Counting each group and ordering groups by how many

When you reach for it

After a child has sorted a pile into groups, the next question is “how many in each group, and which group has the most?” Each group is counted, and then the groups are lined up side by side (cube towers or rows matched one to one) so that most, fewest and “the same” can be seen as well as counted. This lesson puts three or four groups in order; comparing just two groups or two numbers is Comparing quantities and Comparing two numbers to 10.

Start each day with groups that are already sorted, and keep every group at ten or fewer.

Day 1: Count each group

You need: four small boxes or paper plates, and a mixed handful of small things already sorted into them, one kind per box (dark buttons, light buttons, square tiles, triangle blocks).

Point to one box and ask, “How many are in this box?” Let the child count by moving each piece out of the box as it gets its word, the way they count one word per thing. Then put a number card (or a sticky note with the number) beside the box. Do this for every box.

Ask, “Which box has the most? How do you know?” A child who points to the box with the biggest number is using the counts. Keep the number cards out; tomorrow you will check them by lining the groups up.

Practice. Use the picture.

1. How many are in box A? Answer: 4 dark counters.
2. How many are in box B? Answer: 6 open counters.
3. How many are in box C? Answer: 3 squares.
4. How many are in box D? Answer: 7 triangles.
5. Which box has the most? Answer: D, with 7 triangles, the biggest of the four numbers.

Day 2: Make towers and see the tallest

You need: snap cubes, and three sorted groups from your room (crayons by color work well).

Build one cube tower for each group: one cube for each thing in the group. Stand the towers side by side on the table so that all the bottoms are on the same floor. Now the groups can be compared without counting again: the tallest tower is the group with the most, and the shortest is the group with the fewest. The cubes that stick up above a shorter tower show how many more the taller group has.

Ask, “Which tower is tallest? Which is shortest? How many cubes stick up above tower A?” If the bottoms are not lined up, the towers cannot be compared by looking, so check the floor first.

Practice. Use the picture.

1. Which group has the most? Answer: B, with 8 cubes.
2. Which group has the fewest? Answer: C, with 2 cubes.
3. How many more does B have than A? Answer: 3 more. Three cubes of B stick up above A, and 8 is 3 more than 5.
4. How many cubes would tower C need to be as tall as A? Answer: 3, because 2 and 3 make 5.

Day 3: Put the groups in order

You need: counters, four sorted groups, and a strip of paper with a straight left edge drawn on it.

Turn each group into a row of counters, every row starting at the same left edge, with each counter straight under the one above. Ask, “Which row is longest?” Move that row (or its tower) to the front. Then ask, “Of the rows that are left, which is longest?” and move it next. Keep going until the groups stand in order from most to fewest, like stairs going down. Then turn the whole line around: the same groups are now in order from fewest to most.

Ask, “Which group is first? Which is last? Which group is second?” Then cover the picture and ask the same with only the number cards.

Practice. Use the picture.

1. Put the rows in order from most to fewest. Answer: C (9), A (6), D (4), B (3).
2. Put the rows in order from fewest to most. Answer: B, D, A, C. It is the same line read from the other end.
3. Which row has the second most? Answer: A, with 6.
4. Number cards only: put 2, 10 and 5 in order from most to fewest. Answer: 10, 5, 2.

Day 4: The same, and how many more

You need: snap cubes and four sorted groups, two of which have the same count (for example five apples and five bananas from a play kitchen).

Build a tower for each group and stand them on one floor. When two towers are the same height, say, “These two groups have the same number.” Neither one has more. In an order from most to fewest, the two groups share a place, side by side.

Ask, “Which towers are the same height? Which group has the most? How many more does it have than the group with the fewest?” The child can count the cubes that stick up, or count on from the shorter tower.

Practice. Use the picture.

1. Which groups have the same number? Answer: A and C, 5 each.
2. Which group has the most, and which has the fewest? Answer: B has the most (7) and D has the fewest (3).
3. How many more does B have than D? Answer: 4 more, the cubes of B above the top of D.
4. Put the groups in order from most to fewest. Answer: B, then A and C together, then D.

Exercises

1. Count each box. Which box has the most, which has the fewest, and how many more does box B have than box A? Then put the boxes in order from most to fewest.
2. Mia sorted her blocks: 4 red, 1 green and 4 blue. Which colors have the same number? Which color has the fewest? How many more red blocks are there than green blocks?

Where this goes next

The counts beside each group are the start of a table of counts. Towers standing on one floor become the bars and rows of bar graphs and picture graphs, where the same questions (most, fewest, how many more) are read from a picture, and later picture graphs with a key.