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Unit 2 Whole Numbers – grade 6, Learning Goals 1. Read and write whole numbers in standard form, expanded form, and written form 2. Use place value to represent and read whole numbers 3. Compare and order whole numbers 4. Identify and describe multiples and factors to 100 5. Identify and describe composite and prime numbers to 100 6. Use order of operations 7. Estimate sums, differences, products and quotients 8. Use mental math to add, subtract, multiply and divide 9. Add four 3-digit numbers and subtract from a 5-digit number 10. Multiply and divide by a 2-digit number 11. Pose and solve multistep problems p.30 Whole Numbers Key Words (6TB31) Million = one thousand thousand Period = in a large whole number, each group of 3 place values from right to left Billion = one thousand million Trillion = one thousand billion, or one million million Common multiples = a number that is a multiple of two or more numbers; 6 is a common multiple of 2 and 3 Prime number = a whole number with exactly two factors, itself and 1; 7, 13, 19, and 23 are prime numbers Factors = numbers that are multiplied to get a product 24 has 8 factors: 1, 2, 3, 4, 6, 8, 12, and 24. The prime factors of 24 are 2 and 3. A number with more than 2 factors is a composite number. Composite number = a number with three or more factors; 8 is a composite number because its factors are 1, 2, 4, and 8 Expressions = a mathematical statement with numbers and operations. Lesson 1 – Exploring One Million One million = 1000 thousands 1 000 000 = 1000 thousand cubes 1 000 000 mm = 1 km 1 000 000 pennies = $10 000 $1 000 000 = ten thousand $100 dollar bills 1 000 000 min is about 2 years Note: We leave a space between the periods when we write a number with 5 or more digits! When we read large numbers, we say the period name after each period except the units period! Lesson 2 – Understanding Large Numbers (6TB35) Strategy: How to read and write large whole numbers? e.g. 3 159 119 Millions period hundreds tens Thousands period Units period ones hundreds tens ones hundreds tens ones 3 1 5 9 1 1 9 3 000 000 100 000 50 000 9000 100 10 We can read this number as: three million one hundred fifty-nine thousand one hundred nineteen We can write this number in: - Standard form 3 159 119 - Expanded form 3 000 000 + 100 000 + 50 000 + 9000 +100 + 10 + 9 - Number-word form 3 million 159 thousand 119 Note: One thousand million is one billion. One thousand billion is one trillion. trillions billions millions thousands units 9 Lesson 3 – Comparing and Ordering Numbers (6TB39) You can use a place-value chart to order numbers from greatest to least. Lesson 4 – Exploring Multiples (6TB43) Recall that to find the multiples of a number, start at that number and count on by the number. You can use a hundred chart to find the multiples of a number. The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 The multiples of 6 are: 6, 12, 18, 24, 32, 36, … 12, 24, and 36 appear in both lists. They are multiples of 4 and of 6. They are common multiples of 4 and 6. Each common multiple of 4 and 6 is divisible by 4 and by 6. Lesson 5 –Prime and Composite Numbers (6TB45) Numbers multiplied to form a product are factors of the product. 2 factor x 8 = factor 16 product A prime number is a number greater than 1 that is divisible only by 1 and itself. 23 has 2 factors: 1 and 23. A number with exactly 2 factors, 1 and itself, is a prime number. 23 is a prime number. A composite number can be written as a product of prime factors: 24 = 2 x 2 x 2 x 3. 24 has 8 factors: 1, 2, 3, 4, 6, 8, 12, and 24. The prime factors of 24 are 2 and 3. A number with more than 2 factors is a composite number. Lesson 6 – Strategies Toolkit Strategies Make a table Use a model Draw a diagram Solve a simpler problem Work backward Guess and check Make an organized list Use a pattern Draw a graph Use logical reasoning (6TB48) Lesson 7 – Using Mental Math (6TB50) Use mental math to add. Rearrange and use compatible numbers. Compatible numbers are pairs of numbers that are easy to computer. 60 + 35 + 40 = (60 + 40) + 35 = 100 + 35 = 135 Note: Changing the order of the numbers being added or multiplied does not change the sum or product. Use mental math to subtract. When no regrouping is needed, start subtracting from the left. E.g. 687 – 464 = 223. Think: 600 – 400 = 200 80 – 60 = 20 7–4 =3 Use mental math to multiply. Rearrange and use compatible numbers. Compatible numbers are pairs of numbers that are easy to computer. 4 x 19 x 25 = 19 x (4 x 25) = 19 x 100 = 1900 Note: 25 and 4 are compatible numbers. Their product, 100, is easy to multiply with any other factor. Use mental math to multiply. Break one of the numbers apart to make numbers that are simple to work with. E.g. 6 x 27 = 6 x (20 + 7) = (6 x 20) + (6 x 7) = 120 + 42 = 162 Note: Twenty-seven breaks apart to 20 + 7. It’s easy to multiply 20 by 6 and 7 by 6. Lesson 8 – Order of Operations (6TB54) An expression is a mathematical statement with numbers and operations. When we calculate the answer, we solve the expression. The order of operations is: Brackets Multiply and Divide (in order, from left to right) Add and Subtract (in order, from left to right) Lesson 9 – Adding and Subtracting Whole Numbers (6TB60) Use place value to add Keep adding the next number to the previous sum Use place value to subtract Note: Recall that adding to check a subtraction is using the inverse operation. Addition is the inverse of subtraction. Consecutive numbers are numbers such as 100, 101, 102, 103. Lesson 10 – Multiplying Whole Numbers (6TB64) Do you remember? Multiplication and division are inverse operations. You can use one to check the other. You can use an area model to multiply. Sketch a rectangle and label the length and the width. Then divide the rectangle to show hundreds, tens, and ones. Label the dimensions of the sections. Find the area of each section. Add the areas to get your answer. You can break the numbers apart to multiply 197 = 100 + 90 + 7 You can use a short way to multiply 197 x 68 = (197 x 8) + (197 x 60) You can check by dividing Lesson 11 – Dividing by a 2Digit Number (6TB68) Remember the definitions of divisor, dividend, and quotient? 77 divided by11= 7 The divisor is 11. The dividend is 77. The quotient is 7. You can use Base Ten Blocks and place value Lesson 12 – Another Method for Dividing (6TB72) Estimate. You can also estimate by thinking multiplication. 60 x 80 = 4800. So 4840 divided by 58 is about 80. Use place value to divide. Remember to use remainders were appropriate. Unit 2 – Show what you know! 6TB77 Unit Problem – At the Apiary (6TB78) Check List: Your work should show: How you calculated and checked your solutions That you can choose the correct operation An interesting story problem involving whole numbers Clear explanations of your solutions and strategies