Hey there!

I'm wrapping up my third week teaching high school geometry, and I’ve already spotted some major learning gaps that are impacting students' success in this course. I wanted to share these insights with you since many of you teach middle school and have the ability to address some of these skill gaps before students reach high school.

Here are the most significant gaps I’ve encountered so far, along with some actionable tips to help close them:

Simplifying Expressions vs. Solving Equations

There’s a BIG disconnect between combining like terms and moving terms across an equal sign. Students are struggling with recognizing when to use inverse operations and when they aren't necessary, especially when solving equations involving fractions.

Actionable Tips:

• Daily Practice: Include quick daily drills that focus on distinguishing between simplifying expressions and solving equations. Provide a variety of problems that require both skills, so students learn to recognize the difference.
• Use Visuals: Use diagrams or models like balance scales to visually show how moving terms across the equal sign requires inverse operations.
• Fraction Equation Warm-Ups: Incorporate regular warm-ups that include fraction-based equations to desensitize students to the fear of fractions.

Integer Facts

If I had a dollar for every time I’ve heard, "Since they're both negatives, -5 + -3 is positive 15, right?" I’d be enjoying a really nice dinner out tonight. Integer rules and concepts seem to have completely evaporated.

Actionable Tips:

• Number Line Practice: Integrate visual aids like number lines during instruction. Seeing negative numbers in relation to zero often helps students better understand the rules for addition and subtraction of integers.
• Create a Rule Chart: Have students create a "cheat sheet" or chart with the rules for adding, subtracting, multiplying, and dividing integers, and keep it handy for reference.
• Play Math Games: Use engaging, competitive games like integer bingo or "integer war" with card decks to make practicing integer rules and integer concepts fun and memorable.

Rushing and Not Reading

Many of the mistakes I’ve seen have come from students rushing through their work and not reading problems carefully. For example, simple calculations like 6 + 2 are becoming 12, and students are giving the value of x when the problem asked for the segment length.

Actionable Tips:

• Slow Down and Check: Encourage students to always double-check their work, especially for basic arithmetic and when interpreting word problems. Teaching them to “read the question twice, solve once” can help.
• Highlight Key Words: Teach students to highlight or underline important words in a problem like "segment length" or "value of x." This trains them to focus on the actual question being asked.
• Time-Bound Practice: Give students timed practice with increasing difficulty, but emphasize quality over speed. Discuss the balance between working quickly and working accurately.

If you don't already have an intervention program in place to help with skills like these throughout the school year, I highly recommend grabbing one or asking your school to purchase one for you! These skills have all been critical to success, just in the first unit of HS Geometry!

I hope this helps as you continue to prepare your students for high school! If you can focus on reinforcing these skills in middle school, it will make a HUGE difference for them later on.

Lindsay