Math+for+2011-2012+6th+grade

Day 1 Welcome and Expectations Day 2-8 ........[Benchmark assessments during this time as well] Constructions - do the first and maybe second page. Choose from the following links:
 * Week 1-1 and 1-2: Construction Zone for grades 6-8 in math. We will be constructing geometric figures to launch the year. These hands-on labs will come in handy later in the year. We will also benchmark test on DACS (edperformance) and AIMS Web.**

[|Line segments] [|Perpendicular segments] [|Angles]

[] Cool link for CIRCUMCENTER connection

[|Triangles] [|Medians of triangles] [|Altitudes of triangles] [|Angle bisectors] [|Circles]

//Skills/Fluency//: 1/42 place value;estimating differences of whole numbers 2/43 (same)

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 * ===Geometry===
 * Solve real-world and mathematical problems involving area, surface area, and volume
 * 6.G.1. Find the area of **right triangles**, **other triangles**, **special quadrilaterals**, and **polygons** by composing into rectangles or **decomposing** into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.






 * 6.G.2. Find the **volume** of a **right rectangular prism** with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas //V = l w h// and //V = b h// to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
 * 11 Take a small box and stack base ten units in it. How many "ones" can you pack in there?
 * 11 Build a right rectangular prism with link cubes. How many cubes did you use? What does this have to do with volume? What do our boxes have to do with the right rectangular prisms? Record our ideas in our daily notes.
 * 11 []
 * 11 []
 * 12 []
 * 12 Activity created at edhelper about volume of rectangular prisms. Why do they say "right rectangular prism" by the way?
 * 13 [] Identify the problems that have right rectangular prisms and solve these problems. Think about where you are headed with your study of volume. Could you find the volume of a pyramid? How would you approach this after what we did with rectangular prisms?
 * 13 Have you recorded in your notes in our "Stragies" for our review of the volume formula for boxes? What are boxes officially called in math? ;)
 * 13 Have you recorded in your notes in our "Stragies" for our review of the volume formula for boxes? What are boxes officially called in math? ;)

Week **1-4, 1-5**

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




 * 6.G.3. Draw **polygons** in the **coordinate plane** given coordinates for the **vertices**; use coordinates to find the length of a side joining points with the same **first coordinate** or the same **second coordinate**. Apply these techniques in the context of solving real-world and mathematical problems.
 * 14 [] Modify this assignment and find the length of the sides as we create these examples on graph paper.
 * 14 Activity created at the above link.
 * 14 Help! Frau Schlechter needs a real-world connection for this standard yet.
 * 14 Help! Frau Schlechter needs a real-world connection for this standard yet.



Week **1-5**

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




 * 6.G.4. Represent **three-dimensional figures** using **nets** made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
 * 15 [] Remember how to find area of trapezoids? Here is a quick review. This leads us into finding surface area of three-dimensional figures, which you will learn to call **polyhedrons**.
 * 15 See Frau Schlechter's net models that she found over the summer in the __Glencoe Mathematics Course Two Lab Book__.
 * 16 Super Source Lab or unit found at the link above!
 * 17
 * 18 DACS TESTING TIME :) AIMS Web
 * If we have time: Create nets for the figures shown at this link: []
 * If we have time: Create nets for the figures shown at this link: []

Week **1-6, 1-7**

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



>
 * ===The Number System===
 * Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
 * 6.NS.1. **Interpret** and **compute** **quotients** of **fractions**, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. //For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.//
 * 19 Review operations of fractions: build examples using manipulatives for these story problems. Create stories here: [].
 * 20 As we review how to combine or take apart fractions, record notes in our "Strategies" or "Conjectures" section about how to solve addition and subtraction of fractions. What are our own algorithms that we have discovered? We already saw fractions earlier this year with finding area of some figures that had an extra portion or fraction in their measurements. :)
 * 21 [] . Create a review here, Mrs. Schlechter, about adding and subtracting fractions. Are fractions real numbers? Are they integers? Are they always rational? What are all these questions about? ha ha
 * 22 Review multiplication of fractions by creating models for these naked problems: []
 * 23 Multiplying fractions using a Super Source Lab-?
 * 24 Recording observations and we manipulate fractions and multiply. What do you see for a pattern?
 * 25
 * 26 What is the difference between multiplying fractions and dividing fractions? To think about this, back up. What is the difference between multiplying whole numbers and dividing whole numbers? Take notes as we discuss the patterns we see.
 * 27
 * 28 Super Source Lab showing division of fractions. Our objective: to come up with an algorithm that works in all case for dividing fractions
 * *End of quarter ? DACS TESTING TIME :) AIMS Web
 * 29
 * 30
 * 31
 * 32
 * 33 See if you can solve some of these problems created at this link: [] . How do you explain how to solve problems like this?
 * If fraction division is easy, let Mrs. Schlechter show you something else at: [].
 * If fraction division is easy, let Mrs. Schlechter show you something else at: [].

