1. AZ Merit Boot Camp 6 th Grade Math Ms. McClure San Tan Elementary

2. Day 1

3. Day 1 – Expressions and Equations 6.EE.A.3 I can use my knowledge of the order of operations to create equivalent expressions.

4. Day 1 – Expressions and Equations 6.EE.A.3 Equivalent expressions ◦Must have the same value ◦Contain variables ◦Multiplication is repeat addition ◦Division is repeat subtraction ◦Exponents are repeat multiplication ◦Inverse Operations  Multiplication & Division  Addition & Subtraction Order of Operations: GEMS! ◦Grouping symbols ◦Exponents ◦Multiplication/division ◦Subtraction/addition

5. Day 2

6. Day 2 – Expressions and Equations 6.EE.A.1, 6.EE.A.2c, 6.EE.A.4 I can write and understand numerical expressions involving whole number exponents. I can determine the answer to expressions when given the specific value of a variable. I can identify when two expressions are equivalent.

7. Day 2 – Expressions and Equations 6.EE.A.1, 6.EE.A.2c, 6.EE.A.4 Use substitution to evaluate expressions when given the value of a variable. Parts of an expression ◦Coefficient: The number before the variable ◦Variable: Letter that stands for a number ◦Constant: Number that stays the same ◦Terms: Separated by plus or minus signs

8. Day 3

9. Day 3 – Expressions and Equations 6.EE.A.2a and 6.EE.A.2b I can write expressions using numbers and letters (with the letters standing for numbers). I can identify the parts of an expressions using mathematical words. I can understand that in 2(8+7), (8+7) can be thought of as two separate numbers or as 15.

10. Day 3 – Expressions and Equations 6.EE.A.2a and 6.EE.A.2b When defining variables, we must be specific with the units We can either use GEMS or the distributive property to solve 3(5-2) Distribute algebraic expressions just as we distribute numerical expressions Use the distributive property to write an equivalent expression for 8n+16 as 8(n+2) because 8 is a common factor

11. Day 4

12. Day 4 – Expressions and Equations 6.EE.B.5, 6.EE.B.6, 6.EE.B.7, 6.EE.B.8, and 6.EE.C.9 I can understand that solving an equation or inequality is like answering a question. I can use variables to represent numbers and write expressions when solving real-world problems. I can solve real-world problems and mathematical problems by writing and solving equations. I can write an inequality which has many solutions and represent these solutions on a number line. I can use variables to represent two quantities in a real world problem and write an equation to express the quantities. I can use graphs and tables to show the relationship between dependent and independent variables.

13. Day 4 – Expressions and Equations 6.EE.B.5, 6.EE.B.6, 6.EE.B.7, 6.EE.B.8, and 6.EE.C.9 To solve an equation or inequality, determine the number(s) that, when substituted for the variable, makes the number sentence true To solve equations, we must isolate the variable, using inverse operations When representing solutions to inequalities on number lines… ◦Closed circle includes the number (greater than or equal to/less than or equal to) ◦Open circle does not include the number (greater than/less than) ◦When your variable is to the left of the inequality symbol, the inequality symbol is pointing in the direction you shade on the number line The dependent variable depends on the independent variable ◦In a table, the independent variable goes on the left ◦On a graph, the independent variable goes along the bottom ◦In an equation, the dependent variable stands alone

14. Day 5

15. Day 5 – Number Sense 6.NS.A.1 I can divide two fractions. I can solve word problems involving the division of fractions by fractions.

16. Day 5 – Number Sense 6.NS.A.1 When dividing a fraction by a fraction: ◦KEEP, CHANGE, FLIP! ◦If a number is a whole number, change it to a fraction by giving it a denominator of 1

17. Day 6

18. Day 6 – Number Sense 6.NS.B.2 and 6.NS.B.3 I can divide multi-digit numbers. I can add, subtract, multiply, and divide multi-digit numbers involving decimals.

19. Day 6 – Number Sense 6.NS.B.2 and 6.NS.B.3 When dividing decimals, we can multiply our dividend and our divisor by a power of 10 to get rid of the decimal in our divisor and divide normally (or think of it as moving the decimal point over the same amount of times) When adding or subtracting decimals, be sure to line up the decimal point When multiplying decimals, move your decimal to the left in your product as many numbers as there are to the right of the decimal in the problem

20. Day 7

21. Day 7 – Number Sense 6.NS.B.4 I can find the greatest common factor of two whole numbers less than or equal to 12. I can find the least common multiple of two whole numbers less than or equal to 12. I can use the distributive property to show the sum of two whole numbers 1-100 in different ways.

