Grade Seven: Number Sense Sentence Frames
Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.1. _ _ _ to the _ _ _ power equals _ _ _. (whole numbers)
2. Negative _ _ _ to the _ _ _ power equals _ _ _.
3. (_ _ _/_ _ _) to the _ _ _ power equals _ _ _. (positive fraction raised to a whole number power). / Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
1. The fraction _ _ _ is equivalent to the decimal _ _ _.
2. The decimal _ _ _ is equivalent to the fraction _ _ _ and _ _ _ percent.
3. _ _ _ (fraction) , _ _ _ (decimal), and _ _ _ percent are three different representations of the same value.
4. I would convert 3/5 to a _ _ _ first by_ _ _ and then I would convert _ _ _ to a _ _ _ by _ _ _.
5. I would convert 0.84 to a _ _ _ first by_ _ _ and then I would convert _ _ _ to a _ _ _ by _ _ _.
6. I would convert 138% to a _ _ _ first by_ _ _ and then I would convert _ _ _ to a _ _ _ by _ _ _.
Differentiate between rational and irrational numbers.
1. _ _ _ is a rational number because it can be written as the fraction _ _ _.
2. _ _ _ is an irrational number because it cannot be written as a fraction.
3. _ _ _ is a rational number. However, _ _ _ is an irrational number. / Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
1. _ _ _ can be written as a terminating decimal.
2. _ _ _ can be written as a terminating decimal. However, _ _ _ cannot be written as a terminating decimal.
3. _ _ _ can be written as a terminating decimal because the denominator can be written as _ _ _. (product of twos and fives)
4. _ _ _ can be written as a repeating decimal because _ _ _ is a factor of the denominator. (something other than 2 and 5)
Calculate the percentage of increases and decreases of a quantity.
1. If the number 100 is increased by _ _ _ percent, the resulting quantity is _ _ _.
2. If the number 100 is decreased by _ _ _ percent, the reulting quantity is _ _ _. / Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
1. If an item is on sale for _ _ _ percent off, the sale price is _ _ _ percent of the original cost.
2. If $100 is invested at a simple interest rate of _ _ _ percent per year, the amount of interest earned each year is _ _ _ dollars.
Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
1. _ _ _ to the _ _ _ times _ _ _ to the _ _ _ equals _ _ _ to the _ _ _.
2. _ _ _ to the _ _ _ divided by _ _ _ to the _ _ _ equals _ _ _ to the _ _ _.
3. _ _ _ to the _ _ _ raised to the _ _ _ equals _ _ _ to the _ _ _.
4. _ _ _ raised to the zero power equals _ _ _ .
5._ _ _ to the negative _ _ _ is equivalent to one over _ _ _ to the _ _ _.
/ Add and subtract fractions by using factoring to find common denominators.
1. To add the fractions _ _ _ and _ _ _, use _ _ _ as the common denominator.
Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
1.The square root of _ _ _ is _ _ _.
2.Since the square root of _ _ _ is _ _ _, then _ _ _squared must be _ _ _.
3. If the side of a square measures _ _ _, then the area of the square is _ _ _. Therefore, the square root of _ _ _ is _ _ _.
4. The square root of _ _ _ is between _ _ _ and _ _ _.
5. Since _ _ _ squared is _ _ _ , and _ _ _ squared is _ _ _, the square root of _ _ _ must be between _ _ _ and _ _ _.
Multiply, divide, and simplify rational numbers by using exponent rules.
1. _ _ _ to the _ _ _ times _ _ _ to the _ _ _ equals _ _ _ to the _ _ _.
2._ _ _ to the _ _ _ divided by _ _ _ to the _ _ _ equals _ _ _ to the _ _ _.
3._ _ _ to the _ _ _ raised to the _ _ _ equals _ _ _ to the _ _ _.
4._ _ _ raised to the zero power equals _ _ _ .
5._ _ _ to the negative _ _ _ is equivalent to one over _ _ _ to the _ _ _.
Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
1.The absolute value of _ _ _ is _ _ _.
2.The absolute value of _ _ _ is _ _ _ because the distance from _ _ _ to zero on the number line is _ _ _.