September Session #1

Focus: Task analysis to drive instruction.

Process:

Selection: A task is selected per grade level. CKingEducation will select the tasks initially with the intention that we grow towards teacher selection of purposeful, rich tasks. 

  1. Implementation: Students and teachers are given the task to resolve. The task should not take more than 10 minutes for students to complete.

  2. Analysis: Teachers, with guidance from a facilitator, analyze each students’ work sample.  Teachers will be taught how to unpack what the student work means by naming math models, strategies and vocabulary used.

  3. Support: Based on the trends noted teachers, with the guidance of a facilitator, outline 1 to 3 measurable ways to address the identified areas of challenge.  Teachers also identify 1 pedagogical or content knowledge area that they need to gain a deeper understanding of.

  4. Assess: Teachers periodically (6 weeks, 3 months - 6 months) assess growth in targeted areas to determine if the measurable ways to address are working and if knowledge is being retained by students in the short and long-term

TASKS:

Online Resources:

February 3 - 5 Session

Grade 3: Modules 6 and 7

  • Collecting and Displaying Data

  • Geometry and Measurement Word Problems

Slide Deck

Editable Documents for Session: Survey Question, Word Problems List

Interpret the Data Cards

Papers: Dot Paper, Isometric Grid Paper

Focus Standards:

3.G.3 - Use a right angle as a benchmark to identify and sketch acute and obtuse angles. (Not directly addressed in Modules)

3.MDA.2 - Estimate and measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (mL, L) to the nearest whole unit. (Not directly addressed in Modules)

3.MDA.3 - Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar graph to represent the data. (Module 6)

3.MDA.4 - Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units. (Modules 6 and 7)


Grade 4: Modules 6 - Decimal fractions

Slide Deck

Papers: Decimal Squares

Comparing Decimals

Decimals on a Hundredth Disk (.pdf), Number Line , Hundredths Disk (online tool)

Focus Standards:

4.NSF.5 - Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100.

4.NSF.6 - Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction.

4.NSF.7 - Compare and order decimal numbers to hundredths, and justify using concrete and visual models.

4.MDA.2 - Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations.


Grade 5: Module 5 - Addition and Multiplication with Volume and Area

Slide Deck

Demo Lesson Notes and Monitoring Sheet

Volume Fermi Meets 3-Acts Task – How many cubes? What is the volume of the entire object?

5.MDA.3 - Understand the concept of volume measurement.

  • a. Recognize volume as an attribute of right rectangular prisms;

  • b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes;

  • c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes.

5.MDA.4 - Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation.

5.G.3 - Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

5.G.4 - Classify two-dimensional figures in a hierarchy based on their attributes. (volume, area, perimeter, polygon attributes-quadrilaterals)


Additional Materials/Readings

During the 5th grade session, we got into a conversation about multiplication. I mentioned an article, “It Ain’t No Repeated Addition” by Keith Devlin, that stirred up the math community a few years ago. That article was followed up with, “It’s Still Not Repeated Addition”. That article was followed up with, “Multiplication and Those Pesky British Spellings.” A few years later Prof. Devlin followed up with “What Exactly is Multiplication?

February K - 2 Session

KINDER: MODULE 5 - Numbers 10 - 20, Count to 100 by Ones and Tens

Slide Deck for Kinder Module 5

South Carolina Support Document - Kinder

Video: Kinder Math Counting

Video: Kinder Math Make Groups of 10

Video: Math Studio Talk K.CC

Video: Say the “Ten Way”

Video: Build a Rekenrek

How to Make a Rekenrek?

Video: Dice and Rekenrek

Video: 5 Activities for the Rekenrek

K.NS.1 Count forward by ones and tens to 100.

K.NS.2 Count forward by ones beginning from any number less than 100.

K.NS.3 Read numbers from 0 – 20 and represent a number of objects 0 – 20 with a written numeral.

K.NS.4 Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that:

a. the last number said tells the number of objects in the set (cardinality);

b. the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number);

c. each successive number name refers to a quantity that is one more and each previous number name refers to a quantity that is one less.

K.NS.5 Count a given number of objects from 1 – 20 and connect this sequence in a one-to-one manner

K.NSBT.1 Compose and decompose numbers from 11 – 19 separating ten ones from the remaining ones using objects and drawings.


