More, fewer, and the same number

Learning goal: Compare groups of up to ten objects and written numerals from zero to ten using the words more, fewer and the same number. The comparison symbols are not required. Bring two mats and counters of the same size, then repeat with differently sized objects to expose a common misconception.

Put five counters on one mat and three on another. Pair each counter from the smaller group with one from the larger group. Three pairs can be made, but two counters in the group of five have no partners. Therefore five counters are more than three counters, and three counters are fewer than five counters. The two sentences describe the same relationship from different starting points.

In the picture, each counter in row B sits directly below a counter in row A, so each column of two makes a pair; you can draw a line to join each pair. Look for unpaired counters after every possible pair has been made. When none are left over in either group, the groups have the same number. A pair does not mean the objects must be identical: one large button can be paired with one small button because we are comparing counts, not size or weight.

Compare four large paper circles with six small circles. The large circles might cover more tabletop space, but six is the greater number of circles. Name the attribute before comparing: “Which group has more circles?” differs from “Which circle is larger?” Count or pair the objects to justify a comparison of number. Do not decide by the length of a spread-out row.

Now show the numerals 4 and 7 without collections. Say their names and build the matching amounts. Pair four with four of the seven counters; three remain in the seven group. So seven is more than four. Gradually move from building both amounts to thinking about the familiar counting sequence: seven comes after four when counting forward by ones. Earlier and later number names can help compare amounts within the studied range.

Zero fits these relationships too. A mat with no counters has fewer counters than a mat with two. Two empty mats have the same number of counters: zero. Always name the objects being compared so the mats themselves do not become accidental extra objects.

Worked example 1: Group A contains eight buttons and group B contains six. Make six one-to-one pairs. Two A buttons remain, so A has more buttons. A correct explanation names the leftovers, not merely which row looks longer.

Worked example 2: Two cards both show 5. Make two sets of five objects. Every object gets a partner with none left over. Read the comparison as “five is the same number as five.” A different color or arrangement would not change that relationship.

Worked example 3: A puppet says 2 is more than 8 because the printed 2 is physically larger. Build two counters for 2 and eight for 8. Six of the eight remain after pairing. The printed size of a numeral is not its value; eight names the greater quantity.

Guided practice: Give partners two secret sets with no more than ten objects in each. They reveal the sets, pair them, and make two comparison sentences. Afterward write each group’s numeral. Repeat once with equal quantities and once with an empty group.

Independent tasks: Compare 3 and 9, 6 and 6, and 0 and 4 without symbols. Draw or arrange objects to justify one answer. Next compare a spread-out group of four with a closely spaced group of five. Ask the learner to explain why row length is not enough evidence.

Assessment: A complete response identifies the relationship and supports it with counting, matching, or a correct explanation of the number sequence. Award separate credit for the comparison and its explanation. If a child reverses more and fewer, return to the paired objects and begin each sentence by pointing to the named group. Extend by creating two different drawings that both show equal groups.