The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer, based on experience and known information. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it. In this activity, students estimate how many sticky notes are needed to make a row or a column along a piece of paper. There are 4 possible ways to interpret the question: the two orientations of the paper and the two orientations of the sticky notes. Students use their understanding of multiplication of a fraction by a whole number to make and represent their estimate. When students consider assumptions about information not given in a situation, they model with mathematics (MP4).

• Invite previously selected students to share.
• If it doesn’t come up, highlight the different orientations of the sticky notes.
• Consider asking:
  • “What are some other ways you could have arranged the sticky notes?”
• Invite a few students to share their expressions.
• “How does this expression connect to the estimate?” (The whole number represents the number of sticky notes.)
• “How can we use the expression to show if the estimate is too high, too low, or about right?” (We can compare the product of the expressions to the side lengths of the paper.)

The purpose of this activity is for students to use their understanding of multiplication of fractions to make an original design with sticky notes. They may choose:

• The letter to make.
• The orientation of the letter.
• The orientation of the page.
• The arrangement of the sticky notes next to each other.

Before making their design, students determine if their design will fit on the given paper. While not a part of the task, students can be asked to estimate how many sticky notes they need before they make a calculation.

Alternatively, instead of asking students to choose their own letter, the class can choose a joint project, such as making the name of the school or a club. In that case, groups should each get one letter of the project to design and work together.

• Invite previously selected students to share their designs.
• “What were some choices you had to make as you designed your letter?” (I had to decide to use the paper horizontally or vertically, based on my letter. I had to decide how many sticky notes would fit along the side and across my paper. I had to decide where to place sticky notes to make my design look like a letter.)