Listed below are the fourteen big ideas with a brief description of what students of all ages should understand. Following each description are ideas for teachers to help their students learn and understand the big ideas.
1. Numbers
Counting tells how many items there are altogether. When counting, the last number tells the total number of items; it is a cumulative count (Charles 2005, 12).

Ask students to group objects in set with specific number. Have sutdents practice counting the objects and then stating how many objects are in each group.
There is a number word and a matching symbol that tell exactly how many
items are in a group (Charles 2005, 12).

Have students group objects and then write the number symbol and the corresponding word that designates how many are in the group.
–The distance between any two consecutive counting numbers on a given
number line is the same. Numbers can also be used to tell the position of
objects in a sequence (e.g., third) (Charles 2005, 12).

Display a number line in the room that extends above one hundred and below zero.
The numbers are related to each other through a variety of number relationships (Van de Walle 2004, 115).

Introduce the idea of numbers being related through a variety of number relationships by reading two different versions of a familiar story. Below is a link to a lesson plan from the Illuminations website. http://illuminations.nctm.org/LessonDetail.aspx?ID=L295
Every number consists of other numbers. For example the number 5 consists of 1 and 4 and 2 and 3.

Allow students to build cube trains using two different colors. They should find all the different combinations and record the number of each type of cube used to write and number sentence. Charts can be made for all students to see the different combinations.
Counting a set in a different order doesn’t change the total. (Charles 2005, 12)

Allow students to explore and practice counting the same set of objects, but in different orders to see that the total does not change.
By adding one to a number it will be the next number in the counting sequence, for example adding one to five will be six.

Have the students do an activity where they need to figure out the length of a tower they do not now the total by comparing it to a tower length they do know how many are in the tower. Have the students explain how they know how many are in the tower they did not know how many are in the tower.