Number Sense Unit 1 - Weebly

Number SenseUnit 1Math 10FMrs. KornelsenR.D. Parker Collegiate

MA10FNumber SenseLesson One: Rational NumbersNew Definitions:Rational Number –Is every number a rational number?What about the following? Why or why not?a)b)̅c)A rational number can be a decimal as long as it or.Circle the following rational numbers 2 Page

MA10FNumber SenseThe Real Number SystemThe real number system consists of natural numbers, whole numbers, integers, rationaland irrational numbers.Natural Numbers ( )Natural numbers are the (positive integers)Whole Numbers ( )Whole numbers are the counting numbers (non-negative integers)Integers ( )Integers are the natural numbers and theirNoRational Numbers ( )A rational number is a number which can be expressed as a ratio/fraction of twointegers.3 Page

MA10FNumber SenseExample:Irrational Numbers: ( ̅ )The set of numbers that areExamples:Number LineAny number that represents an amount of something, such as a ,a , or thebetween two points, will always be a real number.4 Page

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MA10FNumber SenseFractionsThree types:1): the top number (numerator) is bigger than thebottom number (denominator).Ex:2): the top number (numerator) is smaller than thebottom number (denominator)3)Ex:4): A whole number and a fraction.Ex:Mixed ImproperTake the whole number times the denominator and add the numerator. Put that numberover the original denominator.Example:23Improper Mixed example1)How many times does the denominator go into the numerator? That’s yourwhole number2)How many are left over? That’s your numerator- The denominator stays the same7 Page

MA10FNumber SenseAdding and Subtracting Fractions:1)Put each fraction over the same2)Add or subtract the . Leave the denominator the same.Ex:5Multiplying Fractions:1)2)3)Check to see if you can reduce. Include cross-reducing.Multiply the top x top and the bottom x bottom.ReduceEx.i) ii) iii) iv) 3 x Dividing Fractions:- Flip the second fraction (find the reciprocal)- Multiply using the steps above:Do Fractions HandoutsPrepare for FractionsQuizEx:i)ii)iii)4iv)38 Page

MA10FNumber SenseLesson Two: Rational Numbers In Between NumbersYou can always find a number that fits in-between other numbersExample 1:Write a number in the blank space in each decimal so that the top decimal is greater thanthe bottom decimal.a)b)Example 2:Put a number in the blank space in each fraction, so that the top fraction is greater thanthe bottom fractiona)b)Example 3:Fill in the missing digits so that the value in the middle decimal is between that of thetop and bottom decimala)b)9 Page

MA10FNumber SenseExample 4:Identify a fraction between –and –Example 5:Identify a fraction between the following:andTask1. a. In each of the following number pairs, put numbers in the blank spaces which willmake the top number greater than the bottom number:10 P a g e

MA10FNumber Senseb. In each of the following number pairs, put numbers in the blank spaces which willmake the top number less than the bottom number:2. a. In each of the following fraction pairs, fill in the blank spaces so that the topfraction is greater than the bottom fraction:b. In each fraction pair, fill in the blank spaces so that the top fraction is less thanthe bottom fraction:3. Given the following sets of decimals, fill in the spaces so that, in each group, thevalue of the middle decimal is between that of the top and the bottom decimals:11 P a g e

MA10FNumber Sense4. Write a number in each box to make the following inequalities true:a. b. c. 12 P a g e

MA10FNumber SenseLesson Three: Comparing Rational NumbersHow to compare decimals**Know your place values**tenthshundredthsten thousandthsthousandthsExample 1:Order from least to greatest:In the hundredths place value there is a 2, 3, 3, 3 and 4. Thereforeis thesmallest because 2 is smaller than 3. Andis the biggest because 4 is bigger than 3.From the three decimals left, there is a 0, 1 and 4 in the thousandths place value.Therefore 0.0342 is the second largest because 4 is bigger than 1 and 0.13 P a g e

MA10FNumber SenseHow to compare fractions**Turn them into a decimal**̅On your calculator press 5then pressthen press6 andTo turn mixed numbers in to decimals you divide the fraction and add the wholenumber.On your calculator press 2 then pressThen pressthenthen press5 andandExample 2:Compare and order from least to greatest:̅Example 3:Which fraction is greater?orDo Comparing RationalsAssignmentDo Comparing RationalsExit Slip14 P a g e

