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What is the significance of addition "+" and subtraction "-"?CCSS.MATH.CONTENT.K.OA.A.1
CCSS.MATH.CONTENT.K.OA.A.2
CCSS.MATH.CONTENT.K.OA.A.5

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Students often times confuse the symbols for addition and subtraction while also "thinking addition means 'join together' and subtraction means 'take away'" (ASCD, 2011, p.9).

NLVM applet: (Use  Internet Explorer)http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html

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What does the equal sign really mean?
CCSS.MATH.CONTENT.1.OA.D.7
CCSS.MATH.CONTENT.1.OA.C.6
CCSS.MATH.CONTENT.1.OA.A.1

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Students frequently misunderstand the meaning of equality.  Carpenter found the misconception of equality to "limit students' ability to learn basic arithmetic ideas" (Carpenter, 2012, p. 9).

Addition Scale Math Game

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Can you balance the scale? Put your addition cap on and give it a try! All you have to do is find the missing addend to make the scale balance perfectly.

You can adjust the addition scale game to your level. Simply tap the "min" button to choose the minimum sum and the "max" to select the maximum sum. For example, if students are working on building fluency while adding within 10, set the "min" at 1 and the "max" at 10. Then it's time to play.

Select the addend that belongs where the question mark is from the five options and drag it to the scale. If you're correct, the scale will balance and you'll earn a point for your "Correct" score at the top right-hand side of the screen. If you're wrong, you'll see the correct answer and a point will be added to the "incorrect" score. See how many correct answers you can get!

This online addition game builds a deep understanding of addition! To play, students have to add the addends of the left side to determine the total. Then, they have to figure out the missing addend on the scale's right side to achieve the same sum as the left side. It involves many steps! This online addition game also builds algebraic thinking. Assign it as individual work in class, as homework, or during indoor recess!

Visit classplayground.com for more addition activities and printables.

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This online addition game helps students build fluency in addition and develop algebraic thinking skills. Try it, it's free!

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Why do we focus so much on identifying "key words" when the words can have different meanings?
CCSS.MATH.CONTENT.2.OA.A.1
CCSS.MATH.CONTENT.2.OA.B.2
CCSS.MATH.CONTENT.2.OA.C.3

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Students rely on "Key Words'' which do not always lead to a correct solution.  For example:  Kendra took the 28 stickers she no longer wanted and gave them to Juan.  Now Kendra has 19 stickers left.  How many stickers did Kendra have to begin with?

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Adding Worms: Two-Digit Addition Game | Game | Education.com

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Kids practice adding small numbers in this silly addition game.

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Does the order the numbers are written in a multiplication sentence mean they MUST be  multiplied in the order they are listed?

CCSS.MATH.CONTENT.3.OA.B.5
CCSS.MATH.CONTENT.3.OA.A.1
CCSS.MATH.CONTENT.3.OA.A.3

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How can multiplying factors become more concrete and meaningful?
CCSS.MATH.CONTENT.4.OA.A.2
CCSS.MATH.CONTENT.4.OA.A.3
CCSS.MATH.CONTENT.4.NBT.B.6

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A common misconception in third grade is multiplying numbers in the order they are listed.

Thinking Blocks:

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Generalizations and a lack of concrete representations lead to misconceptions in students' algebraic reasoning foundation.
https://www.education.com/game/pool-creation-math-problems/

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Kids step into the role of contractor by designing a pool in this silly game. Players are challenged to either find the area of a pool or build a pool with a specific area, approaching how to find area using multiple strategies, such as multiplication and repeated addition. This varied approach to learning helps kids strengthen their problem-solving skills and makes gameplay more fun.

Grade

Subject

View aligned standards

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Multi-Digit Multiplication Word Problem Math Game | Game | Education.com

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Kids step into the role of contractor by designing a pool in this silly game. Players are challenged to either find the area of a pool or build a pool with a specific area, approaching how to find area using multiple strategies, such as multiplication and repeated addition.

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How can abstract concepts be made into more concrete, tangible understanding?
CCSS.MATH.CONTENT.5.OA.A.1
CCSS.MATH.CONTENT.5.OA.A.2
CCSS.MATH.CONTENT.5.OA.B.3

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Memorization of "rules without without reasons" leads to instrumental understanding (Skemp, 1976, p.2).