GRADE 1: MODULE 4 - Place Value, Comparison, Addition and Subtraction to 40

Slide Deck for Grade 1 Module 4

Understanding Base 10

Grade 1 Number String

South Carolina Support Document - Grade 1

GFletchy Counting Progression: Addition and Subtraction

Finger Counters by Marc Peyser

Video: Place Value 2.NBT (vertical view)

Video: Adding on a Ten Frame

1.NBT.1 Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number; c. read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; d. read and write in word form numbers zero through nineteen, and multiples of ten through ninety.

1.NBT.2 Understand place value through 99 by demonstrating that: a. ten ones can be thought of as a bundle (group) called a “ten”; b. the tens digit in a two-digit number represents the number of tens and the ones digit represents the number of ones; c. two-digit numbers can be decomposed in a variety of ways (e.g., 52 can be decomposed as 5 tens and 2 ones or 4 tens and 12 ones, etc.) and record the decomposition as an equation.

1.NBT.5 Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations, including concrete models.

1.NBT.3 Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than. es or 4 tens and 12 ones, etc.) and record the decomposition as an equation

1.NBT.4 Add through 99 using concrete models, drawings, and strategies based on place value to: a. add a two-digit number and a one-digit number, understanding that sometimes it is necessary to compose a ten (regroup); b. add a two-digit number and a multiple of 10.

1.NBT.6 Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value.


GRADE 2: MODULES 6 - Foundations of Multiplication and Division

Slide Deck for Grade 2 Modules 7 and 8

Slide Deck for Module 6

South Carolina Support Document - Grade 2

2.MDA.6  Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m

2.MDA.7 Solve real-world/story problems involving dollar bills using the $ symbol or involving quarters, dimes, nickels, and pennies using the ¢ symbol.

2.ATO.4 Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

2.G.2   Partition a rectangle into rows and columns of same-size squares to form an array and count to find the total number of parts



January 3 - 5 Session

GRADE 3: MODULE 4 - Multiplication and Area

Slide Deck for Grade 3 Module 3

South Carolina Support Document - Grade 3

Math Learning Center Apps

Fermi Task #1

Fermi Task #2

3.MDA.5 Understand the concept of area measurement.

  • a. Recognize area as an attribute of plane figures;

  • b. Measure area by building arrays and counting standard unit squares;

  • c. Determine the area of a rectilinear polygon and relate to multiplication and addition.

GRADE 4: MODULE 5 - Fraction Equivalence, Ordering, and Operations

Slide Deck for Grade 4 Module 3

South Carolina Support Document - Grade 4

Math Learning Center Apps

4.NSF.1 Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), a/b, is equivalent to a fraction, n×a/nxb, by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

4.NSF.2 Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 and represent the comparison using the symbols >, =, or <.

4.ATO.5 Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence.

4.NSF.3 Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions.

  • a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation;

  • b. Add and subtract mixed numbers with like denominators;

  • c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

4.NSF.4 Apply and extend an understanding of multiplication by multiplying a whole number and a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100).

  • a. Understand a fraction 𝑎/𝑏 as a multiple of 1/𝑏 ;

  • b. Understand a multiple of 𝑎/𝑏 as a multiple of 1/𝑏 , and use this understanding to multiply a fraction by a whole number;

  • c. Solve real-world problems involving multiplication of a fraction by a whole number (i.e., use visual fraction models and equations to represent the problem).

4.MDA.4 Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot.

GRADE 5: MODULE 4 - Multiplication and Division of Fractions and Decimal Fractions

Slide Deck for Grade 5 Module 3

Vocabulary Tic Tac Toe Template

South Carolina Support Document - Grade 5

Math Learning Center Apps

5.NSF.3 Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., 𝑎/𝑏 = 𝑎 ÷ 𝑏).

5.NSF.4 Extend the concept of multiplication to multiply a fraction or whole number by a fraction.

  • a. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths;

  • b. Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product;

  • c. Interpret multiplication in which both factors are fractions less than one and compute the product.

5.NSF.5 Justify the reasonableness of a product when multiplying with fractions.

  • a. Estimate the size of the product based on the size of the two factors;

  • b. Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number;

  • c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number;

  • d. Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1.

5.NSF.6 Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number.

5.NSF.7 Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.

  • a. Interpret division of a unit fraction by a non-zero whole number and compute the quotient;

  • b. Interpret division of a whole number by a unit fraction and compute the quotient.