22. Day 7 – Number Sense 6.NS.B.4 To find GCF and LCM, we can use the upside- down birthday cake method ◦For GCF, we multiply the numbers we’ve taken out to the left ◦For LCM, we multiply the “L”, or all numbers we’ve taken out to the left as well as the numbers left underneath ◦The greatest common factor will not be greater than both of the numbers ◦The least common multiple will be at least as big as both of the numbers To use the distributive property, we find a common factor of our addends ◦For example, 5+15 = 5(1+3)

23. Day 8

24. Day 8 – Number Sense 6.NS.C.5, 6.NS.C.6a, and 6.NS.C.6b I can understand that positive and negative numbers are used to describe amounts of having opposite values. I can use positive and negative numbers to show amounts in real-world situations and explain what the number 0 means in those situations. I can recognize opposite signs of a numbers as indicating places on opposite sides of 0 on a number line. I can understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.

25. Day 8 – Number Sense 6.NS.C.5, 6.NS.C.6a, and 6.NS.C.6b 62 and – 62 are opposites because they are on opposite sides of 0 and the same distance away on a number line We must be familiar with mathematical vocabulary in real-world situations such as deposit, withdraw, etc. to determine whether an amount is positive or negative We must be able to define 0 in these situations, for example 0 could represent no change in a bank account with a $60 balance, or it could represent $0 On the coordinate plane, ◦(x, y) is located in Quadrant I ◦(-x, y) is located in Quadrant II ◦(-x, -y) is located in Quadrant III ◦(x, -y) is located in Quadrant IV

26. Day 8

27. Day 9

28. Day 9 – Number Sense 6.NS.6c, 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7c, and 6.NS.C.7d I can place integers and other numbers on a number line diagram. I can place ordered pairs on a coordinate plane. I can understand the distance between two numbers including positives and negatives on a number line. I can understand and explain what rational numbers mean in real- world situations. I can understand absolute value as they apply to real-world situations. I can tell the difference between comparing absolute values and ordering positive and negative numbers.

29. Day 9 – Number Sense 6.NS.6c, 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7c, and 6.NS.C.7d We must be consistent with our scale on a number line and on the coordinate plane The x-coordinate of an ordered pair takes you right (positive) or left (negative), the y- coordinate takes you up (positive), or down (negative) on the coordinate plane Rational numbers include integers, decimals, and fractions To determine the distance on a number line between numbers with opposite signs, add their absolute values Absolute value is a number’s distance away from 0, it tells us the number’s magnitude (or size)

30. Day 9

31. Day 10

32. Day 10 – Number Sense 6.NS.C.6b, 6.NS.C.8, and 6.NS.C.9 I can understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. I can graph in all four quadrants of the coordinate plane to help me solve real-world and mathematical problems. I can determine the distance between points in the same first coordinate or the same second coordinate.

33. Day 10 – Number Sense 6.NS.C.6b, 6.NS.C.8, and 6.NS.C.9 To determine the distance between points with the same first coordinate or the same second coordinate, look at the coordinate that’s different, find the absolute values of each, ◦If they have different signs, add the absolute values ◦If they have the same signs, ◦Subtract the absolute values

34. Day 10

35. Day 11

36. Day 11 – Ratios and Proportions 6.RP.A.1 and 6.RP.A.3a I can understand ratios and the language used to describe two amounts. I can make tables of equivalent ratios, find the missing values in the tables, plot those values on a coordinate plane, and use the tables to compare ratios.

37. Day 11 – Ratios and Proportions 6.RP.A.1 and 6.RP.A.3a Ratios are comparisons between 2 amounts Remember: ORDER MATTERS! Common ratio language: “For each”, “For every”, etc. Ratios can be written as fractions, with a colon (:) or with “to” between the two amounts Equivalent ratio tables can be thought of as repeat addition or multiplication by a common factor to help us find the missing values in the tables When making ratio tables, be sure to label what each column or row represents (ex. Miles and Hours) In order to compare ratios, they must have something in common such as the numerator or the denominator ◦Another way we can compare is by dividing When plotting values of ratio tables on the coordinate plane, think of each ratio as an ordered pair

38. Day 11

39. Day 12

40. Day 12 – Ratios and Proportions 6.RP.A.2, 6.RP.A.3b, 6.RP.A.3d, and 6.RP.A.3c I can understand how to find a rate when given a specific ratio. I can solve unit rate problems. I can find a percent of a quantity as rate per 100. I can solve problems involving finding the whole if I am given a part and the percent. I can use what I know about ratios to convert units of measurement.

41. Day 12 – Ratios and Proportions 6.RP.A.2, 6.RP.A.3b, 6.RP.A.3d, and 6.RP.A.3c Be sure to label each part of your ratio or rate To find a unit rate, you must determine “How many for 1/for each/for every/per”, For example if Carlos drives 30 miles in 2 hours, his unit rate is 15 miles/hour Remember, is/of = %/100 = part/whole We can also change the percent to a decimal and multiply by the number to find a percent of a number If we know it takes 5 feet per string, we know it takes 60 inches per string because we can convert our measurement unit by multiplying or dividing by the appropriate amount. In this instance, we knew more inches would fit than feet because they are smaller, so we multiplied.

42. Day 12