Study guide: Equal Groups and Changing Totals
Use pairs and equal rows to organize counts and solve a two-step story.
Ideas to explain in your own words
- Use repeated addition to count objects arranged in equal rows.
- Decide whether all objects can be grouped into pairs.
- Find an array total by adding totals from two smaller arrays.
- Find an array total before subtracting objects that leave.
Watch your reasoning
- Each row contributes five dots. Adding both rows gives 5 + 5 = 10. Adding the number of rows to the dots per row, 2 + 5, would not count all the dots.
- There are eight objects in each of two equal groups. 8 + 8 = 16; this is an even total. Seven plus nine totals sixteen but does not describe two equal groups.
- Two rows give 3 + 3 = 6 dots. Three rows give 3 + 3 + 3 = 9. Adding 6 + 9 gives all 15 dots.
- First count 3 + 3 + 3 + 3 = 12. Then subtract five: 12 − 5 = 7 badges remain.
A worked review example
Count Equal Rows: Three rows of four dots give 4 + 4 + 4 = 12. Counting one row as four, then eight, then twelve gives the same total. Make Pairs to Test Even or Odd: Fourteen counters form seven pairs with none left over: 14 = 7 + 7. Eleven form five pairs and one leftover: 11 = 5 + 5 + 1, so eleven is odd. Split an Array Without Losing Dots: Four rows of five contain (5 + 5) + (5 + 5) = 10 + 10 = 20 dots. Three rows of four can be split as 4 + (4 + 4) = 4 + 8 = 12. Use Two Steps to Count What Is Left: The display starts with 5 + 5 + 5 = 15 badges. Removing four leaves 15 − 4 = 11. Checking 11 + 4 = 15 rebuilds the original display.
Make a practice plan
- Try the supplied lesson problems without looking at the answers.
- Compare your method with the worked examples and explain any correction.
- Use the new review cases, then complete the transfer task on paper or in your own document.