6th+Grade+Math+II

Expressions and Equations

 * Apply and extend previous understandings of arithmetic to algebraic expressions.


 * 6.EE.1. Write and evaluate **numerical** **expressions** involving whole-number **exponents**.
 * 47 [[image:http://www.mathematicsdictionary.com/english/vmd/images/n/numericalexpression.gif width="169" height="120" caption="Click here!"]]


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> > > [] > [] > [|Evaluating variable expressions]
 * 6.EE.2.Write, read, and evaluate expressions in which letters stand for numbers.
 * **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.//
 * **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.//
 * 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 = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.//
 * For days 49-50, evaluate problems using these first two ideas above!
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 * 50 [|Simplifying variable expressions]
 * 50 Discuss and apply formulas that involve expressions...equations... that help us apply the above standard in real life math. Help Mrs. Schlechter find a Super Source activity for this occasion.

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 * 6.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.//
 * 51 Use true and false statements to explore the distributive property, using resource: []
 * 52 [|The distributive property]


 * 6.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. Reason about and solve one-variable equations and inequalities.//
 * //53 What activities did we just discover that covered the idea in standard 6EE4?//

Week **2-6, Week 2-7, Week 2-8**

Skills/Fluency:??????????????

Assessment:???????????????????

Resources used/How it was taught: individual, pair-share and class discussions while utilizing the following materials...

__Glencoe's Math Maintenance 6th GradeWorkbook,__ __Math Puzzlewise,__ __Super Source__, edhelper.com,

[] worksheet activities




 * Reason about and solve one-variable equations and inequalities.

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 * 6.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.
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> > Solving subtraction equations > > Solving multiplication and division equations > > Solving addition, subtraction, multiplication, and division equations > > Write an equation for each problem. Then solve the equation.
 * 6.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. //Prior activities for Expressions and Equations lessons thus far should have provided practice for this standard.//
 * 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 nonnegative rational numbers.
 * 56 Markup, discount, and tax ([|easy])
 * 57 58 59 Solving addition equations


 * CAN YOU FOLLOW DIRECTIONS? []
 * 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.
 * 60 [[image:http://www.algebra-class.com/images/Inequalities-symbols.gif width="223" height="169" caption="Click here to find out more about inequality." link="http://www.purplemath.com/modules/ineqsolv.htm"]]Create our problems and stories to explore this standard further.
 * 61 DACS testing time :) AIMS Web
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**Week 2-9, Week 3-1**

Skills/Fluency:??????????????

Assessment:???????????????????

Resources used/How it was taught: individual, pair-share and class discussions while utilizing the following materials...

__Glencoe's Math Maintenance 6th GradeWorkbook,__ __Math Puzzlewise,__ __Super Source__, edhelper.com,

[] worksheet activities

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 * Represent and analyze quantitative relationships between dependent and independent variables


 * 6.EE.9.Use variables to represent two quantities in a real-world problem that change in relationship to one another; ** write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable **. 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.
 * 63 Create project that will include a dependent and independent variable. For example, what was the science experiment that had to do with catapults and the length of the lever used in the design?
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**Week 3-1, Week 3-2**

Skills/Fluency:??????????????

Assessment:???????????????????

Resources used/How it was taught: individual, pair-share and class discussions while utilizing the following materials...

__Glencoe's Math Maintenance 6th GradeWorkbook,__ __Math Puzzlewise,__ __Super Source__, edhelper.com,

[] worksheet activities



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 * ===Ratios and Proportional Relationships===
 * Understand ratio concepts and use ratio reasoning to solve problems.
 * 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. //For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”//
 * 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. //For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”//1
 * 6.RP.3.Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 * 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.
 * Solve unit rate problems including those involving unit pricing and constant speed. //For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?//
 * Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
 * Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

> 6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. //For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.// > 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. > 6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. > > 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
 * ===Statistics and Probability===
 * Develop understanding of statistical variability.
 * Summarize and describe distributions.
 * 6.SP.5.Summarize numerical data sets in relation to their context, such as by:
 * Reporting the number of observations.
 * Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
 * Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
 * Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

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** Subject - Standard- Skills - Assessment - Resources used/How was it taught?- Week **
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