EUREKA MATHEMATICAL MODELS AND STRATEGIES FOURTH GRADE Rio

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EUREKA MATHEMATICAL MODELS AND STRATEGIES FOURTH GRADE Rio Rancho Public Schools

EUREKA MATHEMATICAL MODELS AND STRATEGIES FOURTH GRADE Rio Rancho Public Schools

Place Value Charts A place value chart is a graphic organizer that helps students

Place Value Charts A place value chart is a graphic organizer that helps students use see the value of a digit. This video shows how to use a place value chart (chip model) for addition, subtraction, multiplication, and division. https: //vimeo. com/71596082

Read, Draw, Write (RDW) RDW is a process that mathematicians and teachers use for

Read, Draw, Write (RDW) RDW is a process that mathematicians and teachers use for problem solving. 1) Read. 2) Draw and Label using a tape diagram or bar model. 3) Write a number sentence (equation). 4) Write a word sentence (statement). https: //www. engageny. org/resource/word-problems-with-tape-diagrams

Tape Diagrams Tape diagrams are pictorial representations of relationships between quantities.

Tape Diagrams Tape diagrams are pictorial representations of relationships between quantities.

Number Bonds Number bonds (also referred to as branching) help students see that numbers

Number Bonds Number bonds (also referred to as branching) help students see that numbers can be “broken” into pieces or parts to make computation easier. With number bonds, students recognize the relationship between numbers through a written model that shows how the numbers relate. Number bonds are a visual representation of the part-whole relationship where the smaller numbers (the parts) make up larger numbers (the whole). http: //www. cleanvideosearch. com/media/action/yt/watch? v=u. SQRl. YRd. SDE

Number Lines The number line is used to develop a deeper understanding of whole

Number Lines The number line is used to develop a deeper understanding of whole number units, fraction units, and measurement units. Rounding on a vertical number line helps students build understanding because numbers are quite literally rounded up and down. http: //greatminds. net/maps/math/video-gallery/vertical-number-line-rounding

Multiplication Students use place value understanding and visual representations to solve multiplication problems with

Multiplication Students use place value understanding and visual representations to solve multiplication problems with multi-digit numbers. Connections are made between the models and written numerical work allowing students to see the role of place value units in multiplication. Area Models Place Value Disks, Partial Products, Standard Algorithm Students are not expected to be fluent with the standard algorithm for multiplication until the end of Fifth Grade.

Multiplication: Multiplicative Comparisons Students learn multiplicative comparison problems including the language of times as

Multiplication: Multiplicative Comparisons Students learn multiplicative comparison problems including the language of times as much in the context of area and perimeter. Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities. http: //www. showme. com/sh/? h=So. M 5 Mi 8

Multiplication: Area Model The area model is a model for math problems where the

Multiplication: Area Model The area model is a model for math problems where the length and width are configured using multiplication. https: //www. khanacademy. org/math/arithmetic/multiplication-division/area-models-multiplication/v/understandingmultiplication-through-area-models

Multiplication: Partial Products multiplication is based on the distributive, or grouping, property of multiplication.

Multiplication: Partial Products multiplication is based on the distributive, or grouping, property of multiplication. When using this algorithm one multiplies each digit of one factor by each of the digits in the other factor, taking into account the place value of each digit. Then all the partial products are added to find the total product. Students are expected to use place value language (unit form and numerical form). Unit form http: //www. sophia. org/tutorials/partial-products-algorithm Numerical form

Division Students use place value understanding and visual representations to solve division problems with

Division Students use place value understanding and visual representations to solve division problems with multi-digit numbers. Connections are made between the models and written numerical work allowing students to see the role of place value units in division. Understanding Groups Number disks, standard algorithm, area model, and number bond Students are not expected to be fluent with the standard algorithm for division until the end of Sixth Grade. The following video shows how to solve division problems using a place value chart and number disk drawings: https: //www. engageny. org/resource/grade-4 -math-represent-and-solve-division-problems-a-three-digit-dividend-4 nbt 6

Division: Place Value Disks When using place value disks, connections are made between the

Division: Place Value Disks When using place value disks, connections are made between the models and written numerical work allowing students to see the role of place value units in division. Students are not expected to be fluent with the standard algorithm for division until the end of Sixth Grade. https: //www. youtube. com/watch? v=2 x 8 Er 6 Cq 0 Fo

Division: Area Model The area model is a model for math problems where the

Division: Area Model The area model is a model for math problems where the area is known and division is used to configure width or length. Students are not expected to be fluent with the standard algorithm for division until the end of Sixth Grade. http: //greatminds. net/maps/math/video-gallery/g 4 m 3 -te-l 20 -2