MA10FNumber SenseComparing and Ordering Rational NumbersNameFill in each blank with , , or to make each sentence true. Write the decimal form beneatheach fraction to check your answer.Example:12 13On your calculator, press 1 press thebutton, thenpress 2 andto get the decimal form of0.5 .71015198.5123169.521043911. 795712. 9710. 41374Write the fractions in order from least to greatest. Write the decimal notation beneath eachfraction as you did in problems 1 - 12.13.38147814.16191720182115.351829243915 P a g e

MA10FNumber SenseLesson Four: Operations with DecimalsExample 1:Estimate and calculatea)b)16 P a g e

MA10FNumber SenseExample 2:Estimate and calculatea)b)17 P a g e

MA10FNumber SenseExample 3:On Saturday, the temperature at the Blood Reserve near Stand Off, Alberta decreased byCelsius per hour for 3.5 hours. It then decreased byC/h for 1.5 hours.a) What was the total decrease in temperature?b) What was the average rate of decrease in temperature?18 P a g e

MA10FNumber SenseLesson Five: Operations with FractionsExample 1:Estimate and calculatec)d)()()19 P a g e

MA10FNumber SenseExample 2:Estimate and calculatec)d)()()20 P a g e

MA10FNumber SenseExample 3:At the start of a week, Maka had 30 of her monthly allowance left. That week, shespent of the money on bus fares, another shopping, and on snacks. How much didshe have left at the end of the week?21 P a g e

MA10FNumber SenseLesson Six: Squares and Square RootsA square is a four-sided figure that has the same length and width. It is a perfect square.Ex. The length and width of this square are 10 units.What is the area of this square?10 units10 unitsunits2, we can say that Sinceand is a perfect square.Think About It!!!What doesequal?Recall your multiplication of negative integers22 P a g e

MA10FNumber SenseThe square root of a number has two answers: a positive and a negativeWhich of these are perfect squares? Evaluate the perfect squares.1. 2. 3. 4. 5. 6. 7. 8. 9. 10. List the perfect squares from 1 to 100.Starting with and ending with Example 1:Draw a diagram that represents 23 P a g e

MA10FNumber SenseExample 2:Determine whether each of the following numbers is a perfect square.a)b)Example 3:Evaluate 24 P a g e

MA10FNumber SenseLesson Seven: Estimating Square RootsTo estimate the square root of a number, find the perfect squares on each side of thenumber.Example 1:Estimate Think: What two perfect squares are on either side of 89.Try It!!!Estimate each square root.1. 2. 3. 4. 5. 6. 7. 8. 9. 25 P a g e

MA10FNumber SenseExample 2:A square trampoline has a side length oftrampolinee.m. Estimate and calculate the area of theExample 3:Estimate and then calculate 26 P a g e

MA10FNumber SenseLesson Eight: Pythagorean TheoremRecall:Pythagorean Theorem:hypotenuseIt doesn’t matter what side isor .But must be the longest side, and the longest side is the side across from the rightangle called the hypotenuse.Example 1:Solve for the missing side.6 cm8 cm27 P a g e

MA10FNumber SenseExample 2:Solve for the unknown side. Round your answer to the nearest hundredth.13 m3mExample 3:A 3m ladder is leaning against a wall. The base of the ladder is 0.5m from the wall.How far up the wall does the top of the ladder reach? Round your answer to the nearesthundredth of a metre. Provide a diagram.28 P a g e

MA10FNumber SenseExample 4:Determine whether the given triangle is a right triangle.8 units6 units7 units29 P a g e

MA10FNumber SenseIrrational NumbersIrrational Number – a number thata is not rationalIt cannot be expressed as a fractionIt cannot be a terminating or repeating decimalThe most common irrational number isSquare roots that are not perfect squares are also irrational numbers, such as .Calculate How was discovered? 30 P a g e

On your calculator press 5 then press then press 6 and To turn mixed numbers in to decimals you divide the fraction and add the whole number. On your calculator press 2 then press then press 5 and . Comparing and Ordering Rational Numbers Name Fill in each blank with , , or to make each sentence true. Write the decimal form beneath