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Teaching Math Without Worksheets

Worksheets have long been a staple in mathematics classrooms. But should they be? Read on to explore how teaching math without worksheets can lead to more engaging and meaningful lessons and actually reduce your prep time.

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For as long as I can remember, worksheets have been used for math practice. I think that stems from the fact that textbooks used to the be primary resource for teaching math. Worksheets are a logical transition from practice pages in a textbook. But recently, I’ve seen worksheets being used during both whole-class and small-group instruction. Observing a recent small-group lesson, the teacher was spending more time explaining the mechanics of the worksheet to students than the math she was trying to teach. And something else that worried me is that there were no manipulatives being used. The concrete, representational, abstract sequence of instruction is a framework proven to increase student understanding. A reliance on worksheets usually means a lack of manipulatives, resulting in instruction that is less impactful.

A word I’ve been thinking about a lot lately is intentional. With so many standards to teach, and more students displaying serious gaps due to missed learning, we have to be intentional about every lesson and every resource. Is that worksheet really the best way to teach students a concept? Is it the best way to provide meaningful practice? Read on to see how to use one resource for whole-class, small-group, and practice.

To demonstrate how we can teach without worksheets, I’m going to use a set of cards showing fractions represented in three ways—pictorial, word form, and fraction notation.

The 48 cards are designed for use with 3rd-grade students. Third grade is a foundational year for fractions, which is an incredibly abstract concept, and it’s important that nearly all instruction includes manipulatives or pictures. That’s actually even written into the standards! The 48 cards can be printed, which is ideal for small-group instruction and workstation games, but they are also provided as Google Slides, which works well for whole-class instruction.

SMALL-GROUP OR WHOLE-CLASS INSTRUCTION

The following mini-lessons can be used for either whole-class or small-group instruction. Consider having students work with a partner for both whole-class and small-group instruction. This fosters mathematical conversations and adds a social component to learning. It makes learning more student-centered, rather than teacher-centered. From a practical standpoint, it also means you only need half the manipulatives and materials.

If using for whole-class instruction, you probably want to use the Google Slides images so they are big enough for the whole group to see. At your small group table, you’d likely use the printed cards. You have a little more flexibility using the cards at the small group table, because you can show more than one card at a time, so you can use them, for example, to compare fractions.

  • Identify the fraction shown. Show a picture card/image. Students write the fraction notation for the fraction shown on their individual whiteboards.
  • Show using a different representation. There are two different versions of this lesson.
    1. Representation is the teacher’s choice. This activity is designed to focus on a single representation as they are learning about each different model (bar, set, number line). Show a word or fraction notation card and students draw a model of your choosing on their individual whiteboards.
    2. Representation is the student’s choice. This activity is used after students have been introduced to all the models to show a fraction using multiple models. Show a card/image. At this point, you could use any of the cards—picture, word form, or fraction notation. Using individual student whiteboards, students show the fraction using a different representation. For example, if a picture card/image of 3/4 is shown, students can represent the fraction in one of these three ways.
  • Generate equivalent fractions. Show a card/image. Students work in pairs with manipulatives to build an equivalent fraction. Fraction tiles would be a great manipulative for this. First students build the fraction shown on the card, then they use their tiles to build an equivalent fraction. Note here that students are likely to come up with different equivalent fractions. For example, there could be many fractions equivalent to 2/4. Students share out the equivalent fractions they built. Have students share what strategy they used to determine an equivalent fraction and what patterns they see among the equivalent fractions.
  • Generate a fraction greater than or less than the fraction displayed. Show a card/image. Students work in pairs with manipulatives to build a fraction that is either less than or greater than (whichever you tell them) the fraction displayed. Again, they build the fraction displayed first and then the one that is greater/less. Like the first activity, this one is very open-ended and many different fractions could be generated. Have students share their strategies and reasoning.
  • Compare two fractions. This works best at your small group table because you need to show two cards. Start with the pictorial cards. Show students two cards and ask them to talk with a partner about which fraction is greater and why. This sets the expectation for the conversations you expect them to have when playing War in a workstation. It also provides you with valuable assessment data. Have students write the inequality on their student whiteboards in two ways. For example 2/3 > 3/6  and  3/6 < 2/3. As students’ understanding of fractions develops, you can repeat this activity using a mix of the three types of cards—pictorial, word form, and symbolic form.

WORKSTATION SUGGESTIONS

Note that the best way to introduce these activities is to use them at your small group table. It’s much more effective than just explaining or modeling a game before putting them in your workstations. At the small group table, you can closely monitor students to make sure they understand the game/task, you can set your expectations for using manipulatives and for student conversations. After you’ve used the game/activity at your small group table, move it into your workstations to provide students with practice for each concept.

  • Fraction Representation Memory—From the full set of 48 cards, create decks of 12 cards made up of 6 pictorial cards and 6 matching word or symbolic cards. Here are two examples of matching pairs of cards.

You would need 6 pairs of cards like this for a total of 12 cards.

Lay the cards face down in a 3-by-4 array. Players take turns turning over two cards. If the cards show/name the same fraction, the player takes the two cards. If not, the player turns them back face down in their original place. The player with the most cards at the end of the game wins.

  • Equivalent Fraction Memory—From the full set of 48 cards, create decks of 12 cards made up of equivalent fraction pairs (e.g., 3/4 and 6/8 ). Initially, you will want to use the pictorial cards. As students become more confident with their skills, you can mix in the word and symbolic cards. Play as outlined in the previous activity.
  • What Was Eaten?—Students draw a picture card, which shows the part of the pizza that’s left on the pan. In their math journal, they write sentences describing the part of the pizza that is left and the part eaten.

_____ of the pizza is left. _____ of the pizza was eaten. _____ equals one whole.

Example:  1/4 of the pizza is left.  3/4 of the pizza was eaten.  4/4 equals one whole.

  • Create Another Representation—Put the cards in a workstation. Students choose a card, sketch the fraction using a different representation in their math journal, and write the fraction name. Examples of different representations include a bar model, set model, or number line.

See the example for in the whole class/small group notes.

  • Fraction War—This game can be played by 2, 3, or 4 players. Initially, use just the picture cards. Over time, as students’ understanding of fractions develops, mix in the word and symbolic cards. Copy the cards on cardstock, laminate (optional), and cut apart into a deck of cards. If you are only using the picture cards, you might want to make two copies of the two pictorial sheets, so students have a deck of 36 cards. Players deal out the cards equally. Each player turns over a card. All players name their fractions. The player with the greatest fraction takes the cards.

If players have equivalent fractions, each player turns over another card and the player with the greatest fraction takes the cards.

As I hope you can see, one set of cards with multiple uses can replace a stack of worksheets and provide more meaningful learning experiences.

For a similar discussion using a 1st Grade example, check out this post.

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