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 Idaho Department of Education Content Standards Objective Sub Objectives Task Analysis Essential Vocabulary Sample Assessment Cognitive level codes: • B: Memorize • C: Perform procedures • D: Demonstrate understanding • E: Conjecture, generalize, prove • F: Solve non-routine problems, make connections Bloom's Equivalent • B = Knowledge • C = Comprehension • D = Comprehension • E = Application and Analysis • F = Synthesis Calculator codes: • NO: student MUST NOT have a calculator while completing this item in order to assess this objective. Shaded objectives should be assessed in the classroom, but not included on the ISAT assessment. Standard 1: Number and Operation Goal 1.1: Understand and use numbers 8.M.1.1.1 Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, decimals, percents, and absolute values.CL: C, D Calc: CN Content Limit: Number lines and symbols <, < , >, > ,=, and ≠ may be used. Items use comparison only (e.g., compare, order), no computation. Decimals to ten-thousandths place. Fraction denominators limited to 2,3 45 6 8 10 12 16 20 25 and 100.Integers only as negative rational numbers • Identify absolute values of rational numbers • Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, decimals, percents, and absolute values. • convert between fractions, decimals, and percents • order positive and negative integers and other positive rational numbers • define and evaluate absolute values • compare magnitude of numbers (including absolute values) using less than, greater than, etc. • integer • rational numbers • absolute value • repeating and terminating decimals • Compare using <, > or = 3.14__3.4 3/4 __75% │-12│ __ -12 8.M.1.1.2 Use rational numbers, including percents and ratios, and π (pi) to solve problems. CL: C, Calc: CN Content Limit: Items may include percents used to find sales tax, discount, simple interest, net cost after discount, and percent increase or decrease. Items use whole numbers, fractions, and decimals. All items should be set in a real-world context. Items may ask for answers to be rounded to the nearest percent, whole number, dollar, cent, etc • Solve problems using rational numbers, including percents and ratios, and π (pi) • see 8.M.1.1.1 • determine appropriate form of percent to solve problems • recognize and apply formulas to solve problems • utilize ratios to solve real life situations • ratio • simple interest • percent increase • percent decrease • net cost after discount • pi as a ratio • tax •discount • An art collector sold ⅓ of his collection to a friend. The collector then donated 50% of what was left to a museum. What part of the original collection did the collector have left? 8.M.1.1.3 Locate the position of rational numbers and positive real numbers on a number line.CL: C Calc: CN Content Limit: Fraction denominators limited to 2, 3, 4, 5, 6, 8, and 10. Decimals to thousandths place. • Locate the position of rational numbers and positive real numbers on a number line • see 8.M.1.1.1 • distinguish magnitude of numbers by placing them appropriately on a number line • real numbers • Plot the following points on a horizontal number line: 8.M.1.1.4 Convert between standard form, scientific notation, and exponential form.CL: C Calc: CN Content Limit: Standard scientific notation of whole numbers and decimals from hundred billions through hundred billionths. Negative exponents should be used in scientific notation only. • Convert between standard form, scientific notation, and exponential form. • use exponents to show repeated multiplication • differentiate between positive and negative exponents within scientific notation • convert from standard form to scientific notation • convert from scientific notation to standard form • standard form • scientific notation • exponential form • Write the number in standard form: 3.2*10-3 • Write the number in scientific notation: 36,500,000 8.M.1.1.5 Apply number theory concepts (primes, composites, prime factorization, LCM, GCF). CL: C Calc: CN Content Limit: Problems involve no more than two numbers, each less than 100. Numbers are not relatively prime. • Identify prime and composite numbers B. Utilize prime factorization to find LCM and GCF • apply rules of divisibility • calculate the prime factorization of composite numbers • find the LCM and/or GCF of two numbers less than 100 • prime • composite • prime factorization • LCM • GCF • factors • multiples • relatively prime • Find the GCF of these numbers 48 & 72. • Find the LCM of these numbers 14 & 21. 8.M.1.1.6 Recognize pertinent information for problem solving.CL: C, D Calc: CN Content Limit: Items should be set in a real-world solve. No more than two unnecessary items in a prose item. Information may be given in text or table form. Data provided should be consistent with the context of the problem (i.e., a table listing start/stop times for movies). • Recognize pertinent information for problem solving • utilize data tables to solve problems • identify necessary information • pertinent • A hiking trail is 43⅝ miles long. There is a cabin every 4½ miles and an outhouse every 10 miles. How many cabins are along the trail? Explain why you chose the method you used. 8.M.1.1.7 Apply integers in one- and two-step common real-world situations. CL: C Calc: CN Content Limit: All items should be set in a real-world context • Simulate real-world situations using integers in one or two steps. • apply integer concepts to calculate solutions to real world situations • ascend • descend • Mount Kilimanjaro has an altitude of 19,340 feet. The lowest point in the Dead Sea has an altidude of - 1,312 feet. Which altitude is farther from sea level? 8.M.1.1.8 Use appropriate vocabulary. CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT • Use appropriate vocabulary. • communicate using correct mathematical terminology • communicate and interpret inequality symbols correctly • Write an algebriac expression for 5 is greater than a number. Goal 1.2: Perform computations accurately. 