7 - Expressions and Equations Guided Notes PDF

6th GRADE MATH GUIDED NOTES Expressions & Equations Mathporium 2020  Table of Contents 3 Terms of Use 4 About this Product 5 Parts of an Algebraic Expression (quick version) 7 Parts of an Algebraic Expression (interactive versi...

6th GRADE MATH GUIDED NOTES Expressions & Equations Mathporium 2020  Table of Contents 3 Terms of Use 4 About this Product 5 Parts of an Algebraic Expression (quick version) 7 Parts of an Algebraic Expression (interactive version) 9 Exponents 11 Writing Expressions 13 Evaluating Expressions (Order of Operations) 15 Properties of Numbers 17 Simplifying Expressions: Combining Like Terms 19 Simplifying Expressions: Distributive Property 21 Writing Equations 23 Solving One-Step Equations 25 Writing Inequalities (quick version) 27 Writing Inequalities (interactive version) 30 Graphing Inequalities 32 Vocabulary Insert © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Terms of Use ❖ For personal or classroom use only. This product may be shared among close friends and colleagues but may not be distributed between schools or school districts. ❖ May not be listed for access on any public domain such as educational platforms, blogs, or social media. ❖ May not be listed for sale or as part of other products listed for sale. ❖ May not by listed as a free product on any other site without permissions. To obtain permissions, email me at [email protected]. ❖ May by printed for distribution in your classroom only. May not be printed for distribution at conferences, trainings, or other educational events. ❖ This is the intellectual property of Mathporium therefore no part of this product may be replicated and packaged as a different product. ❖ To obtain multiple licenses, contact me at [email protected]. ❖ Visit www.teacherspayteachers.com/Store/Mathporium for more products like this. Credits Thank You! Thank you so much for your purchase! I am excited to offer this product to help teachers and students throughout their math journey. This product is a result of years of testing and improving its contents. I hope it is as valuable to you as it has been for me and my students. If you are dissatisfied or feel this product can be improved, please reach out to me at [email protected]. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  About this product What you will find ❖ This product includes 11 sets of notes: 1. Parts of an expression 7. Distributive Property 2. Exponents 8. Solving equations 3. Writing expressions 9. Writing equations 4. Evaluating expressions 10. Writing inequalities 5. Properties of numbers 11. Graphing inequalities 6. Combining like terms ❖ Each set of notes comes with a blank version to use for direct instruction. The “answer keys” are convenient to have for students who missed the lesson. ❖ The notes are perforated so that students can cut them out and paste them into a spiral notebook. ❖ I recommend putting the Vocabulary Insert at the beginning of the unit. Recommendations I recommend that students keep a math notebook with ONLY their notes in it. Warm-ups and practice work should be left out. Minimizing the clutter in their notebooks helps students stay organized and sort through the information a lot faster. The easier it is for them to find the information they need, the more likely they will use their notes as a resource. Invest in colored paper! Separating notes by color, one color per unit, works better than anything because students will remember what colored pages to look for, even when referencing back to previous units. Trust me on this! © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  PARTS OF AN Algebraic Expression TERM VARIABLE The _______ of an expression that A _____________ used to are separated by __ and __ signs. represent a number. Example Example 7a2 + 3b - 6 7a2 + 3b – 6 There are ____ terms. They are _____ , _____ and _____. The variables are ____ & ____. COEFFICIENT CONSTANT A ___________ attached to the front A number that stands __________. of a ___________. This means that the number & letter will be multiplied. Example Example 7a2 + 3b – 6 7a2 + 3b – 6 The ____ & ____ are coefficients. The number _____ is a constant. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium QUICK NOTES  PARTS OF AN Algebraic Expression TERM VARIABLE parts of an expression that The _______ letter A __________ used + and __ are separated by __ - signs. to represent a number. Example Example 7a2 + 3b - 6 7a2 + 3b – 6 3 terms. There are ____ 7a2 , _____ They are _____ -6 3b and _____. a & ____. The variables are ____ b COEFFICIENT CONSTANT number attached to the front A __________ alone A number that stands ________. letter This means that the of a ________. number & letter will be multiplied. Example Example 7a2 + 3b – 6 7a2 + 3b – 6 The ____ 7 & ____ 3 are coefficients. 