Illuminations: Grouping and Grazing

# Grouping and Grazing

Help the alien spaceship move cows into corrals by counting, adding, and subtracting. This activity helps children learn grouping, tally marks, and place value. As they master counting, they can move on to adding and subtracting two-digit numbers.

### Instructions

 General Tools Menu brings you back to the home screen from any activity. Move allows you to move cows in the workspace. Group corrals cows into groups of 5 or 10, depending on the activity. Select the tool, select the appropriate number of cows, and then select the tool again to use. Ungroup removes cows from a corral. Check allows you to input the correct final number of cows. C clears the window, and the checkmark submits the answer. For every correct answer, you will receive a barn at the bottom of the screen.   Count by 5s Count cows by corralling them into groups of 5. Loose cows should be moved into the upper area separately when 4 or fewer remain. Tally counts cows as you group using tally marks. It may be hidden at any time using the green arrow at the bottom of the Tally window. New displays a new problem at any point. Check Count with Me counts cows by selecting first all groups of corralled cows and then all loose cows. The count will also be displayed in the Tally window, if shown. Count Alone lets users input the number of cows into a calculator. The count will also be displayed in the Tally window, if shown.   Count by 10s Count cows by corralling them into groups of 10. Loose cows should be moved into the upper area separately when 9 or fewer remain. New displays a new problem at any point. Check Count with Me counts cows by selecting first all groups of corralled cows and then all loose cows. The count shows tens and units separately to reinforce place value. Count Alone lets users input the number of cows into a calculator.   Add Begin by moving all cows from the top two areas down to the bottom sum area to combine them. Then, group loose cows by 10s if there are enough loose cows. This is the same as carrying using the traditional addition method. Any Numbers displays a new problem at any point using numbers selected by the computer. My Numbers displays a new problem at any point using numbers you select. Value must be between 0 and 20.   Subtract Begin by moving the subtracted number of cows into the lower left area. You may need to ungroup cows to move the correct number. This is the same as borrowing using the traditional subtraction method. Make sure cows are corralled in both the upper and lower left areas if they can be. When you click Check the remaining cows will be moved to the lower right area. Any Numbers displays a new problem at any point using numbers selected by the computer. My Numbers displays a new problem at any point using numbers you select. The value in the first box must be between 0 and 40. The value in the second box must be at least 0 but less than the value in the first box.

### Exploration

 Count Before starting a problem, can you estimate how many groups you will have? Now, try it. Was your estimate correct? After doing the activity many times, does your estimate get better? Is it faster to count the total number of cows before you group them or after you group them? When counting by 10s, how does the written number relate to the final grouping of cows?   Add After trying a few addition problems, can you tell when you will need to group or ungroup cows? How is grouping cows in the addition activity similar to how you normally solve addition problems on paper?   Subtract After trying a few subtraction problems, can you tell when you will need to group or ungroup cows? How is this similar or different from the addition problems? How is ungrouping cows in the subtract activity similar to how you normally solve subtraction problems on paper?

### NCTM Resources

 Principles and Standards for School Mathematics (Book and E-Standards CD)

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.