In this section, students count to answer “how many?” questions and develop their understanding of the connection between quantities and spoken number words.

Students are encouraged to use fingers to count. They may also continue to use tools and resources from earlier work, such as counting mats and 5-frames, and objects brought from home to count. As students count and rearrange objects, they notice the arrangement of objects does not affect the number of objects (conservation of number). They will continue to build this understanding over time.

Students also develop comparison skills. They start with different quantities that can be compared visually, such as 7 and 2 dots, and relate the comparisons to the terms “more” and “fewer,” which may be new. (Students don’t need to produce grammatically accurate language, but the teacher should use “fewer” or “less” as appropriate in context.)

This section includes two optional lessons for students to learn and practice forming numbers 1–10. These lessons are optional because number formation is often taught as part of handwriting. Students will have significant opportunities to practice tracing and writing numbers in future centers and lessons.

Display and write the number associated with a quantity whenever possible. Students begin creating collections to represent numbers and writing numbers to represent quantities in the second half of the unit.

In this section, students develop their capacity to compare written numbers. As they count, students can see that the numbers get larger and that there is 1 more each time. Here, students determine “1 more” and “1 less” than a given number or group of objects. This strengthens their understanding of the relationships between numbers and builds the foundation for comparing numbers.

Students may compare written numbers in several ways:

• Create representations of each number and use the representations to compare.
• Use number sense (for instance, that 10 is a “big” number) or mental images of numbers (for instance, 4 relates to 4 fingers).
• Use the knowledge of the count sequence: Numbers that come later in the count sequence are greater.

Students who use number sense or mental images may be able to easily compare some numbers but not others. For instance, they may know that 9 is close to 10 or all the fingers on two hands, and 4 is associated with fingers on one hand, so 9 is more than 4.

Previously, students counted and made connections between quantities and spoken number words. In this section, students write numbers to represent quantities. To develop students’ familiarity with written numbers, consider providing the Numbers 1–10 with 5-Frames Reference Sheet blackline master.

Students also explore counting images arranged in a circle. Images arranged in a circled are more difficult to count than those in lines, arrays, or 5-frames because there is no defined starting or stopping point. It requires students to develop a method to keep track of which images they have counted.

Students create and draw collections to represent a specified number. This is demanding as students need to keep track of the number they are representing and how many they have already shown. In many activities, students have opportunities to look for and make use of structure to help them with such tasks (MP7).

“Draw a line from each number to the group of dots that it matches.”

Students begin this section by counting images for the first time. This can be more challenging than counting objects because images cannot be rearranged. Also students may have limited experience with keeping track of counted images.

Students encounter groups of images in lines, arrays, 5-frames, number cube arrangements, and on fingers. They may be able to subitize, or determine the cardinality of some groups of images without counting, which is a valid way to answer “how many?” questions.

Images arranged on 5-frames and images of fingers allow students to work with the structure of “5 and some more.” Repeated experience with this structure can help students see that they can count on from 5 to determine how many images there are.

Here, students continue to answer “are there enough?” questions, which directly relates to previous and future comparison work. “Are there enough?” questions encourage students to match as a means to compare, leading students to see which group has “more” and which group has “fewer.”

“Are there enough cartons of milk for each student? How do you know?”