NCTM Illumination applet:
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Pan-Balance----Numbers/

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Applying conceptual understanding of equality to evaluating expressions with variables.

NCTM Illumination applet:
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Algebra-Tiles/

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What is the purpose of a variable and how do I evaluate an expression with a variable in it?
CCSS.MATH.CONTENT.6.EE.A.2
CCSS.MATH.CONTENT.6.EE.A.4
CCSS.MATH.CONTENT.6.EE.B.6

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Read and write algebraic expressions using parentheses

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In this lesson you will learn how to write and read algebraic expressions by using parenthesis.

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When multiplying expressions, what does it mean to combine like terms?
CCSS.MATH.CONTENT.7.EE.A.1
CCSS.MATH.CONTENT.7.EE.A.2
CCSS.MATH.CONTENT.7.EE.B.4

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Simplifying Variable Expressions (aka 7.EE.4A-2 - Combining Like Terms)

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Combining like terms when multiplying expressions.
NLVM applet:
http://nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2.html?open=activities&from=category_g_3_t_2.html

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Another misconception of students occurs when either the slope or the y-intercept is zero.  First of all, if the slope is zero, students don’t know whether the line is a vertical line, a horizontal line, or a line that you cannot draw.  http://funbasedlearning.com/algebra/graphing/lines/default.htm

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How do these applets and interactive games relate to Universal Design for Learning?  Many times within our classrooms we have students with mixed abilities so differentiated instruction is necessary for student success.  Keeping this notion of accessibility in mind, one of the most frustrating elements found in many interactives is a timer or time constraint.  The applets and interactive games included in this Padlet assignment do not have time constraints which I think is beneficial in assessing students’ conceptual understanding since it lessens the pressure placed upon students to answer accurately in an allotted amount of time which can cause students to rush, misread, and make mistakes.

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What does the "m" represent in the linear equations y= mx + b? how do you get a vertical line and horizontal line on a graph?
CCSS.MATH.CONTENT.8.EE.A.1
CCSS.MATH.CONTENT.8.EE.B.5
CCSS.MATH.CONTENT.8.EE.C.7

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Graphing Linear Equations In Slope Intercept and Standard Form - Algebra 1 & 2 Review

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Kindergarten:
Algebraic Thinking. Retrieved from  http://www.corestandards.org/Math/Content/OA/

Association for Supervision and Curriculum Development. (2011).

Base Blocks Addition. (n.d.). Retrieved from http://nlvm.usu.edu/en/nav/frames_asid_154_g_1_t_1.html?from=category_g_1_t_1.html

National Governors Association Center for Best Practices, & Council of Chief State School

Officers. (2011). Common Core State Standards for mathematics: Operations &

1st Grade:
Addition Scale Math Game | 1st Grade Math Games | Toy Theater. (2018, February 23). Retrieved from http://toytheater.com/addition-scale/

Carpenter, T. P. (2012). Thinking mathematically: Integrating arithmetic and algebra in elementary school.             Portsmouth, NH: Heinemann.

2nd Grade:
Education.com. (2016, January 09). Adding Worms: Two-Digit Addition Game | Game. Retrieved from https://www.education.com/game/adding-worms-cuzcuz/

3rd Grade:
Thinking Blocks Modeling Tool. (n.d.). Retrieved from https://www.mathplayground.com/ThinkingBlocks/modeling_tool.html

4th Grade:
Education.com. (2019, February 14). Multi-Digit Multiplication Word Problem Math Game | Game. Retrieved from https://www.education.com/game/pool-creation-math-problems/

5th Grade:
Pan Balance – Numbers. (n.d.). Retrieved from https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Pan-Balance----Numbers/

6th Grade:
Algebra Tiles. (n.d.). Retrieved from https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Algebra-Tiles/

7th Grade:
Algebra Tiles. (n.d.). Retrieved from http://nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2.html?open=activities&from=category_g_3_t_2.html

8th Grade:
Dun, S. (n.d.). Retrieved from http://funbasedlearning.com/algebra/graphing/lines/default.htm