Inspecting Equations!
Primary...Madison Binder
Just the Facts!
Inspecting Equations Block usually lasts between 5-10 minutes of the math block
Inspecting equations activities focus on learning about equality and how symbols are used to express equality relationships.
Students:
- Discuss whether a number sentence expresses a true or false statement of equality
- Use number relationships to reason about equality relationships
- Identify what number(s) replace the unknown quantity to make the number sentence a true statement of equality
- Justify their positions
- Recognize patterns and make conjectures about number properties
- Understand that because of the multiple entry points and open-ended nature of inspecting equations activities, they can often be used as whole class activities.
The Inspecting Equations Block focuses on:
- Concepts of equality
- Asks students to analyze conventional symbols of quantity, operations, and relationships Encourages students to use number relationships as well as computation to confirm equality relationships
- Occurs as a heterogeneous large or small group or as an individual activity
The Big Ideas...
In kindergarten, students are introduced to the equal sign. They learn that it means “the same (amount) as.” Teachers encourage students to say “8 is the same (amount) as 7+1” instead of “8 equals 7+1.” Another way kindergarten teachers set the stage for future inspecting equations activities is to record students’ efforts to find ways to make a given number by writing the sum on the left side of the equal sign and the addends on the right. This makes sense since the students know the quantity they start with and work to determine the ways to make two (or more) addends.
In first grade, students develop their understandings of how to represent statements of equality. They inspect equations such as:
7 = 7
8 + 3 + 5
8 + 2 = 2 + 8
4 + 2 = ___ + 2
Second graders expand their understanding of equations. They begin to use relationships as well as computation to reason about the truth of equality statements. They inspect equations such as:
6+4 = 10 + 0
6 + 4 = 5 + 5
3 + 7 = 7 + 3
3 + 4 = 3 + 3 + ___
Manipulative Sort
Provide a set of manipulatives and some kind of mat on which to sort the manipulatives. ; Ask the students to find all the ways to organize the manipulatives into two parts. For instance, the student can have yellow and silver fish. The student finds all the different ways to make a given number using the two colors of fish.Students can write equations to record the two part combinations that they find. The equations have the whole number first and the two part combination on the other side of the equal sign. For instance, a student finding two-part combinations for 7 writes 7 = 2 + 5 and so on.
Target Number
The teacher writes the target number on the board large enough for the entire group to see. He/she asks the students to think of two numbers they can add to make the given number. After a bit of individual thinking time, students are asked to share their thoughts. The teacher makes a list of all the pairs the students share. ; Students check the accuracy of each pair of numbers. ; The teacher asks if all possible pairs have been listed and why students think they have or have not determined all possibilities.
True or False Number Sentences
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.