Last week we discussed **why re-teaching may not be the best option** for end-of-semester review, and actually may cause some problematic effects. So what do we do instead? Here you’ll find a collection of our favorite review activities to help students synthesize the content and concepts from the semester and prepare for exams.

The big difference between reteaching and these review activities is that we focus on the concepts of the course, not just how to successfully complete certain problem types. Moreover, we’re not standing at the board telling students about these concepts, they’re doing that work on their own through some review structures and games. Since students are looking at content from multiple units, the goal during this review period is to classify, connect, and compare concepts from the semester.

While having students work on some cumulative practice problems is definitely worthwhile (cognitive scientists call this retrieval practice--having to sort through their stored knowledge to find the applicable information, skill, or concept), we want to balance this with more big-picture conceptual review. Here are some of our favorite review activities. We’ve grouped them into two categories: games to review concepts and games to review vocabulary

## Activities to Review Concepts

### Concept Cog

Preparation: Little or none

Materials needed: White sheets of paper, cut in half

Concept Cogs are a great collaborative learning tool and especially helpful when reviewing concepts at the end of a unit or semester. It’s our modified version of a Socratic Circle. We assign each student a different question or prompt related to the topic of study. These questions should help students think about connections between ideas, not fact recall. Students then have 5-10 minutes to answer the prompt on a half-sheet of paper. Their work could include written descriptions, graphs, example problems, etc.We then have students form an inner and an outer circle so that each person in the inner circle has a partner in the outer circle (see image). Students now take turns presenting the question and explanation to their partner. We usually give about 2-3 minutes per person, so about 4-6 minutes for the pair. At the end of this time frame, students switch papers and the inner circle rotates 1 position clockwise. The process then repeats, except that now students aren’t presenting their own topic, but the topic that was just presented to them! You can go through as many rounds as you have time for, listening in on student conversations and encouraging students to use precise vocabulary. Students may wish to have their own paper back at the end of the activity.You can prepare the prompts ahead of time or have students come up with them on their own, making sure that a variety of topics are covered. You can write questions related to just 1 or 2 of the units, or the whole semester.

Possible modification: you could also have students make a short video explaining their question/prompt using a platform like flipgrid. Make sure all the videos are visible and then allow students to watch each other’s videos as they are reviewing at home. For best results, have students prepare their video, present it to a classmate to correct any errors or misconceptions, and then record and post it.

### Whiteboard review by unit

Preparation: None

Materials needed: Medium sized whiteboards, whiteboard markers

Assign each group of four students one of the units studied this semester. On their whiteboard, have them summarize the key ideas, vocabulary, concepts, formulas, etc. from that unit. Give them 10 minutes to do this. This will not be enough time to include everything, but other groups will be adding on to their whiteboard.

After the 10 minutes, have groups rotate to the next whiteboard. They must do the following:

Read what the previous group wrote

Correct any errors

Add additional content

We give students 5-8 minutes to do this, and then have them continue in the same way to the rest of the whiteboards. At the end of class, we let students take pictures of each of the whiteboards to refer back to when they are studying at home.

### Tell Me Something True

Preparation: Medium--prepare a slide deck of 3 or 4 images that could garner a lot of discussion (see below for an example)

Materials: None

Our students loved playing this game that was both competitive and content rich! The class is split into two teams and each team should gather at one end of the room. A prompt will be shown with some information about a function, either in graphical, analytical, or tabular form (Algebra/Precalc), or some figures (Geometry). Then students are given a two minute individual prep period to gather ideas. Teams then go back and forth saying “something true” (and math related!) about the given data. If a team can not come up with “something true” in the given time frame (30 seconds max), the other team receives a point. You can then choose to move on to the next prompt or continue brainstorming ideas. There should be MANY true things to say about each prompt.

It is important that all players on a team take turns saying “something true”. There can not be one spokesperson for the group, or a few students doing all the thinking for the entire group. Students should feel free to jot down ideas while other players are talking and also brainstorm with teammates. In our class, we award bonuses for creative answers.

Example prompt for Geometry:

Sample student responses:

The triangle on the right is a result of two transformations on triangle ABC.

Triangle ABC was reflected, then translated.

The ordered pair rule that describes the reflection is…

Triangle A’B’C’ was translated down 1 and right 2.

The measure of angle C is 85.6˚.

Triangle ABC is congruent to triangle A’’B’’C’’. The corresponding sides are…

Triangle ABC is an acute scalene triangle.

The length of side AB is…

The midpoint of BC is…

Without the coordinate grid and vertex labels, there is not enough information to determine that the triangles are congruent by SSS, SAS, ASA, or AAS.

As you can see, the possibilities for true things to say are endless!

# Activities to review vocabulary

### Taboo

Preparation: little to none

Materials: notecards

We’ve math-ified this **popular game** by using vocabulary games from the semester as the card deck! Choose a large number of vocabulary words and write each one at the top of a separate notecard (to minimize prep, you could have students come up with these themselves, though you want to avoid repeats). Hand out these cards to students. In a different color, students need to come up with four words that game players will NOT be able to use to describe the word. This helps students identify related vocabulary and review the important ideas about a topic. They love making the game challenging for their peers! For example, if the vocab word is “square” students may write “equal”, “right”, “90˚” and “four” as the taboo words.

Once the cards are made, have students play Taboo in groups of 8, with 4 people on each team. If you have the Taboo game and want to bring in the buzzer, feel free! The team with the most cards at the end of the game wins.

### Sentence construction

Preparation: Medium

Materials: small slips of paper

Type or write vocabulary words from one unit on small slips of paper. We like putting each unit’s vocab on a different colored sheet of paper and have groups take turns doing this activity with various card sets.

Have students work in groups of 2, 3, or 4. They should lay out all the vocabulary words face up. Students take turns creating sentences using 2 of the vocabulary words. In the next round, have students make sentences using 3 of the words, and then even 4. You can award a prize for the student that can incorporate the greatest number of vocabulary words into one sentence.

Then have students switch sets and work with the vocabulary from a different unit.

Modification: For an additional challenge, you could mix vocabulary with various units and award extra points for making sentences that cross units.

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