Mrs.+Gillen-MathPlus

Mrs. Gillen-MathPlus 5/12/16  The year is almost at an end! So hard to believe!! We are wrapping up our Algebra unit and ready for our last progress check next week. Students can retake any progress checks from the 4th quarter to improve their scores and overall math grade--last day for retakes will be Friday, May 20. Congratulations to students on a job well done this year! Have a wonderful summer!! :)   4/5/16   We are well into the 4th grading period and rapidly approaching 5th Grade Ohio AIR testing--this year is just flying by!! In MathPlus class, we are nearing the end of our Geometry unit as we wrap up the topic of Volume this week. We will spend the remainder of the year mostly on Algebra concepts. We will cover the following Grade 5 and Grade 6 standards in April and May:
 * 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
 * 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
 * 5.OA.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.


 * 6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
 * 6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.
 * a. Write expressions that record operations with numbers and with letters standing for numbers.
 * b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or moreparts of an expression as a single entity.
 * c. 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).
 * 6.EE.3: Apply the properties of operations to generate equivalent expressions.
 * 6.EE.5: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, makethe equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
 * 6.EE.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that avariable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
 * 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 andx are all nonnegative rational numbers.
 * 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.

2/23/16  Spring is just around the corner, believe it or not!! The end of the 3rd Quarter is March 11, and Ohio AIR testing begins April 18. Students will be assessed in 5th grade math, ELA, and science this year. More information regarding testing will be coming to you as we get closer to April. Currently, in MathPlus class, we have been focusing on Geometry concepts. We began with some basics of geometry, and are currently working on classifying 2-D shapes into a hierarchy based on properties. Through the rest of February and March, we will continue with Geometry and Measurement concepts from both the 5th and the 6th grade curriculum. Here is a list of the standards covered in this unit:
 * 5.G.3: Understand that attributes belonging to a category of 2-D figures also belong to all subcategories of that category.
 * 5.G.4: Classify 2-D figures in a hierarchy based on properties.
 * 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement: volume is measured in cubic units, a solid figure which can be packed without gaps or overlaps using "n" unit cubes is said to have a volume of "n" cubic units.
 * 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
 * 5.MD.5: Relate volume to the operations of multiplication and addition; find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume would be the same as would be found by multiplying the edge lengths; apply the formulas V = l x w x h and V = B x h to find volume of right rectangular prisms; recognize volume as additive; find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.
 * 6.G.1: Find the area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
 * 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 x w x h and V = B x h to find the volume of right rectangular prisms.
 * 6.G.4: Represent 3-D figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.

1/4/16  Happy New Year! We are starting this new year and new grading period with more fraction work. We will start with multiplication with mixed numbers, and apply this concept to finding the area of a rectangle with fractional side lengths. Next we will move on to fraction division (including mixed numbers), using models and the standard algorithm, as well as solving real world problems with fraction division. This will conclude our work with operations on fractions and decimals, but we will be applying these concepts throughout the year, starting with measurement conversions. We will be using a combination of Eureka resources and other outside math resources to cover these topics. We will spend most of January, and possibly a few days into February on the following Grade 5 and Grade 6 Common Core math standards:
 * 5.NF.4b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fraction side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 * 5.NF.5: Interpret multiplication as scaling (resizing) by:
 * a. Comparing the size of a product to the size of one factor on the basis of the other factor, without performing the indicated multiplication.
 * b. Explaining why multiplying a given number by a number greater than 1 results in a product greater than the given number, why multiplying a given number by a number less than 1 results in a product less than the given number, and relating the principle of fraction equivalence to the effect of multiplying by 1 whole.
 * 5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 * 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions; solve real world problems involving division of unit fractions by whole numbers and vise versa, e.g., by using visual models or equations to represent the problem.
 * 5.MD.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving real-world multi-step problems.
 * 6.NS.1: Interpret and compute quotients of fractions and absolve word problems involving division of fractions by fractions, e.g., by using visual models or equations to represent the problem.
 * 6.RPA.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

11/23/15  After spending some time on adding and subtracting fractions and mixed numbers, we are now going to jump back into Eureka Math for Module 4, which introduces fraction multiplication and division. We will try to finish most of this module before we leave for Winter Break. This will cover the following Grade 5 and 6 Common Core math standards:
 * 5.NF.3: Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answer in the form of a fraction or mixed number.
 * 5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction>
 * 4a. Interpret the product "(a/b) x q" as "a" parts of a partition of "q" into "b" equal parts; equivalently, as the result of a sequence of operations ("a" times "q" divided by "b").
 * 4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 * 5.NF.5: Interpret multiplication as scaling (resizing) by:
 * 5a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated operation.
 * 5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number, multiplying by a fraction less than one results in a product smaller than the given number; and relating the principle of fraction equivalence to the effect of multiplying by 1.
 * 5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem.
 * 5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
 * 7a. Interpret division of a unit fraction by a non-zero whole number and compute such quotients.
 * 7b. Interpret division of a whole number by a unit fraction and compute such quotients.
 * 7c. Solve real world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
 * 6.NS.1: Interpret and compute quotients of fractions, and solve real world problems involving division of fractions by fractions, e.g. by using visual fraction models and equations to represent the problem.

