● Materials develop children’s capacity to ask thoughtful questions.
● Materials develop children’s capacity to recognize problems in their environment. ● Materials develop children’s capacity to use mathematical reasoning with familiar
materials in the classroom and world outside the classroom.
Meets 4/4
Materials intentionally develop the students’ ability to problem solve by developing their capacity to ask thoughtful questions, recognize problems in their environment, and use mathematical reasoning to solve problems in the classroom and outside world.
Evidence includes but is not limited to:
In Unit 1, the students use mathematics to solve problems in various environments, and the teacher models questioning and thinking about problem-solving. In the “Construction” center, the teacher introduces measuring vocabulary in the first week of school. The teacher shows the children two blocks of different sizes, asking them to describe their shape, size, color, etc. The teacher models vocabulary for the students, like larger or smaller, to make comparisons. During the “Sorting Game,” the teacher puts a variety of objects in a center, and the students have to decide how to sort them. The teacher models open-ended questions about attributes they chose for sorting; these are designed to promote metacognitive reasoning. Math is also carried over into outdoor activities in this unit. The students must say something kind to three different people while playing outside. The teacher takes the students on a “Five Senses Nature Walk.” The teacher introduces some problem solving and counting via a scavenger hunt, which reinforces these skills with simple challenges: “Bring me 3 small rocks.” “Find 2 sticks.” In another lesson, the teacher models questioning, asking students, “Who is wearing red shoes?” “Who is wearing blue shoes?” “Who is wearing a bracelet?” (How many children are wearing red shoes, blue shoes, a bracelet, or other items).
In Unit 3, students practice counting and creating patterns using theme-related materials. During small groups, students count the petals on a group of flowers. After the teacher models creating patterns, students create and describe their own patterns. Following the “Teacher Tips” for this unit, the teacher supports mathematical thinking by asking thoughtful questions, modeling recognizing problems in the environment, and creating solutions to the issues using
the student has ever seen or been in a skyscraper; the teacher can also ask what shapes the student is using to create the skyscraper. In another example, the class creates a growth chart by placing paper on the wall; students measure each other and compare heights. The teacher keeps the chart for students to compare their height throughout the year. In a lesson about classification and patterns, the teacher uses questioning to support the development of mathematical reasoning. Along with lessons, teachers find times during free play to ask
students questions to encourage them to notice patterns and sort. Questions include “Why did you sort these objects into a group?” “How are these the same?” “How are they different?” The Teacher Tip also highlights the importance of giving students time to share their thoughts: “Children should be able to describe in their own words why they sorted objects in a certain way, or how they know something is a pattern, in order to show that they have an in-depth understanding of the concept of patterning.” During a “Math and Science” center, the teacher provides the students with various sizes of seeds in different cups (suggestions include
sunflower seeds, pumpkin seeds, corn kernels, beans). The teacher labels the cups. The students place each type of seed in a small cup and write down the number of seeds that can fit. The teacher guides the students in observing and discussing that objects of different sizes take up different amounts of space, pointing out that larger items take up more space than smaller items.
In Unit 6, students explore shapes in their environment. A Teacher Tip reminds teachers that shape knowledge comes from exposure, and students need to manipulate and engage with shapes in multiple ways, such as by identifying shapes in their environment or creating their own. After reviewing the online activity “All About Shapes,” students make cloud shapes, creating shapes with cotton balls. For example, students put four cotton balls together to create a square and then count the side and corners. The teacher models how to create clouds in different shapes and thinks out loud about the shapes he/she may create. In another activity, students explore pictures of rockets, helicopters, and airplanes and discuss which ones they would want to go on. The teacher asks students to point out shapes they see in the pictures and then draw one of the vehicles, identifying the shapes they use to create each vehicle. The teacher also uses snacks and lunch as a time to ask students to identify different shapes they see in their food or containers. A Teacher Tip highlights how math concepts can be reinforced through music, including recognizing patterns, rhythm, and counting. The teacher capitalizes on this by using music in transitions, activities, and centers (which include instruments). Students use mathematical reasoning to explore the concept of sink and float in the Math and Science center. An anchor chart in the center contains a picture of each item. Students use this chart to mark which items sink and which ones float, comparing how many there are in each column. Students also use a number chart to point out the numbers that correspond with how many items sink or float. Following the Teacher Tip for a measurement small group, the teacher
supports developing measurement skills by “increasing the level of questioning,” “providing real-life problem-solving activities,” and “varying the forms of measurement activities.” In the activity, students use different types of tennis balls to explore motion. Students roll and bounce the balls on different surfaces and compare what happens. The teacher creates a chart for students to record their observations, measuring which ones bounced high or low and how far they rolled.