6 is a constant. The number ____ © 2020 Mathporium www.teacherspayteachers.com/store/mathporium QUICK NOTES  PARTS OF AN Algebraic Expression 3 m + 5g - 6 are parts that make up an expression. The expression above has ____ terms. They are ____, ____ and ____. Cut out the vocabulary words and definitions below. Match each vocabulary word with its definition. Paste each pair into the correct space above to match the part of the expression. terms Also known as a power, it indicates repeated A letter used to represent a number. variable multiplication. A number in front of a letter. A number that stands exponent It means that the number alone. constant and letter will be multiplied. coefficient © 2020 Mathporium www.teacherspayteachers.com/store/mathporium INTERACTIVE NOTES  PARTS OF AN Algebraic Expression exponent coefficient Also known as a power, it A number in front of a letter. indicates repeated It means that the number multiplication. and letter will be multiplied. 3 m + 5g - 6 variable constant A letter used to A number that stands represent a number. alone. are parts that make up an expression. terms The expression above has ____ m3 ____ 3 terms. They are ____, 5g and ____. -6 © 2020 Mathporium www.teacherspayteachers.com/store/mathporium INTERACTIVE NOTES  Exponents Exponents are a simplified way of expressing repeated ____________________. 3 5x5x5 = 5 example 1 53 = × × =. BE CAREFUL! (base) (base) (base) 5 does NOT mean 5 × 3. 3 example 2 Rewrite each problem in exponential form. 7 7 7 7 7 = ______ A A A = ______ (m)(m)(p)(p)(p)(p) = ______ 3 × 3 × h × g × g = ______ s Special Exponent Name Symbols for Multiply 52  _______ 53  _______ × ( ) © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Exponents Exponents are a simplified way of expressing repeated ____________________. multiplication 3 exponent or power 5x5x5 = expanded form 5 base example 1 53 = 5 × 5 × 5 = 1 25. BE CAREFUL! (base) (base) (base) 5 does NOT mean 5 × 3. 3 example 2 Rewrite each problem in exponential form. 5 3 7 7 7 7 7 = ______ 7 A A A = ______ A 2 4 2 (m)(m)(p)(p)(p)(p) = ______ mp hg2 or 9hg2 3 × 3 × h × g × g = 3______ mes Special Exponent Na Symbols for Multiply 52  squared 53  cubed × ( ) © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Writing Expressions An expression is a math problem that does not have ____________________________. Expressions can be made up of just numbers (called numerical expressions) or they can have both numbers and variables (called algebraic expressions). Math Language Addition + Subtraction – deposit more than decrease minus gain plus difference take away greater than put together *fewer than withdraw increase sum *less than Multiplication × ( ) Division ÷ double (×2) times break up separate product twice (×2) cut up share evenly quadruple (×4) triple (×3) quotient split into Exponents to the power of squared2 (exponent of 2) cubed3 (exponent of 3) Writing Expressions example 1 the product of 1 5 and n *With “less than” or “fewer than” you example 2 9 less than 32 must switch the order of the terms. example 3 the sum of 45 and p, doubled © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Writing Expressions An expression is a math problem that does not have __________________________. an equal sign or an answer Expressions can be made up of just numbers (called numerical expressions) or they can have both numbers and variables (called algebraic expressions). Math Language Addition + Subtraction – deposit more than decrease minus gain plus difference take away greater than put together *fewer than withdraw increase sum *less than Multiplication × ( ) Division ÷ double (×2) times break up separate product twice (×2) cut up share evenly quadruple (×4) triple (×3) quotient split into Exponents to the power of squared2 (exponent of 2) cubed3 (exponent of 3) Writing Expressions example 1 the product of 1 5 and n 15 × n *With “less than” or “fewer than” you example 2 9 less than 32 must switch the order of the terms. 9 – 32 32 - 9 example 3 the sum of 45 and p, doubled ( 45 + p ) × 2 © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Evaluating Expressions with Order of operations When solving problems with multiple steps, follow the order of operations. Step 1 : Parenthesis ( ) or [ ] Step 2: Exponents 53 Step 3: Multiply & Divide (from left to right) Step 4: Add & Subtract (from left to right) example 1 example 2 62 – 5 × 2 + [24 ÷ 6] 8(12 – 7) ÷ 23 A number next to parenthesis means to _______. example 3 example 4 The fraction bar means ____________. Evaluate the expression. To solve the problem, solve the top first. Let h = 8 and g = 9. Then solve the bottom. Then divide. 