Tag Archives: expressions

K-12 Math Education is a Line of Dominoes

Critical dominoes in math education start falling in 6th and 7th grade with the last ones falling in college. If you have a student who struggles with math and is entering or returning to middle school, now is the time to intervene to avoid more serious issues related to math education in the future. If your student is not going to college or is not accessing the general curriculum, I suggest you read this.)

Below is a chart showing the different categories of Common Core of State Standards (CCSS) math (called domains) at different grade levels. For the majority of students who will attend college, the traditional algebra based sequence (algebra 1, algebra 2, and maybe pre-calculus, calculus) is the path of math courses to be taken. Given this, for students who struggle in math but have a post-secondary education as a goal, the domains I emphasize in middle school are Expressions and Equations, Ratios and Proportional Relationships, and Functions. For high school, I emphasize Algebra and Functions.

Looking at the overviews for CCSS math standards (below) you can see the dominoes line up.

  • In 6th grade, Ratios and Proportions are an entry point for Functions in 8th grade which leads to Functions in high school.
  • In 6th grade, Expressions and Equations are the entry point for Expressions and Equations in 7th and 8th grade, which lead to Algebra in high school.

If your student is struggling with the middle school topics I cited and the gaps are not filled, the struggle will be carried with them into high school and into college.

I recommend the following:

  • Focus IEP math objectives on the priority units of the math curriculum, as cited above.
  • Ask for examples of mastery for the objectives to help you evaluate progress and mastery. Have this in place from day 1.
  • Focus on study skills, not just content mastery.

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Simplifying Expressions (Combine Like Terms)

Simplifying expressions (see photo below) is one of the most challenging algebra tasks for many students receiving special education services. A major problem is that it is typically presented as symbol manipulation…addressed in very symbolic form.

combine like terms

My approach is to make math relevant and more concrete. Below is a scaffolded handout I use to help unpack the concept. In the handout I start with items the student intuitively understands, tacos and burritos or tacos and dollar bills. In the top left of this handout the student is asked how many tacos he or she has. 3 tacos eventually is written as 3T. See next photo to see how the handout is completed as NOTES for the students.

simplifying expressions tacos

As I work with the problems below I remind the student that the “T” stands for taco so “3T” stands for 3 tacos. This takes the student back to a more concrete understanding of what the symbols mean.

simplifying expressions tacos completed

To address negatives I use photos of eating a taco or burrito. “-2T” is eating 2 tacos.

So “3T – 2T” means I have 3 tacos and ate 2. I have 1 taco left… 1T. For students who may need an even more concrete representation, use actual tacos or other edible items.

simplifying expressions tacos with negatives

 

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Equation with variable on both sides scaffolded

intro to variable on both sides

 

Solving equations with a variable on both sides proves to be exceedingly tricky for many students. My approach is to focus on the individual expressions taken from both sides of the equation and to present them in the context of a relevant real life situation. The photo shows a snippet of the handout I use. The table is scaffolded to help students compute costs based on number of toppings. The pizza places charge the same at 3 toppings. Domino’s charges more for 0-2 toppings and Pizza Hut charges more for 4 or more toppings. The color coding fleshes this out.

Overall the kids are actively engaged and the variable, expressions and the overall equation has meaning.

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