Division: Tape Diagrams Tape diagrams are pictorial representations of relationships between quantities. Students are

Division: Tape Diagrams Tape diagrams are pictorial representations of relationships between quantities. Students are not expected to be fluent with the standard algorithm for division until the end of Sixth Grade. http: //www. cleanvideosearch. com/media/action/yt/watch? v=Lrz. Rd. Tc. KKNk

Division: Partial Quotients Although partial quotients is not a strategy taught in Eureka it

Division: Partial Quotients Although partial quotients is not a strategy taught in Eureka it builds understanding as students move toward the traditional algorithm. Students are not expected to be fluent with the standard algorithm for division until the end of Sixth Grade. https: //www. youtube. com/watch? v=q. Wst. A 8 EZr 2 w

Fractions: Decomposition and Equivalence In 4 th Grade, students begin to explore fraction equivalence

Fractions: Decomposition and Equivalence In 4 th Grade, students begin to explore fraction equivalence through decomposition of non-unit fractions into unit fractions and the decomposition of unit fractions into smaller unit fractions. Students use visual models to represent these decompositions and to prove equivalence. Decomposition using a tape diagram and number bonds. Scroll down the page to see the two videos: http: //www. onlinemathlearn ing. com/decomposefractions-tapediagrams. html Decomposition using an area model. https: //learnzillion. com/lesso ns/618 -generate-equivalentfractions-using-area-models Equivalence on a number line https: //learnzillion. com/lessons/619 generate-equivalent-fractions-usingnumber-lines Students are not expected to be fluent in simplifying fractions.

Fraction: Addition Students begin to understand that everything they know to be true of

Fraction: Addition Students begin to understand that everything they know to be true of addition with whole numbers now applies to fractions. Addition is finding a total by combining like units. Number Line https: //learnzillion. com/lessons/1631 -add-fractions-with-likedenominators-using-a-number-line Area Model or Tape Diagram https: //learnzillion. com/lessons/1634 -add-fractions-with-likedenominators-using-an-area-model

Fraction: Subtraction Students begin to understand that everything they know to be true of

Fraction: Subtraction Students begin to understand that everything they know to be true of subtraction with whole numbers now applies to fractions. Subtraction is finding an unknown part. Number line Tape diagrams and number bonds https: //learnzillion. com/lessons/ 1632 -subtract-fractions-with-like -denominators-using-a-numberline https: //learnzillion. com/lessons/1633 -subtract-fractions-with-likedenominators-using-an-area-model

Fractions: Adding Related Units Students add fractions with related units (common denominators), where one

Fractions: Adding Related Units Students add fractions with related units (common denominators), where one denominator is a multiple (or factor) of the other. In order to add such fractions, a decomposition is necessary. All numerical work is accompanied by visual models that allow students to use and apply their known skills and understanding. https: //learnzillion. com/lessons/973 -add-fractions-with-different-denominators-using-fraction-bars

Fractions: Addition and Subtraction by Decomposition Students apply their understanding of adding and subtracting

Fractions: Addition and Subtraction by Decomposition Students apply their understanding of adding and subtracting fractions to adding and subtracting mixed numbers. http: //www. cleanvideosearch. com/medi a/action/yt/watch? v=S 0 M 8 w 1 Nw. NHQ https: //learnzillion. com/lessons/2443 subtract-fractions-and-mixed-numbers-bydecomposing

Decimal Fractions Students use their understanding of fractions to reason about decimal numbers. In

Decimal Fractions Students use their understanding of fractions to reason about decimal numbers. In fourth grade, students work with tenths and hundredths. Tenths Hundredths http: //www. cleanvideosearch. com/media/action/yt/watch? v=2 FH 6 Yi. LWIu. E

Thank You to the following teachers and instructional coaches for collaborating on this project.

Thank You to the following teachers and instructional coaches for collaborating on this project. 2014 -2015 Transition Team: Instructional Coaches: Benjamin Steiner-CAE Ashley Randall-CDNE Rachel Wallace-EHE Tina Lautt-ESE Joy Christopherson-MCE Elizabeth Northness-MLK Kristy Straley-PDSE Michael Menor-RRE Neil Rambaldi-SVE Elizabeth Lockhart-VGE Joy Morales-District Dora Montano-District Stephanie Estes-CAE Jennifer Bartley-CDNE Clara Trimboli-CDNE Dana Petro-EHE & VGE Amanda Bell-ESE Erik Johns-MCE Tosha Young-MLK & SVE Diane Earnest-PDSE Barbara Smith-PDSE Leslie Strommen-RRE