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While they certainly did not want a "paper-driven" curriculum, they did want every math experience to include at least some option for recording the activity. Of course, try some new things; some will reveal surprising abilities you might never have guessed the children would have. But also remain alert and flexible.

Not everything will work with every child, and it doesn't need to. You can't do everything that is suggested, and are not expected to do everything. Four and five year olds -- even the ones who can't count -- are, in many ways, thinking like little mathematicians. All of this gives kindergarten teachers wonderful opportunities -- already naturally built into the child's way of playing -- to help these young children notice what clever little mathematicians they already are, and then to refine and extend their ideas naturally and still playfully, building their power as mathematical thinkers.

Just by virtue of being adults, let alone college educated, teachers' logic and knowledge are way beyond what these children can learn, even about the topics like counting that are age appropriate. The children are little mathematicians, but in their own way, and not as consistent as adults are. They are also intrepid and ready to learn because they have not yet had the experiences that, unfortunately, leave some adults forgetting how mathematically intelligent they once were and really still are, if they let themselves play again.

The very beginning of each chapter describes that chapter's "morning time" activity. Because it appears only at the beginning of the chapter, and is not repeated with each lesson, it is sometimes not noticed. If you do the morning time activity faithfully and engagingly every day, and nothing else, your children will be ready for first grade.

Of course, there is much, much more that your children can do, and that is what the other components of Think Math! FAQs Many kindergarten programs start with shapes and then go to numbers. Can you tell me why numbers are first in the kindergarten curriculum? Part of the answer is that, though we start with number, there is a lot of attention to shapes from the beginning as well.

Here's a quick overview. In Lesson 1, we have children select from all the pattern blocks -- square, triangle, diamond, trapezoid, hexagon -- and describe one pattern block. In Lesson 1, children also make pattern block designs and explore connecting cube towers. Throughout the chapter we have a heavy emphasis on studying pattern blocks and their attributes, as well as making designs with them. Quantity cards are used frequently to practice number, but they also picture numbers using a variety of shapes. Children continue to explore cube patterns.

Headline stories feature shapes, such as stars in Lesson 3, and circles and triangles in Lesson Lessons 12 and 13 have activities with Cuisenaire rods. Lesson 14 has an activity where different shapes are used to make a real-object graph. Chapter 2 explores many of the same topics, but with somewhat more direct focus on shapes and somewhat less on quantity. Both are certainly important in both chapters.

One reason that kindergarten programs often start with shapes is because shapes are interesting and accessible to young children and because they are important for the study of mathematical ideas in a way that kindergarten children can understand and express. Describing the shapes typically with colors and sizes is also seen as part of the language development of young children.

We do this too. However we also introduce number early for two reasons. Only some can read or write those numbers despite being able to use several numbers correctly , just as only some know their letters despite having a huge vocabulary of words that they speak and use correctly. The reading and writing of numbersâ€”just like all of the written work in Kindergartenâ€”is provided for use at the discretion of the teacher.

Some teachers prefer to emphasize reading and writing; some prefer to de-emphasize it; because we needed to support both judgments, we had to provide the options, but from a mathematical learning perspective, either approach is fine. So we start with both.

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Much of the number-related work, especially early in the year, can be seen as an exploratory activity so that children experiment with the concept of grouping and counting objects as well as looking at their attributes. For the children who are developmentally ready to think about number and can use correspondence, the number part of this chapter and the organization that the number line provides supplies a fun challenge. For children who are not there yet, they learn the number part of the chapter more like one learns a song or poetry.

## Kindergarten

Both developmental groups find the activities fun. No single child will do all of the activities of any lesson. The large range of activities gives all developmental groups activities that challenge them, but do not overwhelm them. Each lesson in Think Math!

## Math In Kindergarten Through Second Grade - Setting The Foundation

Structuring all of these activities into one minute block of math may feel overwhelming, especially at the beginning of the year. Below are five models that teachers have developed to make this work in their classrooms. Find a structure that works best for you. You may choose to adapt as the year progresses, or even each day, depending on the amount of support you have in your room.

Everyone agrees that once a game or an exploratory center has been introduced to and practiced with the whole class, it is easier for children to successfully work at an independent center.

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One of the simplest ways to structure a Think Math! All students will work on the same activity, but the activity may be differentiated to meet the variety of needs in the classroom. In this model, you choose the three activities that you consider the most important from the lesson.

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Part A, the one you decide is most important, can be a whole-group lesson taught by the teacher and followed by a whole group activity. If a child completes the activity in part B, the child takes the materials for the activity for part C. Not all children need to get to this activity. In this model, the teacher is able to support children needing extra help during Part A, while others go on to B and C.

### Understanding Student and Teacher Roles in Mathematical Discourse

Prepare and introduce materials for B and C ahead of time. Students work at their own pace. The teacher begins with the whole group lesson. Then, students go to designated tables to work at one of the centers. The Teacher Guide usually gives ideas for three centers, but for a large class over 18 , you may want to create a fourth center to reduce the number of children in one center at one time children is ideal. The teacher will direct students to switch tables after a designated amount of time generally 10 minutes. Ideally, all students visit each center in one lesson.

Alternative: Some teachers choose to keep the same centers available all week, so that the students have multiple opportunities to work at a center. This model also allows students to visit a center for longer; they can visit other centers the next day. This model begins with a whole group lesson. Then the students go to designated tables to work at one of the centers. Bar graphs that distinctly display information give the children practice in creating and comparing sets:. A good graph arises out of the children's natural desire to share information with their peers, quantify the results, and compare the outcomes.

Graphs can be especially motivating to cognitively advanced children since they provoke a high level of thinking. As Halloween approached, Laura engaged the children in graphing based on predictions. She introduced pumpkins with a graph titled "How Do Pumpkins Grow? Pumpkins growing various ways illustrated the choices: on a pumpkin tree, on a pumpkin bush, on a vine, or under the ground. The children's names were on cardboard rectangles and available for them to choose.

Laura called the children over individually and presented each choice again and asked them to put their name by how they thought pumpkins grew. This activity showed again that young children think differently or do not have knowledge assumed by adults. The majority of the children chose correctly that pumpkins grew on vines. Sid, however, stated, "Pumpkins grow underground like potatoes. When questioned, she said, "Because they [pumpkins] do. She asked if anyone could see how the pumpkins were growing.

All the children agreed that pumpkins did indeed grow on vines. Figure 2. Graphing display of "How Do Pumpkins Grow? In the play episode described above, Rachel also demonstrated her behavioral understanding of seriation by systematically placing the bears from largest to smallest. Ordering is a higher level of comparing seeing differences and involves comparing more than two objects or more than two sets.

Ordering or seriation involves putting more than two objects or sets with more than two members into a sequence. Ordering also involves placing objects in a sequence from first to last, and it is a prerequisite to patterning. Ordering is the foundation of our number system e.