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Grade 6: Number Sense Sentence Frames Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. 1. _ _ _ is greater than zero and less than _ _ _. 2. _ _ _ is greater than _ _ _ and less than zero. 3. _ _ _ is greater than _ _ _ because it is to the right of _ _ _ on the number line. 4. _ _ _ is less than _ _ _ because it is to the left of _ _ _ on the number line. Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 1. If the scale of a map is one inch equals _ _ _ miles, then _ _ _ inches represents _ _ _ miles. 2. If the lengths of corresponding sides of two similar triangles are _ _ _ and _ _ _, then the ratio of the lengths of the corresponding sides is _ _ _ to _ _ _. Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a/b, a to b, a:b ). 1. If a bag contains _ _ _ red marbles and _ _ _ blue marbles, then the ratio of red to blue marbles is _ _ _ to _ _ _. 2. If the ratio of boys to girls is _ _ _ : _ _ _ and there are _ _ _ boys, then there are _ _ _ girls. 3. If a pet store has _ _ _ puppies and _ _ _ kittens, then the ratio of puppies to kittens is _ _ _ to _ _ _. Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. 1. _ _ _ percent of _ _ _ is _ _ _. 2. If a sweater is on sale for _ _ _ off, then the sale price of the sweater is _ _ _ percent of the original price. 3. A twenty percent tip on a lunch that costs _ _ _ is _ _ _ dollars and _ _ _ cents. Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. 1. If _ _ _ is added to _ _ _ , the lowest common denominator is _ _ _. 1. The sum of negative _ _ _ and positive _ _ _ is negative _ _ _. Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 = 2/3). 2. The sum of negative _ _ _ and positive _ _ _ is positive _ _ _. 1. Dividing _ _ _ by _ _ _ and multiplying _ _ _ by _ _ _ yield the same result. 2. To find _ _ _ of _ _ _, the operation used is _ _ _. (Example: To find two-thirds of 60, the operation used is _ _ _.) 3. The product of negative _ _ _ and positive _ _ _ is negative _ _ _. 4. The product of negative _ _ _ and negative _ _ _ is positive _ _ _. 5. Positive _ _ _ minus negative _ _ _ is the same as positive _ _ _ plus positive _ _ _. Grade 6: Number Sense Sentence Frames