4g + gh 6(5 – 3) + 8 = ___ = 5 10 – 6 A number is next to a letter (like 4g) or a letter is next to a letter (like gh) means ______________. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Evaluating Expressions with Order of operations When solving problems with multiple steps, follow the order of operations. Step 1 : Parenthesis ( ) or [ ] Step 2: Exponents 53 Step 3: Multiply & Divide (from left to right) Step 4: Add & Subtract (from left to right) example 1 example 2 62 – 5 × 2 + [24 ÷ 6] 8(12 – 7) ÷ 23 62 – 5 2 + 4 A number 8 × (12 – 7) ÷ 23 next to 36 – 5 2 + 4 parenthesis 8 × (5) ÷ 23 means 36 – 10 + 4 8 × (5) ÷ 8 to 26 + 4 _______. multiply 40 ÷ 8 30 5 example 3 example 4 division The fraction bar means ____________. Evaluate the expression. To solve the problem, solve the top first. Let h = 8 and g = 9. Then solve the bottom. Then divide. 20 4g + gh 12 + 8 4×9 + 9×8 36 + 72 6(2) + 8 20 = 55 108 6(5 – 3) + 8 = ___ 10 – 6 4 A number is next to a letter (like 4g) or a letter is next to a letter (like gh) 4 to multiply means ______________. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Properties of Numbers Commutative Property Associative Property When adding or multiplying, you When adding or multiplying, you can ____________ the numbers in can _____________ the numbers any way. in any way. Examples Examples (2 + 3) + 5 = 2 + 3 + 5 2 + 3 = ___ + ___ 2 (3 5) = 2 3 5 5 × 2 = ___ × ___ a (b c) = a b c a × b = ___ × ___ (Here the ________________ move.) (Here the _______________ move.) Identity Property Zero Property Any number plus _____ equals itself. Any number times zero equals ________. Examples 5 + 0 = ___ Examples n + 0 = ___ 5 × 0 = ___ n × 0 = ___ Any number times ____ equals itself. 3 × 4 × 0 = ___ Examples a × b × 0 = ___ 6 1 = ___ n 1 = ___ © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Properties of Numbers Commutative Property Associative Property When adding or multiplying, you When adding or multiplying, you can order the numbers in any can group the numbers in any way. way. Examples Examples (2 + 3) + 5 = 2 + (3 + 5) 3 + ___ 2 + 3 = ___ 2 2 (3 5) = (2 3) 5 5 × 2 = ___ 2 × ___ 5 a (b c) = (a b) c a × b = ___ b × ___ a numbers & variables move.) (Here the __________________ parentheses move.) (Here the _____________ (terms) Identity Property Zero Property Any number plus zero equals itself. Any number times zero equals zero. Examples 5 + 0 = ___ 5 Examples n + 0 = ___ n 5 × 0 = ___ 0 n × 0 = ___ 0 Any number times one equals itself. 3 × 4 × 0 = ___ 0 Examples a × b × 0 = ___ 0 6 1 = ___ 6 n 1 = ___ n © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Simplifying Expressions Combining Like Terms Like terms are terms that have a ___________________________. They can be added or subtracted from each other. Terms with different variables __________ be added or subtracted. example Simplify the expression 5a + 2p – 2a + p. Model Think of the a’s as apples and the p’s as pears. +2p 5a (or 5 apples) (add 2 pears) –2a +p (minus 2 apples) (add a pear) Mathematically ( ___ + ___ + ___ + ___ + ___ ) + ( ___ + ___ ) + ( ___ ) Mental Math Add & subtract the like terms. (5a – 2a) = ____ (2p + p) = ____ Since _____ and _____ are not like terms, they cannot be added or subtracted. Therefore, 5a + 2p – 2a + p = ___________. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Simplifying Expressions Combining Like Terms common variable (letter) Like terms are terms that have a ___________________________. They can be added or subtracted from each other. cannot be added or subtracted. Terms with different variables __________ example Simplify the expression 5a + 2p – 2a + p. Model Think of the a’s as apples and the p’s as pears. +2p 5a (or 5 apples) (add 2 pears) –2a +p (minus 2 apples) (add a pear) Mathematically a + ___ ( ___ a + ___ a + ___ a + ___ a ) + ( ___ p + ___ p ) + ( ___ p ) Mental Math Add & subtract the like terms. 3a (5a – 2a) = ____ 3p (2p + p) = ____ Since _____ 3a and _____ 3p are not like terms, they cannot be added or subtracted. Therefore, 5a + 2p – 2a + p = ____________. 3a + 3p © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Simplifying Expressions Distributive Property Use distributive property when you need to multiply one term by a group of terms within parentheses ( ). This lets you simplify the expression when the terms cannot be combined. Distributive Property is Repeated Multiplication The expression 3(2a + 5p) means 3 ________ of (2a + 5p). 3(2a + 5p) ( ___ + ___ ) + ( ___ + ___ ) + ( ___ + ___ ) To simplify, just combine the like terms. ____ + ____ + ____ = ____ ____ + ____ + ____ = ____ Therefore, 3(2a + 5p) = ____ + ____. Here’s the Shortcut Another method is to ____________ the outside term by every term inside the parenthesis. 