Inspecting Equations!
Intermediate...Madison Binder
Just the Facts!
Inspecting equations activities focus on learning about how the equal sign expresses equality relationships
Students:
- Discuss true/false or open number sentences (equations)
- Use number relationships to reason about equality relationships
- Recognize patterns and make conjectures about number properties
- Justify their thinking mathematically
Inspecting equations activities can provide a whole class experience because of many entry points
The Inspecting Equations Block focuses on:
- Concepts of equality and the meaning of the equal sign
- Involves students analyzing conventional symbols of number, operations, and relationships
- Encourages students to look for and use number relationships as well as computation to confirm equality relationships
- Can be used interchangeably with the Number Work block
- Utilizes about 15 minutes of a math hour
- Occurs as a heterogeneous large or small group activity
The Big Ideas...
Number, Operations and Algebraic Relationships
- Analyze equations to understand the equal sign as a mathematical symbol of equality rather than a signal to compute
- Understand and use conventional symbolic notation
- Represent the idea of a variable as an “unknown quantity” using a letter or a symbol Develop and use number relationships Seeing an entire equation across the equal sign before responding
- Justify conjectures about number properties
- Understand and use the commutative, associative, and distributive properties
- Use number relationships to compute more fluently
During grades 3-5, students refine and expand their understanding of base-ten concepts, fractions, and operations. They use their knowledge of facts, basic properties, and number relationships rather than computation to reason about equations such as:
- 25 + 47 = a + 26
- 67 + 28 - 29 = 66
- g + g + 4 = 16
- 75 x 45 x 0 = y
Exploring the Equal Sign
Equal Sign-pg.239
Families of Numbers
The teacher writes three numbers on the board large enough for the entire group to see. Ask students to use the three numbers with an operation symbol and an equal sign to express a true equality relationship, for instance, 8, 7 and 56 or 12, 5, and 60. After several seconds of thinking time, ask students to share their thoughts, listing as many true number sentences as they can think of. Students share reasons for their decisions, working with the others to determine that the number sentences (equations) they have created make sense. Continue the discussion for all eight equations. The teacher writes a new set of three numbers, deciding upon what number relationship or number property relationship to highlight based on the points made during the student discussion.
True or False Number Sentences - pages 243-247
Teacher writes a closed number sentence for the class to decide if it's true or false. Students are asking to share their reasoning for their decision, working to convince others that their thinking makes sense. The teacher then writes a new number sentence (equation) below the first, deciding what number relationship or number property relationship to highlight based on the points made during the student discussion. For example: A teacher begins by writing a familiar equation such as 3 + 5 = 8. After hearing the students reason why this is a true statement, the teacher writes an unfamiliar equation, in this instance 8 = 3 + 5. The students discuss their thoughts about whether or not this equation is a true statement of equality.