Introducing Daphne Drawing Dragonfly

Hi, I’m Daphne the Drawing Dragonfly.
Draw a mathematical picture to give my strategy a try.
Read the problem and draw what’s going on;
Then write a number sentence for what you have drawn. 

Daphne Drawing Dragonfly is our newest animal in our Problem-Solving Pond: A Common Core Math Strategy Unit. The Problem-Solving Pond was created to help teachers overcome Common Core math challenges and employ problem-solving strategies with confidence and fidelity. Daphne’s unit is perfect for general education, special education, RTI and math intervention. Read more about Daphne’s strategy below or download the complete unit here.

WHAT is drawing? Students make a visual representation of the story problem such as a picture, bar model, tens frame or array.

Jake bar model

WHY is drawing important? When students use the drawing strategy, they are making a concrete representation, strengthening understanding of the mathematical concepts.  Effective math classrooms include frequent use of pictorial representations to help students process and visualize mathematical concepts learned.

HOW do I teach drawing?Teach students to create neat, organized drawings with labels and numbers. Students will need to be taught the bar model and arrays, but it is best to let students create the pictorial representation that they see and works for them.

WHEN should I use drawing? This strategy is ideal for presenting a new mathematical operation.  Most teachers use this strategy with K-2 mathematicians, but this is also beneficial for older students as it works especially well with money, fractions, ratios and percentages. Drawing is a great way to double-check solutions because the visual representation increases understanding of the problem.

Helpful hints:

  • Create drawing guidelines. As a class, decide important components to include in a mathematical drawing. Possible components include:
    • Simple drawings
    • Appropriate spacing
    • Neat labels (words or numbers)
    • Easy to read

Guidelines for math pictures

  • Encourage students to use a variety of pictorial representations.  Often students will get in a “strategy rut”, relying on one strategy for many different kinds of story problems. While drawing is an effective strategy for most problems, the type of pictorial representation used depends on the type of story problem.

Types of Pictorial Representations2_Page_1


Presenting Tallying Toad

Hello, I’m Tallying Toad.
I get you started on the problem-solving road.
A tally mark is a straight line to show one;
Group tallies into five is how it’s done.
First make four tallies, nice and straight;
Then make a diagonal fifth tally and you’re doing great!

Todd Tallying Toad is our newest animal in our Problem-Solving Pond: A Common Core Math Strategy Unit. The Problem-Solving Pond  was created to help teachers overcome Common Core math challenges and employ problem-solving strategies with confidence and fidelity.  Read more about Todd’s strategy below or download the complete unit here.
WHAT is tallying? Students use tally marks to show the numbers represented in the story problem.


WHY is tallying important? When students use the tally strategy, they learn to count and notate groups of 5, strengthening number sense in the process. Tallying is an easy, quick way to double-check solutions for kindergarten and first-grade students.

Ella working

HOW do I teach tallying? Teach tallies in isolation first so that students become proficient making neat, organized tally marks. After proficiency is demonstrated, introduce tallying as a problem-solving strategy and teach students to apply within a mathematical context.

Tally example

WHEN should I use tallying? This is an ideal strategy for beginning mathematicians who are learning to count and record numbers. Tallying is a great way to represent smaller numbers in story problems. Students get comfortable with tallies and will try to apply to larger numbers, making some teachers cringe. Refrain from discouraging use of tallies for larger numbers; students must independently develop understanding that tallying is not an efficient, effective strategy for story problems with larger numbers.

Helpful hints:

• Supply models and provide kinesthetic practice. Beginning mathematicians often lack dexterous fine motor skills, which can impede formation of neat, straight tally marks. Provide craft sticks, Wikki Sticks or pipe-cleaners (cut in half) and have students make a model of the tallies before drawing them on paper. Allow students to practice kinesthetically in salt or Jell-o trays or trace on bumpy paper. Students can also practice making tallies with Play-Doh.

tally mark craft sticks Include visual support. As beginning mathematicians start to use tally strategy, they need visual support to ensure that tally marks are straight neatly organized into groups of 5.


• Practice counting by 5’s. Some students struggle with skip counting and could benefit from repeated practice. Chanting 5’s while walking in line, calendar time, even clean-up time all serve as opportunities for fun skip counting practice.

Counting by 5 hands

Why? The Simple, Yet Essential Question

As teachers, we are programmed to listen for the correct answer and are appeased when we hear it, assuming that students understand and are ready to move on. However, this is a serious misconception as students are missing out on a vital opportunity to explain and justify their thinking.  Asking “Why?” provides critical insight to student understanding as students give the following responses:

  • A strong explanation that describes process to class
  • An inaccurate explanation that shows a student’s misunderstanding or inability to justify an answer

Besides assessing understanding, asking “Why?” provides students with opportunities to:

  • Notice mistake(s) and self-correct the answer
  • Reveal mistake(s) or misunderstanding shared by the class
  • Take risks and build confidence
  • Strengthen communication skills
  • Give alternate explanations
  • Summarize explanations given by other students

Including this simple question has major consequences: it promotes a language-rich classroom; supports inquiry-based instruction; and builds classroom community.

Asking good follow-up questions can open the door “why-d” to learning.

Download our FREE Essential Questions & Prompts, a sneak peek at our upcoming Common Core Problem Solving Unit.

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