10(8h – 5c) (10 ____ ) – (10 ____ ) ____ – ____ Remember that unlike terms __________ be added or subtracted. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Simplifying Expressions Distributive Property Use distributive property when you need to multiply one term by a group of terms within parentheses ( ). This lets you simplify the expression when the terms cannot be combined. Distributive Property is Repeated Multiplication groups of (2a + 5p). The expression 3(2a + 5p) means 3 ________ 3(2a + 5p) 2a + ___ ( ___ 5p ) + ( 2a 5p ) + ( ___ ___ + ___ 2a + ___ 5p ) To simplify, just combine the like terms. 2a + ____ ____ 2a + ____ 2a = ____ 6a 5p + ____ ____ 5p + ____ 5p = ____ 1 5p 6a + ____. Therefore, 3(2a + 5p) = ____ 1 5p Here’s the Shortcut multiply the outside term by Another method is to _________ every term inside the parenthesis. 10(8h – 5c) (10 ____ 8h ) – (10 ____ 5c ) 80h – ____ ____ 50c cannot be added or subtracted. Remember that unlike terms __________ © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Writing Equations An equation is a math problem that shows two amounts are ________. Equations are different from expressions because they have an _______________ and an __________. Addition + Subtraction - Exponents deposit decrease to the power of gain difference squared 2 greater than fewer than cubed 3 increase less than more than spend sum withdraw Multiplication × ( ) Division ÷ Equals Sign = double (x2) break up as much as product quotient equal quadruple (x4) separate equivalent twice (x2) share evenly is triple (x3) split into the same as The price of a pair of shoes was recently increased by $ 1 2. The new price of the shoes is $115. Write an equation that can be used to find (p), the original price of the shoes. LOOK FOR KEY WORDS. The term “increased” Equation: means the price __________ so you ________ ________ = ________ can _______ to find (original price) (How did the price change?) (new price) the new price. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Writing Equations An equation is a math problem that shows two amounts are ________. equal Equations are different from expressions because they have an _______________ equal sign and an __________. answer Addition + Subtraction - Exponents deposit decrease to the power of gain difference squared 2 greater than fewer than cubed 3 increase less than more than spend sum withdraw Multiplication × ( ) Division ÷ Equals Sign = double (x2) break up as much as product quotient equal quadruple (x4) separate equivalent twice (x2) share evenly is triple (x3) split into the same as The price of a pair of shoes was recently increased by $ 1 2. The new price of the shoes is $115. Write an equation that can be used to find (p), the original price of the shoes. LOOK FOR KEY WORDS. The term “increased” means the price Equation: __________ goes up so you p ________ + 12 ________ = 1 15 ________ can _______ add to find the new price. (original price) (How did the price change?) (new price) © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Solving Equations Solving an equation means finding the value of the missing number. This number is usually represented by a _____________________. Solve the equation for m. m + 12 = 19 Since the value of the missing number (m) is ____ we say that the + 12 = 19 solution to the equation is ______. You can also solve equations by using opposite (or inverse) operations. Addition & ____________________ are opposites. Multiplication & __________________ are opposites. Solve the equation for n. n. = 15 The fraction bar means ___________ so you can solve the 5 problem with _________________. ___ × ___ = The solution is _________ because ____ ÷ 5 = 1 5. A fraction bar means _____________. A number next to a variable means _______________. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Solving Equations Solving an equation means finding the value of the missing number. This number is usually represented by a variable (letter). Solve the equation for m. m + 12 = 19 Since the value of the missing number (m) is 7 we say that the 7 + 12 = 19 solution to the equation is m = 7. You can also solve equations by using opposite (or inverse) operations. Addition & subtraction are opposites. Multiplication & division are opposites. Solve the equation for n. n. = 15 The fraction bar means division so you can solve the problem with 5 multiplication. 1 5 × 5 = 75 The solution is n = 75 because 75 ÷ 5 = 1 5. A fraction bar means divide. A number next to a variable means multiply. