6.1 math vocabulary for Unit 4

• Addition Property of Equality: Adding the same number to each side of an equation produces an equivalent expression.

• Constant of proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the constant of proportionality. In a proportional relationship, y = kx, k is the constant of proportionality, which is the value of the ratio between y and x.

• Dependent variable- A variable that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.

• Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: A=kB, where k is the constant of proportionality.

• Division Property of Equality: States that when both sides of an equation are divided by the same number, the remaining expressions are still equal

• Equation: A mathematical sentence that contains an equal sign

• Independent variable: A variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.

• Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤.

• Inverse Operation: A mathematical process that combines two or more numbers such that its product or sum equals the identity.

• Multiplication Property of Equality: States that when both sides of an equation are multiplied by the same number, the remaining expressions are still equal.

• Proportion: An equation which states that two ratios are equal.

• Solution: the set of all values which, when substituted for unknowns, make an equation true.

• Substitution: the process of replacing a variable in an expression with its actual value. 

• Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.

• Term: A number, a variable, or a product of numbers and variables.

• Variable: A letter or symbol used to represent a number or quantities that vary.

6.1 Math standards that we will continue in January

The student will be able to reason about and solve one-variable equations and inequalities.

MGSE6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

MGSE6.EE.6 Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

MGSE.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.

MGSE.6.EE.8 Write an inequality of the form x < c or x > c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x < c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Represent and analyze quantitative relationships between dependent and independent variables.

MGSE6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. b. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝑑 = 65𝑡 to represent the relationship between distance and time. Understand ratio concepts and use ratio reasoning to solve problems.

MGSE.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems utilizing strategies such as tables of equivalent ratios, tape diagrams (bar models), double number line diagrams, and/or equations.

MGSE.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

MGSE.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.

MGSE.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); given a percent, solve problems involving finding the whole given a part and the part given the whole.

MGSE.6.RP.3d Given a conversion factor, use ratio reasoning to convert measurement units within one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities. For example, given 1 in. = 2.54 cm, how many centimeters are in 6 inches?

BIG IDEAS 
• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
• Relate and compare different forms of representation for a relationship.
• Use values from specified sets to make an equation or inequality true.
• Develop an initial conceptual understanding of different uses of variables.
• Graphs can be used to represent all of the possible solutions to a given situation.
• Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
• Students will solve one-step equations.

ESSENTIAL QUESTIONS
• How is an equation like a balance? How can the idea of balance help me solve an equation?
• What strategies can I use to help me understand and represent real situations using proportions, equations and inequalities?
• How can I write, interpret and manipulate proportions, equations, and inequalities?
• How can I solve a proportion and an equation?
• How can I tell the difference between an expression, equation and an inequality?
• How are the solutions of equations and inequalities different?
• What does an equal sign mean mathematically?
• How can proportions be used to solve problems?
• How can proportional relationships be described using the equation y = kx?
• How can proportional relationships be represented using rules, tables, and graphs?
• How can the graph of y = kx be interpreted for different contexts?
• How does a change in one variable affect the other variable in a given situation?
• Which tells me more about the relationship I am investigating, a table, a graph or a formula?

Alliance presentation photos

Update for 12/19

        Dear Parents,

        Our Literacy tests are today as well as our final draft of the student's opinion pieces.  Signed papers also go home today.  We will have the PBIS celebration for those students who earned 120 points on Wednesday.  Our Winter Centers will be on Thursday from 11:30-12:30.  Please make sure your student is bringing a coat each day.  Thanks for all of your support!

       Jenny M-G

Update for 12/12

     Dear Parents,

     I hope you survived the cold and that your kiddos enjoyed the snow like mine did!  Our Science test on cells and microorganisms has been postponed until tomorrow, 12/13.  In math, students will be making their test corrections on the 5.1 multiplying & dividing decimals and the 6.1 algebraic expressions tomorrow as well.  Our narrative digital presentations that Mr. Funn from the Alliance Theater has been helping the students create will be on Friday, 12/15 from 11:30 to 12:30.  Please come if you are able!  Also, we will finish up our opinion piece final drafts next Monday, 12/18.  Please let me know if you have any questions about the 5.1 and 6.1 rubrics I sent out on Remind.  Thank you, as always, for your support!!

