One Way to Think When Solving 5th Grade Geometry Questions

Odd or Even? - Compare Whole, Two-Digit Numbers and Determine if They are Odd or Even

Hamburgers - Compare And Order Whole Numbers

Foreheads: a game to develop math fact automaticity in + and x

Foreheads

Objective: Develop Addition and Multiplication Automaticity

Number of Players: 3

Materials: Deck of cards

Game Objective: Collect the most cards

Procedure:

1. Setup
1. Organize students into groups of three
1. Two players are called Foreheads
2. One player is called the Leader
2. Place the students in a triangle so that they can see each other (see Figure 1)
3. Put a deck of cards in the middle of the group so that the students can pull cards easily; the deck should be face-down
4. Card Values
1. cards 2 - 10 are worth the number posted on the card
2. Jacks, Queens, and Kings are worth 10
3. Aces are worth 1
4. Variation:
1. Jack = 11
2. Queen = 12
3. King - 13
4. Joker = 0
2. Playing
1. The Leader says "GO" and the Foreheads pick up a card and place it on their forehead
1. The Foreheads should not look at the card they place on their head
2. The Leader looks at the cards on the Foreheads and states the sum or product of the two cards
3. After hearing the sum or product, the Foreheads look at each other's heads and use the card they can see to identify the card that is on their head.
1. The Foreheads call out the number they think is on their head.
4. The Leader listens to their answers and rewards the cards to the first Forehead who guesses the correct card on their forehead.
5. The Forehead who guessed first and accurately collects the two cards and places them in a neat pile in front of them.
6. Repeat steps 1 - 6 for five rounds.  
7. When 5 rounds have been completed, the Foreheads count the number of cards in front of them and the Forehead with the most cards is declared the winner.
1. A new Leader is chosen from the Foreheads and play continues until the teacher ends the activity.
3. Ties
1. If the Leader cannot tell which Forehead said their answer the fastest and both students called out accurate answers, the two cards are placed in front of the Leader.
1. Repeat steps 1 - 5 described in the playing section above.

Resource

Bay-Williams, J. M., & Kling, G. (2014). Enriching Addition and Subtraction Fact Mastery through Games. Teaching Children Mathematics, 21(4), 238–247. 

Figure 1

Percentage of Released Questions on NYS Math Exams, 2018 - 2015

Never too Early to Teach Math- A Case Study with a Preschool Child learning the Concept of Equivalence

Shukaili Al, J. (2015). Never too Early to Teach Math- A Case Study with a Preschool Child learning the Concept of Equivalence Unpublished manuscript, SUNY College at Buffalo, Buffalo, NY.

When students are Mathematically Proficient, they possess:

1. A Productive Disposition which means they believe in one’s own mathematical efficacy
2. Adaptive Reasoning which means they can: 
1. compare two or more plausible arguments 
2. identify correct logical thought 
3. correct flawed logical thought
3. Strategic Competence which means they can formulate, represent, and solve novel mathematical problems
4. Conceptual Understanding, which means they: 
1. can see the connections among concepts and procedures 
2. can see the relationship between representations of math concepts and abstract symbols 
3. know when different representations can be used for different purposes 
4. can represent mathematical situations in different ways
5. the ability to Mathematically Reason, which means they: 
1. can formulate a mathematical problem using knowledge of mathematical solution strategies 
2. know when to use an appropriate mathematical solution strategy 
3. can solve a mathematical problem accurately 
4. can represent the essential components of a mathematical problem using numbers, symbols, drawings and mental images
6. the ability to be Procedurally Fluent, which means they can skillfully: 
1. use algorithms 
2. follow and create written procedures and rules
3. use tools to help them make calculations such as: 
1. manipulatives (concrete, representational and virtual) 
2. mental methods 
3. calculators 
4. computers 

2nd Grade Student

based on the work of Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding+ it up: Helping children learn mathematics. National Academies Press. Shannon E. Bostiga, Michelle L. Cantin, Cristina V. Fontana, & Tutita M. Casa. (2016). Moving Math in the Write Direction: Reflect and Discuss. Teaching Children Mathematics, 22(9), 546.

The PhET Team Released Four new HTML5 sims for Math in the Area Model Suite

The New Area Model sims are: 

(1.) Area Model Introduction is an approachable introduction to the concept of multiplication as area. Students can develop a strategy that uses an area model to simplify a multiplication problem.

(2.) Area Model Decimals allows students to apply their previous understandings of multiplication using an area model to multiply of rational numbers.

(3.) Area Model Multiplication extends the area model to multi-digit numbers. Students can explore the product of multi-digit numbers on a proportional grid and progress to using a generic model.

(4.) Area Model Algebra includes an additional Variables screen that allows students to multiply polynomial expressions, and a game screen to test their multiplication and factoring skills.

[Link] to Math Sims

Student Perceptions of the Flipped Classroom in Middle School Mathematics

Student Perceptions of the Flipped Classroom in Middle School Mathematics 

Andrews, K. (2017). Student Perceptions of the Flipped Classroom in Middle School Mathematics Unpublished manuscript, SUNY College at Buffalo, Buffalo, NY.

Using Technology in a Mathematics Classroom: Investigating the Usability of the Desmos Graphing Tool

Using Technology in a Mathematics Classroom: Investigating the Usability of the Desmos Graphing Tool

Molony, A. (2017). Using Technology in a Mathematics Classroom: Investigating the Usability of the Desmos Graphing Tool  Unpublished manuscript, SUNY College at Buffalo, Buffalo, NY.