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Writing Inequalities An inequality is a statement using the symbols < , > , < or > to compare two amounts. Symbols & Meanings < > < > Less than Greater than Less or equal to Greater or equal to Fewer than More than At most At least Maximum Minimum No more than No less than You must be at least 16 years old to drive a car. age of driver 16 years When writing your inequality, you can use a variable (like A) to represent the age of a driver. Check all options that are solutions to the inequality n < 9. n = -3 n = 12 A solution is a “N” can be number that anything _______ n=9 makes the statement true. ____________ 9. n = 1½ © 2020 Mathporium www.teacherspayteachers.com/store/mathporium QUICK NOTES  Writing Inequalities An inequality is a statement using the symbols < , > , < or > to compare two amounts. Symbols & Meanings < > < > Less than Greater than Less or equal to Greater or equal to Fewer than More than At most At least Maximum Minimum No more than No less than You must be at least 16 years old to drive a car. age of driver > 16 years When writing your inequality, A > 16 you can use a variable (like A) to represent the age of a driver. Check all options that are solutions to the inequality n < 9. ✓ n. = - 3 n = 12 A solution is a “N” can be number that anything _______ less or ✓ n. = 9 makes the equal to ____________ 9. ✓ n. = 1 ½ statement true. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium QUICK NOTES  Writing Inequalities Symbols & Meanings © 2020 Mathporium < > < > INTERACTIVE NOTES You must be at least 16 years old to drive a car. Check all options that are solutions to the n < 9. age of driver 1 6 years n = -3 When writing your A solution is a “N” can be inequality, you can n = 12 number that anything use a variable (like n=9 makes the __________ A) to represent the statement true. ________ 9. age of a driver. n = 1½ Page 1 of 2  Writing Inequalities (cut-out page) Cut out the phrases below. Paste each phrase into the table to match the correct inequality symbol. More than At least Fewer than At most Less than Greater than Minimum No less than No more than Less than or Greater than or Maximum equal to equal to Writing Inequalities (cut-out page) Cut out the phrases below. Paste each phrase into the table to match the correct inequality symbol. More than At least Fewer than At most Less than Greater than Minimum No less than No more than Less than or Greater than or Maximum equal to equal to © 2020 Mathporium INTERACTIVE NOTES Page 2 of 2  Writing Inequalities Symbols & Meanings © 2020 Mathporium < > < > You must be at least 16 years old to drive a car. www.teacherspayteachers.com/store/mathporium Check all options that are solutions to the n < 9. age of driver > 1 6 years ✓n.= -3 When writing your A solution is a “N” can be inequality, you can n = 12 number that anything A > 16 use a variable (like makes the __________ A) to represent the ✓n.= 9 statement true. ________ 9. age of a driver. ✓n.= 1 ½ Answer Key  Graphing Inequalities We graph inequalities to show all the values that make the inequality _______. Open Circles Closed Circles < > < > Less than Greater than Less or equal to Greater or equal to Open vs. closed circles An open circle means that the value A closed circle means that the “ 1 ” _________ part of the solution. value “ 1 ” ____ part of the solution. n < 1 n < 1 Points vs. Lines Graph a line if it makes sense to have Graph separate points if you can values between the whole numbers. only have whole number values. Sophia has at least $6 in her wallet. The car fits 6 passengers, at most. dollars 6 passengers 6 4 5 6 7 8 9 10 2 3 4 5 6 7 8 It IS possible to have part of a dollar. It’s NOT possible to have part of a passenger. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  Graphing Inequalities true We graph inequalities to show all the values that make the inequality _______. Open Circles Closed Circles < > < > Less than Greater than Less or equal to Greater or equal to Open vs. closed circles An open circle means that the value A closed circle means that the is NOT part of the solution. “ 1 ” ________ value “ 1 ” ____ IS part of the solution. n < 1 n < 1 Points vs. Lines Graph a line if it makes sense to have Graph separate points if you can values between the whole numbers. only have whole number values. Sophia has at least $6 in her wallet. The car fits 6 passengers, at most. dollars > 6 passengers < 6 4 5 6 7 8 9 10 2 3 4 5 6 7 8 It IS possible to have part of a dollar. It’s NOT possible to have part of a passenger. © 2020 Mathporium www.teacherspayteachers.com/store/mathporium  EXPRESSIONS & EQUATIONS Vocabulary Associative property: When adding or multiplying, you can group the numbers in any way without changing the answer. At least ( > ) : The lowest possible