Math+Workshop

PS 10 uses a combination of several different math curriculums. We use EngageNY, Georgia Math, and Contexts for Learning. The faculty at PS 10 has worked together to pick the best aspects of each of these math curriculums.

Georgia Math Common Core Georgia Math 5th Grade Level Overview

**Unit 1: Order of Operations and Whole Numbers**
 Resources: * Here is a link to a multiplication game that uses the open array model for multiplication. It might make it a little more fun for your child to practice this model, and it has 3 different levels.  @http://downloads.bbc.co.uk/skillswise/maths/ma12pape/game/ma12pape-game-written-multiplication/multiplication.swf * Here is a video of a teacher doing division using an open array. The southern accent is strong.  @http://www.schooltube.com/video/731abef4faea4155ab68/Division%20Using%20an%20Open%20Array * Here is another example of a 4th grader dividing with the open array model:  @https://www.youtube.com/watch?v=u7M7G9bnQy0

Unit 8: Show What We Know
EngageNY EngageNY 5th Grade Mathematics Overview Module 1: Place Value and Decimal Fractions (20 days) Module 2: Multi-digit Whole Number and Decimal Fractions Operations (35 days) Module 3: Addition and Subtraction of Fractions (22 days) Module 4: Multiplication and Division of Fractions and Decimal Fractions (38 days) Module 5: Addition and Multiplication with Volume and Area (25 days) Module 6: Problem Solving with the Coordinate Plane (40 days)

Contexts for Learning Investigations

Big Ideas · Equivalence: the numbers in different place-value positions are related by powers of ten. · Multiplication and division by ten make the whole shift to the right and to the left in a decimal representation. · If the whole is shifted, one can work with decimals using whole-number arithmetic. · The accumulated increase of a constant rate is the rate times the time. · The constant rate can be determined if the accumulated rate and time are known. Strategies · Counting on instead of removal subtraction · Using repeated addition for multiplying · Using landmark decimals · Using the associative property to make “friendly” numbers and adjusting at the end · Generalized use of a repertoire of strategies for whole-number operations · Using place value understanding to multiply and divide by powers of ten Models · Analog electric meter · Ratio table
 * Investigation: The Mystery of the Meter **

Big Ideas · Fractions represent a relation. · The whole matters. · To maintain equivalence, the ratio of the related numbers must be kept constant. · The properties (distributive, associative, and commutative) that hold for whole numbers also hold for rational numbers. · The relationship between multiplication and division of fractions. Strategies · Skip-counting and/or using repeated addition to find a fraction of a whole · Using multiplication and division to make equivalent relations · Using landmark fractions to make partial products · Using decimal and/or percentage equivalents · Doubling and halving and the more generalized use of the associative property to eliminate a fraction · Using the standard algorithm for multiplication of fractions · Interchanging numerators (or denominators) to simplify first when multiplying Models · Double open number line · Open array · Ratio table
 * Investigation: Exploring Parks and Playgrounds **

Big Ideas · The commutative property of multiplication · The place value patterns that occur when multiplying by the base · The associative property of multiplication · The dimensions of length and width can be used to produce a square unit measurement of area for rectangles · The dimensions of length, width, and height can be used to produce a cubic unit measurement of volume for rectangular solids · The surface area of rectangular solids increases as the measures of the three dimensions (length, width, height) diverge · Doubling each dimension of a rectangular solid results in a new solid, with a volume that is 2 3 times the original solid Strategies · Using repeated addition · Skip-counting · Using partial products · Using ten-times · Doubling and halving · Factoring and grouping flexibly Model · Open array
 * Investigation: The Box Factory **

Big Ideas Strategies
 * Investigation: Best Buys and Ratios **
 * Fractions are relations - the size of the amount of the whole matters.
 * Fractions may represent division with a quotient less than one.
 * With unit fractions, the greater the denominator, the smaller the piece is.
 * Pieces don't have to be congruent to be equivalent.
 * For equivalence, the ratio must be kept constant.
 * To compare, add, or subtract fractions, a common whole is needed.
 * Using landmark unit fractions or using common fractions
 * Using decimal or percentage equivalents
 * Using a ratio table as a tool to make equivalent fractions
 * Using multiplication and division to make equivalent fractions
 * Using a common whole to compare and add fractions
 * Using proportional reasoning
 * Using decimal or money sense
 * Simplifying to make a common whole

Models
 * Fair sharing
 * Ratio table
 * Measurement
 * Fraction bars
 * Clock
 * Money

Online resources: Lattice Multiplication Explained

Prime Numbers Explained

Introduction to Division

<span style="background-color: #ffff00; color: #800000; font-family: 'Comic Sans MS',cursive;">Long Division and Remainders

Challenging Math Problems for 5th Graders

<span style="background-color: #ffff00; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 110%;">partial quotients lesson Engage Decimal Dividing

<span style="color: #008080; font-family: 'Comic Sans MS',cursive; font-size: 16px;">For fraction games, check out the website below!

<span style="background-color: #ffff00; color: #008080; font-family: 'Comic Sans MS',cursive; font-size: 16px;">Sheppard

<span style="color: #008080; font-family: 'Comic Sans MS',cursive; font-size: 16px;">For tutorials, the website below is very helpful.

<span style="background-color: #ffff00; color: #008080; font-family: 'Comic Sans MS',cursive; font-size: 16px;">IXL

<span style="color: #008080; font-family: 'Comic Sans MS',cursive; font-size: 16px;">Also, Khan Academy has some great video tutorials. Go to the link below, and type "fractions" into the search box.

<span style="background-color: #ffff00; color: #008080; font-family: 'Comic Sans MS',cursive;">Khan Academy