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Understanding the Equal Sign

Equality is a hugely important concept in math, and that begins with truly understanding the equal sign. Today I’m sharing with you a mini-lesson that can be used for whole-class instruction or at your small group table and incorporates productive struggle, mathematical discourse, and the use of manipulatives.

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Both the Common Core and Texas standards include a 1st grade standard related to the equal sign:

CCSM 1.OA.7 Understand the meaning of the equal sign, and determine if equations
involving addition and subtraction are true or false. For example, which
of the following equations are true and which are false? 6 = 6, 7 = 8 – 1,
5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

TEKS 1.5.E Understand that the equal sign represents a relationship where expressions on each side of
the equal sign represent the same value(s).

First of all, this means that students should routinely see equations written as 5 = 2 + 3 as well as 2 + 3 = 5. That in itself is a huge, and often overlooked paradigm shift. Check out this post to read suggestions on introducing the concept using manipulatives and grab a free resource!

Moving on to today’s lesson. I love having students work in pairs both during whole-class instruction and at my small group table because I always want students to collaborate and discuss math. It’s especially helpful with this activity because students will see that each of their sides of the equal sign must be equal. The two sides of the equation must balance.

Provide students with manipulatives. In my example, I’m using ten frames and two-color counters. Linking cubes in two different colors would be another good option. For illustration purposes, I’m using equation cards, but you can accomplish the same thing by writing equations on index cards. One student will be responsible for the expression before the equal sign and the other will be responsible for the expression after the equal sign. Be sure to have the unknown move around on the cards so both students experience having the missing addend.

Show the students a card. If you are teaching this lesson whole class, write the equation on the board or show it on your interactive whiteboard.  At your small group table, you can use the printed or index cards.

Ask students what they notice and wonder. This is a GREAT strategy for getting students to observe carefully and discuss their observations. Don’t worry if all the observations aren’t related to the task. For example, a student might observe that the numbers used are 2, 3, and 4. Not really relevant, but an interesting observation. When students make an observation related to the task, be sure to follow up with a question. Here are a couple of examples.

  • I notice there’s an empty box (square) after the plus sign. Huh, what do you think that means? (Don’t assume they know that means there’s a missing number.)
  • I notice there’s two numbers after the equal sign. Huh, a lot of times we only see one number after the equal sign. What do you think that means? (We add those numbers together to get one number.)

Once you establish that the box (square) means a number that we don’t know, have partners build their side of the equation on their ten frames. Be careful not to give too much instruction about how to do this. Let them give it a try first and then guide them to the correct process, introducing a little productive struggle into the lesson.

understanding the equal sign

Ask students what number is represented on each ten-frame (3 on the first one and 6 on the second). Remind students that the two sides of the equal sign must balance and ask them if the sides are balanced right now (No, because 6 is greater than 3 or 3 is less than 6). Tell them to work together to figure out what they should do to balance the sides (add three yellow counters to the first side, so both sides equal 6). Again, let them struggle! It’s not important that each pair of students figure out the solution. You really just need one pair of students to be successful so they can share their process with the others. Then you will summarize the learning (Both sides of the equal sign must represent the same number. You had to figure out what the missing part was for the two sides to balance.) and students will have the opportunity to practice a few more “puzzles.”

You can grab both print and digital versions of the cards, along with a Capture 4 game for your math workstations, here.

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  1. I love reading your blog and think your explanations and resources are wonderful…thank you!! Have you ever written about a scope and sequence for Grade 1 and 2 Math? I would be very interested in reading your perspective on the order of skills to teach our young learners…

    1. Thank you for the kind words, Diana! I have not created any scope and sequences, because the schools/districts where I worked always had district pacing guides. That said, for K, 1, and 2 I feel the skills should loop throughout the year using successively larger numbers and strategies. For example, in 2nd-grade multi-digit addition and subtraction should be spread out over the entire year, moving through the concrete, pictorial, and abstract sequence, allowing students to work with multiple strategies and increasingly larger numbers. Too often, teachers want to jump right to the standard algorithm.

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