       Jenny M-G

5.1 math resources:

MGSE.5.NF.2   Solve word problems involving addition and subtraction of fractions, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7, by observing that 3/7 < ½. Simplify Fractions: https://www.youtube.com/watch?v=U-1KjlJAA6M https://www.youtube.com/watch?v=fp0wJ9d3pKE https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-visualizing-equiv-frac/e/simplifying_fractions Improper Fractions: https://www.youtube.com/watch?v=GpumUOiGS6Q https://www.youtube.com/watch?v=ggYdPef3Nuk https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-mixed-number/v/changing-an-improper-fraction-to-a-mixed-number https://www.mathsisfun.com/improper-fractions.html https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-mixed-number/e/converting_mixed_numbers_and_improper_fractions Area Models & Algorithm w/ Fractions https://learnzillion.com/lesson_plans/7075-subtract-fractions-with-unlike-denominators-by-creating-area-models https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/v/visually-subtracting-fractions-with-unlike-denominators https://learnzillion.com/lesson_plans/6861-add-fractions-with-unlike-denominators-by-creating-area-models https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/v/subtracting-small-fractions-with-unlike-denominators https://learnzillion.com/lesson_plans/8178-add-and-subtract-fractions-with-unlike-denominators https://braingenie.ck12.org/skills/102628 Fraction Interactive board: http://www.mhhe.com/math/ltbmath/bennett_nelson8e/VMK.html?initManip=geoboards Word Problems https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-frac-word-probs/v/adding-fractions-with-unlike-denominators-word-problem https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-frac-word-probs/v/subtracting-fractions-with-unlike-denominators-word-problem Practice: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/e/subtracting_fractions https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/e/adding_fractions https://braingenie.ck12.org/skills/102628 https://braingenie.ck12.org/skills/102631 https://braingenie.ck12.org/skills/102630 Games: http://mrnussbaum.com/fractions-workshop-2/ http://www.sheppardsoftware.com/mathgames/fractions/mathman_fractions_add_uncommon.htm https://quizlet.com/181947531/adding-fractions-subtracting-fractions-flash-cards/ 6.1 math resources: MGSE6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. MGSE6.EE.6 Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. https://quizlet.com/191854052/ algebra-flash-cards/ 6.1 math Inequality word problems https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1-inequalities/v/real-world-situations-with-inequalities 6.1 math Plotting Inequalities https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1-inequalities/v/plotting-inequalities-on-a-number-line 6.1 math Balancing inequalities https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-solving-equations/v/why-we-do-the-same-thing-to-both-sides-simple-equations 6.1 Inequality Relationships https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-solving-equations/v/representing-a-relationship-with-a-simple-equation Writing resource: https://learnzillion.com/lesson_plans/7761-use-words-and-phrases-to-link-opinions-and-reasons

Update for 12/3

        Dear Parents,

        This week in science we are moving into studying microorganisms such as bacteria, mold, and protists.  Our cells and microorganisms test will be next Monday, 12/11.  In writing, students will be working on their opinion essay regarding whether or not chocolate milk should be sold in school.  In 5.1 math, we will be wrapping up our exploration of adding, subtracting, multiplying, and dividing.  Our Unit 3 test will be this Friday, 12/8.  In 6.1 math, we will also be wrapping up our algebra unit with our Unit 3 test this Friday, 12/8.  Please make sure your student is reviewing the work on Remind.

         Please let me know if you have any questions!

         Jenny M-G



5.1 grade math standards:
MGSE5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to the hundredths.
MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

BIG IDEAS • Students will understand that the placement of the decimal is determined by multiplying or dividing a number by 10 or a multiple of 10. • Students will understand that multiplication and division are inverse operations of each other. • Students will understand that rules for multiplication and division of whole numbers also apply to decimals.

ESSENTIAL QUESTIONS • How can we use exponents to represent powers of 10? • How does multiplying or dividing by a power of ten affect the product? • How can we use models to help us multiply and divide decimals? • How do the rules of multiplying whole numbers relate to multiplying decimals? • How are multiplication and division related? • How are factors and multiples related to multiplication and division?


