Strategy
# Alligator Crunch: Missing Number

## Use the hundreds chart to teach students to find the missing number.

Students should be able to rote count to 100 by the end of the kindergarten. Found in every early elementary classroom, the hundreds chart is used as a tool to help teach number sense. A hundreds chart is a 10×10 grid with the numbers 1 – 100 printed in the squares. The purpose of a hundreds chart is to provide framework to think about our base ten number system and to enable students to **build a mental model **of the the mathematical structure of our number system. Hundreds charts encourage students to explore concepts from counting to adding two-digit numbers.

As Teachers of the Visually Impaired (TVIs), we know how challenging math is for our students. Math is highly visual in nature and requires good spatial concepts and mental mapping. The general education math curriculum uses tactile tools and embeds mental mapping in every day math activities. TVIs, are you aware of these opportunities to expand the mental mapping concepts for students with visual impairments? Try highlighting these general education principles and elaborating on them so that your students can build stronger foundational spatial and mental mapping concepts!

Use the hundreds chart to reinforce numbers sense by determining the missing number.

Kindergarten Common Core State Standards: Counting and Cardinality

Know number names and the count sequence.

- CCSS.Math.Content.K.CC.A.1 Count to 100 by ones and by tens
- CCSS.Math.content.k.CC.A.2 Count forward beginning froma. given number within the known sequence (instead of beginning at 1)

- APH Hundreds Chart (Nemeth version)
- APH Hundreds Chart (UEB version)
- Plastic alligator action toy (Any action figure alligator with an open mouth will work; this particular alligator’s mouth opens and closes!)

- Student can read braille numbers
- Student can rote count or has some understanding of number sequence

Tell the student a story about the hungry alligator who loves to crunch numbers while the student quickly explores the action figure alligator. If you (the student) can identify the correct number, the alligator will give back the number!

Secretly, remove one number from the hundreds chart and place it in the alligator’s mouth. Ask the student to find the missing number (blank spot) and to identify the number that the alligator is munching on.

In the video below, Logan (a kindergarten student) demonstrates how he determines the missing number in the tactile hundreds chart by APH. Note how Jessica, TVI extraordinaire, allows Logan to explore the hundreds chart independently, then gently provides a *subtle* leading prompt to “try looking around at some of the other numbers nearby”. Jessica only jumps in with a direct prompt (in this case a physical prompt) when Logan unknowingly jumped down to the next line and when he is unsure how to move to the next line.

The video starts with Logan’s fingers scratching the Velcro in the square with the missing number.

Now, let’s dive a little deeper into this activity and see how we – TVIs – can pull out spatial concepts and mental mapping that will provide foundation concepts for digital math.

What additional concepts did Logan practice in this activity? He practiced dragging his finger across the row in a straight line to read the numbers in the line. Jessica physically demonstrated how to drag his finger back to the beginning of the line and down, to read the next line. Yes, this is similar to tracking and reading braille from left to right and then back to the beginning of the row and down to the next row. It is slightly different than reading braille, as Logan was dragging his finger across the squares on a bigger surface than a braille page instead of tracking across braille letters in a row. While dragging his finger across the row, Logan can be introduced to the “time and distance” of ten squares in a row on the hundreds chart. (“Time and distance” is an O&M concept and term in which the student uses these concepts to determine where he is in his environment or in this case, where he is on the hundreds chart.)

Could you bring out more spatial concepts? How about which numbers are on the left side of the hundreds chart? The right side? Where would a number ending in 0, be located? ending in 5? What if you called out a number and asked Logan to jump his fingers directly or close to that number, starting with easier numbers such as 1, 10, 91 or 100. (Numbers located in the corners.) Can you talk about and use the terms “row” and “column”?

Once the student understands looking to the right/left of the blank square to read the previous and next numbers, the student may be ready for a challenge. Tell the student that the alligator does not want to give up his number and you (the student) need to be sneaky! Can you sneak up to the blank square and determine the missing number without checking the number before or after the blank square? (Try finding the number above or below the number; this requires moving/counting by ten starting from a given number.) Ask the student to start from the top of column with the missing number and read the available numbers in that column in order to figure out the pattern!

In this video, Logan started to read the numbers in the row above his missing number. When the activity is repeated with a different missing number, do you think Logan will figure out to look to the left or right square (same row) as his missing number?