5.NSF.8 Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations.

5.MDA.2 Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot.

5.NSBT.7 Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings.

5.ATO.1 Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).

5.ATO.2 Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases.


January K - 2 Session

KINDER: MODULE 4 - Number Pairs, Addition and Subtraction to 10

Slide Deck for Kinder Module 4

South Carolina Support Document - Kinder

GFletchy Counting Progression: Addition and Subtraction

Finger Counters by Marc Peyser

Splat

K.ATO.1 Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, and equations.

K.ATO.2 Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10.

K.ATO.3 Compose and decompose numbers up to 10 using objects, drawings, and equations.

K.ATO.4 Create a sum of 10 using objects and drawings when given one of two addends 1 – 9. (CCSS: K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.)

GRADE 1: MODULE 3 - Ordering and Comparing Length Measurements as Numbers

Slide Deck for Grade 1 Module 3

South Carolina Support Document - Grade 1

How Big Is a Foot? (read aloud)

Math Learning Center Apps (Geo Board)

1.ATO.1 Solve real-world/story problems using addition (as a joining action and as a partpart-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 20 with unknowns in all positions.

1.MDA.1 Order three objects by length using indirect comparison.

1.MDA.2 Use nonstandard physical models to show the length of an object as the number of same size units of length with no gaps or overlaps.

1.MDA.4 Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-charts and tallies.

GRADE 2: MODULES 8 - Time, Shapes, and Fractions as Equal Parts of Shapes

Slide Deck for Grade 2 Modules 8

South Carolina Support Document - Grade 2

GFletchy Counting Progression: Fraction Comparison and Equivalence

2.MDA.6 Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m.

2.G.1 Identify triangles, quadrilaterals, hexagons, (and cubes). Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.

2.G.3 Partition squares, rectangles and circles into two or four equal parts, and describe the parts using the words halves, fourths, a half of, and a fourth of. Understand that when partitioning a square, rectangle or circle into two or four equal parts, the parts become smaller as the number of parts increases.

Read Alouds:

The Math Curse

The Greedy Triangle

Online Tools:

Visnos Clock

Math Learning Center Apps (Geo Board)

U.S. Mint H.I.P. POCKET CHANGE KIDS SITE

November K - 2 Session

KINDER: MODULE 3 - Comparison of Length, Weight, Capacity and Numbers to 10

Slide Deck for Kinder Module 3

Shape People Images

South Carolina Support Document - Kinder

K.NS.7 Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies.

K.NS.8 Compare two written numerals up to 10 using more than, less than or equal to.

K.MDA.1 Identify measurable attributes (length, weight) of an object.

K.MDA.2 Compare objects using terms such as shorter/longer, shorter/taller, and lighter/heavier.

GRADE 1: MODULE 2 - Introduction to place value through addition and subtraction within 20

Slide Deck for Kinder Module 2

South Carolina Support Document - Grade 1

Dr. Nicki’s Video on the Beaded Number Line

GRADE 2: MODULEs 4 & 5 - addition and subtraction withIN 100, withIN 1,000

Slide Deck for Kinder Modules 4 and 5

South Carolina Support Document - Grade 2

Standards Explained: 2.ATO.1, 2.NSBT.5, 2.NSBT.6, 2.NSBT.7, 2.NSBT.8

Math Studio Talk: 2.NBT, 2.OA


November 3 - 5 Sessions

Grade 5: Module 3 - Adding and Subtracting Fractions

Research Worth Reading from TurnonMathCC: Fractions

Standards Explained: 5.NSF.1, 5.NSF.2

Gr. 5 Module 3 Slide Deck

Grade 4: Module 3 - Multiplication and Division

Research Worth Reading from TurnonMathCC: Multiplication and Division

GFletchy: Progression of Multiplication and Division

Standards Explained: 4.NSBT.5, 4.NSBT.6

Gr. 4 Module 3 Slide Deck

Grade 3: Module 5 - Fractions

Research Worth Reading from TurnonMathCC: Fractions

GFletchy: Progression of Fractions: Meaning, Equivalence and Comparison

Standards Explained: 3.NSF.1, 3.NSF.2, 3.NSF.3

Gr. 3 Module 5 Slide Deck

Chin Sen Bop Finger Multiplication

Fraction Bars w/ Dr. Bennett

True/False Hold-ups - Fractions

September Module Unpacking