8.M.1.2.1 Recall the common equivalent fractions, decimals, and percents of halves, thirds, fourths, fifths, and tenths.CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Recall the common equivalent fractions, decimals, and percents of halves, thirds, fourths, fifths, and tenths • memorize common fractions, decimals and percents • quarter • Write 66⅔ % as a fraction 8.M.1.2.2 Add, subtract, multiply, and divide rational numbers.CL: C Calc: NO Content Limit: Fraction denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, and 100. Integers only as negative rational numbers. May use up to three numbers and two operations. No grouping symbols. Expression must be clearly stated. • Add, subtract, multiply, and divide rational numbers • use common denominators to add and subtract fractions • evaluate expressions containing decimals without calculators • perform multiplication and division of fraction utilizing appropriate reduction techniques • evaluate expressions using positive and negative integers • state answers in simpliest terms • reduce • simplify • evaluate • reciprocal • multiplicative inverse • Write answers in simpliest form: 3/4 + 7/8 4.5*56 5/8 ÷ 1/2 (-2) + (-5) - (-3) 8.M.1.2.3 Evaluate numerical expressions with whole number exponents.CL: C Calc: NO Content Limit: Exponents must be whole numbers between 2 and 6. Results must be less than 200. • Evaluate numerical expressions with whole number exponents • expand and simplify exponential terms • squared • cubed • base • exponent • power • evaluate 34 8.M.1.2.4 Evaluate numerical expressions with rational numbers using the order of operations. (337.02.c) CL: C Calc: NO Content Limit: Operations include addition, subtraction. multiplication, division, and use of exponents and roots. Items are limited to three nestings within grouping symbols. Identifying correct order of operations shown (calculation not required) is allowed Roots are limited to whole number square roots and cube roots. The ‘square root’ means the principal square root. Only the cube root of 8, 27, 64, 125, or 1,000 will need to be computed. • Evaluate numerical expressions with rational numbers using the order of operations • evaluate square and cube roots • recognize and apply correct order of operations • see 8.M.1.2.2 • roots • square roots • cube roots • grouping symbols such as parenthesis, brackets, etc • 15 + 3(6-22) 8.M.1.2.5 Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three. CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Select and apply an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three. • simplify mental calculations first when possible • differentiate between appropriate use of pencil and paper or calculator • Four picture frames cost \$5.98 each. Which would you use to find the total cost-mental math or paper and pencil? Explain your choice. 8.M.1.2.6 Use a variety of strategies including common mathematical formulas to compute problems drawn from real life situations. (338.01.a)CL: C Calc: CN Content Limit: Word problems use content limits of other objectives at this grade level. Word problems could be such that a variety of strategies could be used. Do not assess strategies. Formulas will be given in problem and limited to area of a parallelogram, triangle, and circle, circumference of a circle, distance formula, simple interest formula, and volume of a rectangular prism. • Apply a variety of strategies including common mathematical formulas to compute problems drawn from real life situations • replace variables in formulas with appropriate quantities from the problem and evaluate • formula • variable • Tyrone drove 1,560 miles in 20 hours. Using the formula d=rt, find his average rate per hour. 8.M.1.2.7 Use appropriate vocabulary and notations.CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Use appropriate vocabulary and notations • communicate using correct mathematical terminology • read numbers in exponential and radical form correctly • Write 23 as a word sentence Goal 1.3: Estimate and judge reasonableness of results. 8.M.1.3.1 Estimate or predict computation results. CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Estimate or predict computation results • use a variety of appropriate strategies to estimate solutions • compatable numbers • predict • reasonable • About 41% of the 13 million people in Guatemala live in cities. Estimate how many people live in cities. 8.M.1.3.2 Identify when estimation is appropriate and apply to problem solving situations. (337.03.b) CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Identify when estimation is appropriate and apply to problem solving situations • solve problems involving approximate answers • approximate • Shaneekqua has \$40 in her pocket. Can she leave a 15% tip for a restaurant bill of \$31.49? 8.M.1.3.3 Identify whether a given estimate is an overestimate or underestimate.CL: E Calc: NO Content Limit: Estimates will involve multiplication or division only. • Identify whether a given estimate is an overestimate or underestimate • explain the method used to find the estimate. • conclude whether given estimate is above or below appropriate estimate • overestimate • underestimate • Bobby took 938 students on a field trip. Each bus holds 47 students. He ordered 20 buses. Is this an overestimate or underestimate? 8.M.1.3.4 Use a four-function calculator to solve complex grade-level problems.CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Use a four-function calculator to solve complex grade-level problems • identify limitations of four function calculators in regards to order of operations • conjecture • justify • formulate • Use a four function calculator to evaluate for n=-3: 5n2-5(2n-3)2 8.M.1.3.5 Formulate conjectures and justify (short of formal proof) why they must be or seem to be true. CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Formulate conjectures and justify (short of formal proof) why they must be or seem to be true • predict reasonable solutions • explain appropriate problem solving strategies 8.M.1.3.6 Use appropriate vocabulary and notations. CL: Calc: Content Limit: Assessed in the classroom, not on the ISAT. • Use appropriate vocabulary and notations • communicate using correct mathematical terminology