value. It means greater than or equal to. At most ( < ) : The highest possible value. It mean less than or equal to. Base: The number that gets multiplied when using an exponent. Closed circle : A filled circle that is used to graph numbers on a number line. It shows that a number CAN be equal to something. Use it for the symbols < or >. Coefficient: A number in front of a letter. It means to multiply the two terms together. Commutative property: When adding or multiplying, you can change the order of the numbers without changing the answer. Constant: In a math expression, a constant is a number that stands on its own. Cubed3: An exponent of 3 Decrease (-) : To go down or to get smaller. It usually means to subtract. Deposit (+) : To put money into a bank account. It usually means to add since the total in the account goes up. Difference (-) : The answer to a subtract problem Distributive property: Use distributive property when you need to multiply one term by a group of terms within parentheses. 3(2a + 4n) Double (×2) : Two times as much. Equation: A math problem that shows two amounts are equal. It has an equal sign and an answer. Expanded form: Expanded form is an expression using multiplication without an exponent. (expanded form → 5 × 5 × 5 = 53  exponential form) Exponent2 : A small number that appears to the right of another number. It symbolizes repeated multiplication. Exponents are also called powers. Exponential form: A multiplication problem that is written with an exponent. (expanded form → 5 × 5 × 5 = 53  exponential form) Expression: A math problem that does not have an equal sign or an answer. It can be made up of both numbers and letters. Evaluate: It means to solve the problem. Identity property: Any number plus zero equals itself. Any number times one equals itself. Increase (+) : To go up or to get bigger. It usually means to add. © 2024 Mathporium www.teacherspayteachers.com/store/mathporium Page 1 of 2  EXPRESSIONS & EQUATIONS Vocabulary Inequality (< , > , < , > ) : A statement that shows when one number is greater or less than another number. Inverse: The opposite of something. Inverse operations are opposite operations. Addition and subtraction are inverses. Multiplication and division are inverses. Like terms: Terms that have the same variable (or letter). This means they can be added or subtracted. Unlike terms cannot be added nor subtracted. Maximum ( < ) : The highest possible value. It means less than or equal to. Minimum ( > ) : The lowest possible value. It means greater than or equal to. No less than ( > ) : The lowest possible value. It means greater than or equal to. No more than ( < ) : The highest possible value. It means less than or equal to. Open circle : An empty circle that is used to graph numbers on a number line. It shows that a number CANNOT equal something. Use it for the symbols < or >. Order of operations: When solving problems with more than one step, you must follow the order of operations (P.E.M.D.A.S.). Parenthesis ( ) [ ] : Grouping symbols that indicate which steps need to be calculated first in a math problem. Power2: It is an exponent which is a small number attached to the right of another number. It symbolizes repeated multiplication. Product (× ) : The answer to a multiplication problem. Quadruple (×4) : Four times as much. Quotient (÷ /) : The answer to a division problem. Simplify: To reduce an expression to the fewest terms possible. Simplify an expression by combining the like terms, using distributive property or solving it for an answer if possible. Solution: In an equation or inequality, the solution is the value or values that make the statement true. Squared2 : An exponent of 2. Sum (+) : The answer to an addition problem. Term: The parts that make up an expression. They are separated by + and – signs. Triple (×3) : Three times as much. Twice (×2) : Two times as much. Variable: A letter used to represent a number. Withdraw (-) : To take money out of a bank account. It usually means to subtract since the total in the account goes down. Zero property: Any number times zero equals zero. © 2024 Mathporium www.teacherspayteachers.com/store/mathporium Page 2 of 2  Liked this product? Here are some other resources you might like. Guided Notes Bundle (all 6th grade math standards) A group of math guided notes A group of math expressions and equations unit bundle Description automatically generated Description automatically generated Expressions & Equations Unit Bundle A cartoon calculator and pencil Description automatically generated (lessons for all EE standards) Follow me on TPT and Leave a review and get notifications on earn credit towards future products, sales future TPT purchases. & freebies!