Week **1-8, 1-9, 2-1, 2-2**

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

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Assessment:???????????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">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



Mrs. Schlechter: Remember "Prime Builders" activity with shapes. (Misconceptions book) Objectives: identify and find the prime factorization of any positive integer. Apply divisibility rules.
 * Multiply and divide multi-digit numbers and find common factors and multiples.
 * 6.NS.2. Fluently divide multi-digit numbers using the standard algorithm.
 * 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. These two standards are addressed in our weekly maintenance sets of problems. Please check out the work we do each Monday to "maintain" our skills! :)

> //The Sieve of Eratosthenes.// > //When the multiples sublime,// > //The numbers that remain are Prime.// ||> ” || > —Traditional, [|[][|11][|][|[][|12]|
 * Use activity about the SIEVE OF ERATOSTHENESES to review prime and composite numberes...the Sieve of Eratosthenes in verse:
 * < “ || //Sift the Twos and sift the Threes,//

>> 35 Then, create mini-examples of numbers generated at these links to help us explore composite and prime numbers as we create prime factorization models. >> []
 * 6.NS.4. Find the **greatest common factor** of two **whole numbers** less than or equal to 100 and the **least common multiple** of two whole numbers less than or equal to 12. 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 factor. //For example, express 36 + 8 as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.//
 * 34 Review properties with homework prior to class: [] What properties were not reviewed in this activity? Note: on this project, the properties are called "laws." Are you okay with this? IN CLASS, Distributive Property []

[]


 * 36 What does prime factorization have to do with GCF and LCM? Can you help me not be confused?



<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Week **2-2, 2-3**

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Skills/Fluency:??????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Assessment:???????????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">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




 * Apply and extend previous understandings of numbers to the system of rational numbers.


 * 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
 * 37 Before using the **//Algebra Survival Guide//** by Josh Rappaport, explore integers with our counters on a mat. What does the set of numbers called integers look like? What happens when we put two positive numbers together? two negative numbers? one positive and one negative? Is zero an integer? Can you subtract integers? Activity to explore integers found at: [] and exploring the values of integers more: []
 * 38 Discuss and record our observations and compare that to the text listed above for combining integers. List where you have seen integers in your world. Do this activity: [] and interact at [] adding and subtracting integers on-line here ;)


 * ??? Super Source



<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Week **2-4**

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Skills/Fluency:??????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Assessment:???????????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">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





41 ...What does the above paragraph mean to us now? []
 * 6.NS.6.Understand a **rational number** as a point on the **number line**. Extend number line diagrams and **coordinate axes** familiar from previous grades to represent points on the line and in the plane with **negative number coordinates**.
 * 39 Do number line activity like we did in math camp 2011. Hand out fractions and have students place them on the number line and give their rationale for putting the number where they did. Next, add other types of rational numbers. As a class define rational numbers and describe what they look like and behave like. Can one add a decimal and a fraction together? What are some more green hat ideas related to our exploration of rational numbers? **//Algebra Survival Guide//** by Josh Rappaport
 * 40
 * ** Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. **
 * **Understand signs of numbers in ordered pairs as indicating locations in** quadrants **of the** coordinate plane**; recognize that when two ordered pairs differ only by signs, the locations of the points are related by** reflections across one or both axes
 * Transformation Golf** []
 * 42 Find and position integers and other rational numbers on a **horizontal** or **vertical** number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Do activity created at this link:



<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Week **2-5, week 2-6**

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Skills/Fluency:??????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Assessment:???????????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">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




 * 6.NS.7.Understand ordering and **absolute value** of **rational numbers**.
 * Interpret statements of **inequality as statements** about the relative position of two numbers on a number line diagram. //For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.//
 * Write, interpret, and explain statements of order for rational numbers in real-world contexts. //For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.//
 * Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. //For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.//
 * Distinguish comparisons of absolute value from statements about order. //For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.//
 * 43 Explore absolute value...



Another activity, but it could be a little difficult for this level: [] Note: absolute value is described very well in **//Algebra Survival Guide//** by Josh Rappaport
 * 44 Speaking of inequalities: []



<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Week **2-6**

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Skills/Fluency:??????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">Assessment:???????????????????

<span style="background: white; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">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

> Modify to meet the standard.
 * 6.NS.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
 * 45 Use an activity from this link to launch: []
 * 46 Real world connection? Discuss and record. **Transformation Golf** []
 * 47
 * 48 DACS time

<span style="background: #c5c3c3; line-height: 12pt; margin: 0in 0in 10pt; tabstops: list .5in; text-indent: -0.25in;">·

** Subject - Standard- Skills - Assessment - Resources used/How was it taught?- Week **
 * <span style="background: white; color: #3b3b3a; line-height: 12pt; margin: 0in 0in 7.5pt; tabstops: list 1.0in; text-indent: -0.25in;">o **

<span style="background: #c5c3c3; color: #0000ff; line-height: 12pt; margin: 0in 0in 10pt; text-indent: -0.25in;">Mathematical Practices for grades K-8

**//<span style="background: #c5c3c3; line-height: 12pt; margin: 0in 0in 10pt; tabstops: list .5in; text-indent: -0.25in;">Habits of Mind of a Productive Mathematical Thinker //** 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.

**// Reasoning and Explaining //** 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.

**// Modeling and Using Tools //** 5. Use appropriate tools strategically. 6. Attend to precision.

**// Seeing Structure and Generalizing //** 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.