11/9/15  We have wrapped up our unit on Rational Numbers, Integers, and the Coordinate System. Our next area of focus will shift to Fractions. We will spend a short time reviewing addition and subtraction with fractions (including mixed numbers, borrowing and carrying), which is a 5th grade standard (5.NF.1-2) that was likely introduced to MathPlus students in 4th grade. We will spend a longer amount of time on multiplying and dividing fractions, which covers both 5th and 6th grade fraction standards (5.NF.3-7 and 6.NS.1), and should be new to most students. We will be using a combination of Eureka math resources and some outside resources for our Fraction unit. This should take us up through Christmas break, possibly extending into January. 10/19/15  Students have worked very hard in the last few weeks to become fluent in their multiplication and division of multi-digit whole numbers and decimals. This week, we will begin a new topic--rational numbers and integers and their application on the coordinate plane and in the real world. This will consist entirely of 6th grade math standards (6.NS.5, 6, 7, 8). We will be defining rational numbers and integers, locating rational numbers and integers on a number line, comparing and ordering rational numbers and integers, developing an understanding of opposite integers and absolute value, and graphing points in all four quadrants of the coordinate plane (including rational numbers and integers as coordinates). 9/25/15  With the MathPlus class, it is important to make time this year to cover the 6th grade math standards. So, I am "condensing" Module 2 of Eureka since it has a lot of whole number multiplication and division that the MathPlus students have already mastered in 4th grade MathPlus. PLEASE LOOK FOR HOMEWORK HELP, ANSWER KEYS, AND RESOURCES UNDER THE NEW TAB: ** "Eureka MathPlus Resources." ** We will be taking the 1-2 weeks to work on the 6th grade math standard, which is fluently multiplying and dividing multi-digit whole numbers and decimals using the standard algorithm (6.NS.2, 6.NS.3). This includes multiplying decimals by decimals and dividing decimals by decimals. Also, Eureka has released a new parent support resource called Homework Helpers. Below, you will find the Homework Helpers for both Module 1 and Module 2. Look for the lesson number at the top of the page to find the homework helper you need. 9/22/15  We have reached the end of Module 1 in Eureka math. The last half of the module covered the following grade 5 Common Core standards: Next week we will begin extending into the grade 6 standards for whole number and decimal operations, which will include: using the standard algorithm to fluently divide multi-digit whole numbers, using the standard algorithm to fluently add, subtract, multiply, and divide multi-digit decimal numbers.
 * Module 1 Homework Helpers (Lessons 1-16):[[file:Homework_Helper-Grade_5_Module_1.pdf]]
 * Module 2 Homework Helpers (Lessons 1-18):[[file:Homework_Helper-Grade_5_Module_2.pdf]]
 * 5.NBT.4--Use place value understanding to round decimals to any place.
 * 5.NBT.7--Add, subtract, multiply, and divide decimals using concrete models or drawings and strategies based on place value, the properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

9/8/15 We have made it halfway through Module 1! In Lessons 1-8 we have worked on the following grade 5 and 6 Common Core math standards:
 * 5.NBT.1--Recognize that each place value position is 1o times greater than the place to its right and 1/10 as large as the place to its left.
 * 5.NBT.2--Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10. Explain patterns in the placement of the decimal point when multiplying and dividing numbers by powers of 10. Use whole number exponents to denote powers of 10.
 * 5.NBT.3--Read write and compare decimal numbers to thousandths:
 * Read and write decimals in word, standard, unit, and expanded form.
 * Compare two decimals to thousandths based on meanings of the digits in each place, using >, <, and = symbols to record the results of the comparisons.
 * 5.NBT.4--Use place value understanding to round decimals to any place.
 * 6.EE.1 Write and evaluate numerical expressions involving whole number exponents.

In the rest of Module 1, we will be adding, subtracting, multiplying and dividing decimals using visual models, place value understanding, and/or the standard algorithm (Lessons 9-16).  8/24/15 We are starting out this year with decimals and place value. We have covered the first 3 lessons of Eureka, which include multiplying and dividing whole numbers and decimals by powers of 10. We will be applying these concepts to measurement conversions within the metric system. Click on the EUREKA RESOURCES tab in the menu to the right to find lesson notes, extra copies and answer keys.