Grade 7 Math Vocabulary

Transcription

1 Ratio, Rate, Unit Rate, Rate Unit Grade 7 Math Vocabulary Ratio, Rate, Unit Rate, Rate Unit Representing Equivalent Ratios Double Number Line 0 Ratio: An ordered pair of numbers which are not both zero. 0:, 0 to,. Ratio Relationship: The set of all ratios that are equivalent 0:, to,, etc. (will generally use measurement quantities, i.e. $0 for packs of diet soda) Tape Diagram Rate: Indicates how many units of one quantity there are for every unit of the second quantity. Ratio relationship given by $0 for every packs of diet cola can be written as the rate. dollars/ pack. Unit Rate: The unit rate is. because it is the value of the ratio. Rate Unit: The rate unit is dollars/ pack of diet cola because it costs. dollars for every pack of diet cola. Proportional Relationship (Chart) Proportional Relationship (Graph) Scale Factor Additive Inverse ( ) a ( a + =0 + ) =0 ( 3 ) + ( + 3) =0 Two quantities are proportional to each other when there eists a constant (number) such that each measure in the first quantity multiplied by this constant gives the corresponding measure in the second quantity. Graphical representation of a proportional relationship is a straight line that includes the point (0,0). y Scale factor = 3 A scale factor is synonymous to the constant of proportionality. It describes the multiplicative relationship between an original and its image either through reduction or enlargement. An additive inverse of a number (or epression) is a number such that the sum of the two numbers is 0. When subtraction is comple, adding the additive inverse is sometimes easier to comprehend or manipulate. 3 = ( 8) + ( 8) Here a student can add integers with confidence, resulting in fewer errors.

2 Multiplicative Inverse 3 0 = = 3 Area Model Bar Model Common Denominators 3 A multiplicative inverse of a number is a number such that the product of both numbers is. Multiplicative inverses do not always have to be the reciprocal. 3 3 = Model shows a shaded region representing 3 of the whole, divided into equal pieces, resulting in smaller pieces, each th of the whole. The 0 circled portion represents the solution: 3 3 = 0 The model shows how many copies of are in This may be used to finding 3 = 9 Using common denominators, the problem becomes: = or, 0 Epression Forms of Epressions Equivalent Epressions Equation 8 3() Height (h) + 8 = + y l + w bh An epression is a numerical epression, or it is the result of replacing some (or all) of the numbers in a numerical epression with variables. Epressions, have no equal sign so may be evaluated but never solved. Area or Product of 3 and (a + ) Epanded Form a + + a + + a + Factored Form 3 ( a + ) Standard Form 6 a + Base (b) Epressions for finding the perimeter of a rectangle: b + h + b + h b + h (b + h) Epression Epression 3 = = () 8 = 6y l w = A An equation is a statement of equality between two epressions.

3 Adding Integers Using -Color Chips Model + (-) = - Circles Absolute Value Model shows positive (Y chips) added to negative (R chips). Positives and negatives cancel each other one for one, resulting in negative remaining. Model (-3) + (-) = - Model shows how negatives added to negatives will always result in more negatives. CIRCUMFERENCE: The circumference of a circle is the distance around a circle. PI: The number pi, denoted by ππ, is the value of the ratio given by the circumference to the diameter, C that is π =. d The most commonly used approimations for ππ are 33. or 7. Area: A = π r The absolute value of a number is the distance between the number and zero on the number line. A number and its opposite have the same absolute value. Double Number Line Percent Model Absolute Value/Distance Between Two Numbers Bo Plot Interquartile Range(IQR) Model shows use of a double number line to find 3% of 0. This model may also be used to find the percent 7 equivalent for the fraction. 0 Whole What is the distance between and -3? ( 3) or ( 3) If pp and qq are numbers on a number line, then the distance between pp and qq is pp qq. Note: it doesn t matter which number is chosen as p and which is q. The five-number summary is as follows: Min = 0 Q = 3 Median = 3 Q3 = Ma = A bo plot divides the data into four parts, with each containing about % of the data values. The bo section of the bo plot shows where the middle 0% of the data values are. The bo plot does not show us specific data values. The IQR is the difference between the upper quartile and the lower quartile, which is the length of the interval that includes the middle half of the data. IQR = Q3 - Q = 3 The IQR is 8

4 Center of a Data Distribution (Mean as fair share) Center of a Data Distribution (Mean as balance point) Variability Probability (Sample Space) The balance point (Mean) of 3, 7, and 8 is 6 The sample space of a chance process is the set of all possible outcomes. For eample, the sample space for the eperiment of rolling a die is the set {,, 3,,, 6}. One interpretation of the mean is as a fair share. The mean is a measure of center appropriate for data distributions that are approimately symmetric. It is the average of the values in the data set. Absolute Deviation One interpretation of the mean is as a balance point. The mean is a measure of center appropriate for data distributions that are approimately symmetric. It is the average of the values in the data set. Variability of a data set is the etent to which data values are spread out from each other. Mean Absolute Deviation Methods for finding a sample space for compound (multistage) events include use of tree diagrams and tables/ charts. The probability of compound events may be calculated by multiplying the probabilities of the outcomes for each stage. Mean = 63ᵒF An absolute deviation is the distance of a data value from the mean (balance point) of the data set. The sum of the distances to the left of the mean is =. The sum of the distances to the right of the mean is =. The sum of the absolute deviations is. The MAD is, or ~ 3.7 degrees. The mean absolute deviation (MAD) is computed by finding the mean of the absolute deviations (distances from the mean) for the data set. The value of MAD is the average distance that the data values are from the mean ). A small MAD indicates that the data distribution has very little variability. A large MAD indicates that the data points are spread out and that at least some are far away from the mean.

5 Vertical Angles Complementary Angles Calculator Fluency Vertical angles are congruent (have equal measures). m a m b m c m d Supplementary Angles Supplementary angles are two angles whose measurements sum to 80. Complementary angles are two angles whose measurements sum to 990. Complementary angles do not need to be adjacent to each other. Slicing 3-D solids The number of edges intersected by a plane will determine the resulting cross-section polygon. # Edges intersected Resulting crosssection polygon 3 triangle Quadrilateral pentagon n-gon 7 th Graders should be using the following calculator functions on a regular basis: basic operations ( +,,, ) and π,, y Students should also be fluent at using the calculator to: convert fractions to decimals and percents calculate unit rates and constant of proportionality calculate scale factor calculate a mean and/ or MAD calculate compound probabilities Calculators should be available to all students whenever working on problemsolving tasks.