The hundreds chart is a **10×10 grid.** Why is this important? First, our math system is based on tens. Counting by tens is a foundational concept. Students start by rote counting ten, twenty, thirty, etc. and students are introduced to counting cubes that connect together into blocks of ten (and eventually blocks of one hundred). The hundreds chart is created to be rows of ten. When a student drags his finger down a column, he is automatically counting by ten. It is easy to count ten, twenty, thirty; what happens if the student starts on a different number and wants to count by ten? Example: Have your student place his finger on the number 12. Now, drag down the column to count by tens starting from 12: 12, 22, 32, etc. What is the pattern? (Only the first number changes.)

In the second row, is the biggest number on the right or left side? Where is the smaller number in that row? In the second column, is the bigger number at the top or the bottom of the column? Where is the smaller number? Where are the bigger numbers in each row? in each column? Where are the smaller number in each row? in each column? Is there a pattern? (Numbers become bigger as you move to the right of the hundreds chart – just like numbers in a number line. Numbers become bigger as you move to the bottom of the hundreds chart.)

All students first use manipulatives or tactile models to learn a new concept, then they move to using a “paper copy” (In this case, a manipulative hundreds pocket chart or the APH hundreds chart then a paper or braille copy of a hundreds chart. ) Once a student with visual impairments understands the grid concept, can he transfer this knowledge to a digital grid on a touch screen device? After that, can he apply these skills to a computer and navigate a grid using screen reader keyboard commands?

Logan’s TVI shares that she introduced the Alligator Crunch activity to Logan in kindergarten – as a fun exposure game. Kindergarten students were exposed to counting by ones and tens in kindergarten (and “how can you figure it out” logical thinking). At that time, Jessica was simply exposing Logan through game playing; kindergarteners were not expected to master and apply these concepts. In 1st grade, Logan’s class frequently had activities where they had to fill in portions of the hundreds chart.

In this first grade activity, the alligator was stealing numbers and Logan had to figure out the missing numbers. This hand drawn activity which was done in class resembles a crossword puzzle rather than a specific grid. There are 6 squares in the “grid”; three of these squares have numbers. (The full grid would have been 3 rows and four columns with 12 squares.) With this “grid” the first row has one square (in the second colum); this square has the number 12. The second row has four squares; moving from left to right, the first square is blank, 22, blank, 24. The third row has one square in the third column which is blank. Note: Logan would be given a tactile represenation of this grid.

Want another hundreds chart activity? Ally the Alligator is an activity for learning/practicing the greater than and less than math concept.

Ask the student to read the Ally the Alligator poem. (Emerging readers can open this poem on a tablet and use the screen reader to read the story aloud.) Ally the alligator only likes to munch on BIGGER numbers. Choose a starting number, such as number 11. Ask the student to place Ally (the action figure alligator) on that number. Ally is VERY hungry; help her munch across the numbers *in that row* that are bigger than the number 11. Be sure that Ally’s open mouth is facing the larger numbers. Make a munching sound for each number that she munches across and say each number aloud. As the student progresses, ask the student to say the munched number (such as “12”), is bigger than the first number (“11”). (The student should say, “12 is bigger than 11, crunch!”) Talk about how Ally’s mouth needs to be wide open and facing the bigger number.

Have the student repeat the activity using his hand as the alligator’s mouth. Open the hand (spread all five fingers out) and chomp on each bigger number (quickly bring all five fingers together to eat the number). Discuss that the student’s hand (alligator’s mouth) is open facing the BIGGER number. Note: It is easier to use the left hand when chomping on larger numbers – as BIGGER numbers are to the right. If chomping on SMALLER numbers, use the right hand, as SMALLER numbers are to the left. Discuss that correlation between “bigger”/”greater than” and “smaller”/”less than”. Pair this activity with the “greater than” and “less than” signs.

There are many more math concepts taught through the hundreds chart, including addition and subtraction concepts. The image below (from the blog post, HappyNumbers.com) shows a hundreds chart with numerous missing numbers. The 6th column displays 6, 16, 26, 36, 46, 56, blank, blank, 86, and 96. Between the 56 and 86 is a ladder. Beside the hundreds chart is the equation, 56 + (blank square) = 86. Jumping down the column (by tens) 3 times is equivalent to adding 30.

This additional activity requires the student to move vertically through the chart (down the column) in order to determine the math equation.

APH also has consumable hundreds charts available for low vision and for braille students.

How do you use the hundreds chart with students who are visually impaired? What spatial and mental mapping opportunities are you teaching?

https://www.perkins.org/sites/elearning.perkinsdev1.org/files/Ally%20the%20Alligator.docx

By Diane Brauner