale factor exists between similar figures (sometimes, it’s obvious, but other times you must write and solve a proportion) 3.2 cm 2.1 cm x 4.3 cm

27. Unit rates • 3 pencils for $1.20 • 5 pencils for $1.95 • 2 pencils for $0.94 • Unit means “one” • UNIcorn • UNIcycle It’s like Spanish: -uno, un, or una • These are DIVISION problems. • If I can buy 3 for $1.20, they are 40 cents each. • If I can buy 5 for $1.95, they are 39 cents each. • If I can by 2 for 94 cents, they are 47 cents each. The BEST buy is 5 for $1.95, because that is the lowest unit rate.

28. nth term, Sequences • 4, 7, 10, 13… +3 +3 y = 3x +1 +3

29. Angles • Complementary A pair of angles that add up to 90° • Supplementary A pair of angles that add up to 180° 30° 120° 60° 60°

30. Coordinate Graph • A graph that uses ordered pairs to name locations II I (-,+) (+,+) C x (+,-) (-,-) III IV y

31. Reflection: • A transformation that “flips” an image, usually over the x or y axis. X axis Y axis

32. Translation • A transformation that “slides” an image up/down, left/right, or a combination of both , I am the new, or prime, image I am the original, or pre-image This transformation was “to the right and up”

33. Venn diagram • Allows similarities and differences to be made between data Set A Both sets Set B Neither set

34. Histogram • Used to make comparisons and show distribution of data • Very similar to a bar graph, but data is grouped into intervals Notice that the bars are touching and represent a range of data: 0 to 10, 10 to 20, etc.

35. Bar Graph • Used to make comparisons Notice that the bars do not touch and each one represents a single piece of data on the x-axis.

36. Line Graph • Shows change over time

37. Line Plot • Shows distribution of data

38. Circle graph: • shows the parts of a whole, often in percentages Make sure you know what the “whole” is. It might be a number given in the problem or on a chart.

39. Measures of Central Tendency • Mean – find the sum of the values and divide (makes all the data the same size) • Median – least to greatest, find the middle (cuts the data into the top and bottom half) • Mode – the most, or favorite (indicates frequency or distribution of data)

40. Another measure of data… • Range – the difference between the largest and smallest piece of data (used to show variation or consistency of data)

41. Perimeter/Circumference • The distance around the outside of a polygon or circle • For perimeter, add • For circumference, use the formula • Measured in linear units: feet, inches, cm • Can be “disguised” as fencing, a frame, a revolution on a ferris wheel, the distance a tire rolls

42. Area • The amount of space inside a 2-dimensional object • Measured in square units: ft2, in2, yd2 • Use the appropriate formula for the shape • Can be “disguised” as grass in a yard, paint on a wall, glass over a picture

43. Volume fills • The amount needed to fill (capacity) a 3-dimensional object • Measured in cubic units: yd3, ft3, m3 • Use the correct formula for the shape

44. Sample Space • All the possible outcomes • Example: IF you have the choice of a ham or turkey sandwich, and either an apple or an orange • 2 sandwiches x 2 fruits = 4 outcomes Turkey and apple Turkey and orange Ham and apple Ham and orange

45. Probability • The likelihood of a single event occurring • P(event) = • Written as a fraction, it can be simplified or converted into other equivalent forms

46. Compound Probability • Examples: • a spinner and a number cube • flipping a coin 3 times • an experiment WITH replacement • P (event, another event) • Write a fraction for each event and then multiply (each action gets a fraction)

47. Don’t know where to Begin? Could you… Draw a picture? Work backwards from the answers? Use another part of the test for help? Use your formula chart? Eliminate answer choices?

48. Did you ?????? -Show your work? -Check your addition, subtraction, multiplication and division? -Check to see if your answer is reasonable? (Does it make sense?)

49. Save time to bubble! In the past, time was not an issue. Now, you MUST make sure to have all answers bubbled BEFORE time is up!!!! Don’t wait! Make sure your fingers are clean before you touch your answer sheet. If you make a mistake erase it completely.

50. Circle-Bubble-check a Circle: Outline the answer choice. a a Bubble: Fill in your choice. Check: Look for stray marks to erase Don’t leave any blank! a