Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

Helping Ladybug Hide with Arrows and Angles

Pre-K-2
1

In this lesson, students use an applet (technology tool) to hide a ladybug under a leaf. This requires experimentation, planning, and understanding of spatial relationships and visual memory.

Begin the class by projecting the Hiding Ladybug Applet.

Show students how to show the leaf by clicking on the “Show Leaf” button. Then demonstrate how to move the ladybug in a line or to make a turn. Students should use the Arrows for Moving Ladybug Activity Sheet as a reference for the directions given during your demonstration.

Note that the arrows indicate the direction in which the ladybug moves.] It is most important for students to observe the angle at which the ladybug moves (45 or 90 degrees and their directions, left and right). Review the navigation tools on the interactive applet and invite students to describe what they do.

Allow several students to use the mouse to demonstrate the steps in moving the ladybug with the arrows and angles. This is an excellent opportunity to introduce directional vocabulary, such as move forward, move backward, turn right, and turn left. The unique characteristics of your students will determine when it is appropriate to identify the “small” right turn, “large” right turn, “small” left turn, and “large” left turn as 45-degree and 90-degree right and left turns. Students can use the Making Turns Activity Sheet to identify these turns.

Have students practice hiding the ladybug. If you do not have enough computers for each student, they may work in pairs or take turns. Use the guiding questions provided [or others that are appropriate in your context] to focus students’ attention on the mathematical ideas central to this lesson. As students work with the applet, check for a match between the length of the arrows and the distance that the ladybug moves with each arrow.

Remember to document the understandings students demonstrate as they move the ladybug about the screen.

Assessment Option

You may choose to use the Class Notes recording sheet to document student progress in this unit.

Extension

Move on to the next lesson, Handy Map.

Questions for Students

1. Clear your screen. How can you hide the ladybug under the leaf?
2. Describe what you did. Why you did you do that?
3. What was the most difficult part of this activity? What was the easiest part of this activity? Why?
4. What did you have to think about as you planned the trip the ladybug would take in order to hide?
5. How could you describe the nonstandard units used in the applet?
6. How is this activity like the one we did with the paper ladybugs? How is it different?

Teacher Reflection

• Which students readily associated the direction in which the ladybug needed to move with the visual reference of the arrow buttons (left, right, or both left and right)? Which did not?
• What additional learning experiences do these students need?
• Which students readily associated the turns that the ladybug needed to make with the visual reference of the arrows? Which did not?
• What additional learning experiences do these students need?
• Which students readily associated the “size” of the turn with the degree of change in direction? Which did not? What additional learning experiences do these students need?
• What experiences would have better prepared students to be successful with this lesson?

Measuring with Teacher’s Feet

Pre-K-2
In this lesson, students use nonstandard units to measure the distance between objects found in their classroom. They create a nonstandard unit by using an outline of the teacher’s foot and cutting around it to use as a “measurer.” Students generate a list of four or five objects in the classroom from which they will measure the distance to their work space.

Measuring with Our Foot

Pre-K-2
Students measure the same distances as in the previous lesson using an outline cutout of their own foot. This enables students to practice using nonstandard units and to compare the measurement totals using their feet and the teacher’s foot.

Pre-K-2
The mathematical foci of this lesson are geometric concepts, location, navigation, direction, and spatial relationships and measurement concepts, using nonstandard units to measure a distance, and the iteration of units, measurement by using the same unit of measure repeatedly to determine the total. Students practice measuring with multiple units and a single unit following the methods modeled by the teacher and those appropriate for their level of understanding.

Handy Map

Pre-K-2
This lesson engages students in creating a map of their hands. It provides purpose for using directional or positional words with mapping. The teacher draws a map of his or her hands and begins mapping them using words the students suggest. This allows the teacher to assess positional concepts students currently know and to build on that knowledge. Students create a simple map.

Facing Up

Pre-K-2
In this lesson, students create a map of their face and practice locating different parts using the geometric and measurement concepts they have learned in previous lessons, including location, navigation, spatial relationships, and measurement with nonstandard units. Students reproduce their face and describe it to reinforce their knowledge and skills of measuring and mapping. Using these familiar territories connects mathematics with daily encounters.

Learning Objectives

Students will:

• Recognize and use the attributes of length by measuring with nonstandard units.
• Learn how iteration of a nonstandard unit enables the ladybug to move to a “safe” location under the leaf.
• Demonstrate an understanding that left or right turns are required to hide the ladybug.
• Demonstrate an understanding that forward and backward moves accomplish different purposes.

NCTM Standards and Expectations

• Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance.
• Relate ideas in geometry to ideas in number and measurement.
• Recognize the attributes of length, volume, weight, area, and time.
• Understand how to measure using nonstandard and standard units.

Common Core State Standards – Mathematics

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.1
Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.