6th grade math standards:
MGSE6.EE.1 Write and evaluate expressions involving whole-number exponents.
MGSE6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. MGSE6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5-y.
MGSE6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
MGSE6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉 = 𝑠3 and 𝐴 = 6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠 = 1 2.
 MGSE6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. MGSE6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them.) For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
MGSE6.NS.4 Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100. a. Find the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factors. (GCF) Example: 36 + 8 = 4(9 + 2) b. Apply the least common multiple of two whole numbers less than or equal to 12 to solve real-world problems.

ESSENTIAL QUESTIONS • How are “standard form” and “exponential form” related? • What is the purpose of an exponent? • How are exponents used when evaluating expressions? • How is the order of operations used to evaluate expressions? • How are exponents useful in solving mathematical and real world problems? • How are properties of numbers helpful in evaluating expressions? • What strategies can I use to help me understand and represent real situations using algebraic expressions? • How are the properties (Identify, Associative and Commutative) used to evaluate, simplify and expand expressions? • How is the Distributive Property used to evaluate, simplify and expand expressions? • How can I tell if two expressions are equivalent?

5.1 and 6.1 math resources

5.1 standards and Tiger Time: MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths,  using concrete models or drawings and strategies based on place value,  properties of operations, and/or the relationship between addition and  subtraction; relate the strategy to a written method and explain the  reasoning used. MGSE5.NBT.2 Explain patterns in the number of zeros of the product when  multiplying a number by powers of 10, and explain patterns in the placement  of the decimal point when a decimal is multiplied or divided by a power of 10.  Use whole-number exponents to denote powers of 10. Dividing Decimals Supports: Video: https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-dividing- decimals/v /division-strategies-for-decimal-quotients https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-dividing- decimal s/v/dividing-decimals-completely https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-dividing- decimals/v /long-division-with-decimals https://www.youtube.com/watch?v=HlEx1TN-dqY https://www.youtube.com/watch?v=X78xis8NbF8 https://learnzillion.com/lesson_plans/5338-divide-decimals Practice: https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-dividing- decimals/e /divide-decimals-visually https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-dividing- decimals/e /dividing_decimals_3 https://www.mathgames.com/skill/5.22-division-with-decimals Games: https://quizlet.com/163562383/dividing-by-decimals-flash-cards/ https://jeopardylabs.com/play/dividing-decimals http://www.fortheloveofteachingmath.com/wp-content/uploads/2012/03/Dividing- Decimals-Board -Game.pdf http://mrnussbaum.com/decimals-workshop/ https://www.teacherspayteachers.com/Product/Multiplying-Decimals-Dividing- Decimals- Adding-Decimals-Subtracting-Decimals-1517495 Powers of 10 Supports: Videos: https://learnzillion.com/lesson_plans/5023-multiply-decimal-numbers-by-a -power-of-ten https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place -value- decimals-top/cc -5th-mult-powers-of-10/v/multiplying-a-decimal-by-a-power-of-10 https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place- value- decimals-top/cc -5th-mult-powers-of-10/v/dividing-a-decimal-by-a-power-of-10 https://www.youtube.com/watch?v=VwjTUTUB2xw Practice: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place- value- decimals-top/cc -5th-mult-powers-of-10/e/multiplying-and-dividing-by-powers-of-10 https://www.ixl.com/math/grade-5/multiply-a-decimal-by-a-power-of- ten https://www.math-drills.com/powersoften.php https://www.mathgames.com/skill/6.46-multiply-and-divide-decimals-by- powers-of-ten https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place-value -decimals-top/cc- 5th-mult-div-decimals-10-100-1000/a/multiplying-by-10-100-1000 https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place-value- decimals-top/cc -5th-mult-div-decimals-10-100-1000/a/multiplying-and-dividing-by-powers-of-10 Slides: https://www.slideshare.net/bayoung/multiply-and-divide-decimals-by- powers-of-10 -presentation  6.1 resources Turning word problems into algebraic expressions for 6.1;  https://learnzillion.com/lesson_plans/8009-write-word-problems-as-algebraic- expressions http://mrnussbaum.com/sixth-grade-math/