Algebraic Thinking

 

1. Problem: Sara, Ann, and Eric were collecting baseball cards. Sara had 210 cards. Ann had twice as many cards as Sara. Eric has as many cards as Sara and Ann together. How many baseball cards did Eric have? 

Methods:

• Estimate

• Write algebraic equation(s)

Promotes Mathematical Understanding: The answer is not enough. Students must use variables to reason abstractly.

Solution: Write algebraic equation- If A= Ann, E=Eric, and S= Sara, then S = 210. We need to find out how many cards Ann has in order to determine how many Eric has. Thus we can write an algebraic equation to help us determine. 2(S)=A and S+A=E. In other words A = 2 x 210 = 420 and E = 210 + 420 = 630 cards. Eric has 630 cards.

Problem Source: http://www.portangelesschools.org/students/grade-5-AS.html

Web 2.0 Tools: Educreations Whiteboard App, Microsoft Word

 

2. Problem: Find two different ways to make 9 using the operations of addition, subtraction, and multiplication. You can use parenthesis as many times as you like and each of the numbers 1, 2, 3, and 4 once.

Methods:

• Create an algebraic equation using multiplication and subtraction

• Create an algebraic equation using multiplication and addition 

• Create an algebraic equation using addition and subtraction

Promotes Mathematical Understanding: This task promotes mathematical understanding in that it provides students the opportunity to work creatively with three of the four fundamental arithmetic operations (multiplication, addition, and subtraction). More so, this task helps students to develop fluency with multiplication, addition, and subtraction of single digit numbers.

Solution: Create an algebraic equation using multiplication and subtraction- knowing that 3 x 3 =9, we can create the following algebraic equation: 9 = 3 x (4 – 1). Create an algebraic equation using multiplication and addition- knowing that 8 + 1 = 9, we can create the following algebraic equation: 9 = (4 x 2) + 1.

Problem Source: https://www.illustrativemathematics.org/illustrations/1596

Web 2.0 Tools: Educreations Whiteboard App, Google Document

 

3. Problem: How does the product of 60 x 225 compare to the product 30 x 225?

Methods:

• Draw picture

• Write an equation

Promotes Mathematical Understanding: This task promotes mathematical understanding in that students are encouraged to activate and apply prior knowledge of multiplication. The task builds on the following standards of previous grades: 3.OA.5- Apply properties of operations as strategies to multiply and divide and 4.OA.1- Interpret a multiplication equation as a comparison.

Solution: 60 is two times larger than 30. Thus the product 60 x 225 is two times larger than the product 30 x 225. In knowing this we can create the following equation to demonstrate our understanding: 60 x 225 = (2 x 30) x 225 = 2 x (30 x 225).

Problem Source: https://www.illustrativemathematics.org/illustrations/139

Web 2.0 Tools: Doodle Buddy, Educareations Whiteboard App, Microsoft Word