There has been a growing need for a focused and coherent mathematics curriculum in the United States to improve achievement in mathematics. To address this need, the **United States Common Core Standards (USCC)** for mathematics for each grade have been laid out. The standards are described in detail to help educators plan appropriate pedagogical approaches to ensure achievement of outcomes. These standards are drawn in from research in math education and models of best mathematical practices across the world.

Here are the highlights of the grade specific standards.

**GRADE 2**

In grade 2, extending the understanding of the base-ten system is given utmost importance. Understanding addition and subtraction of numbers up to 1000 and generalizing methods to compute sums and differences using place value and the properties of operations are some of the key areas of focus under number sense. In measurement, students recognize the need for standard units of measure and learn to use measurement tools. In addition to analyzing 2-D and 3-D shapes, students are encouraged to identify sides and angles of 2-D shapes.

In order to facilitate mastery of abstract concepts by young learners, **Cuemath adopts a Concrete-Pictorial-Abstract (CPA) approach**. The curriculum is aided with concrete models and visuals as much as possible to make the transition from concrete to abstract concepts seamless.

The curriculum for grade 2 spreads across four major domains.

- Operations in Algebraic Thinking
- Numbers and Operations in Base Ten
- Measurement and Data
- Geometry

**Operations and Algebraic Thinking**

From early years, USCC standards focus on algebraic thinking as the building blocks that lead to unraveling of new concepts. A good example of this would be how addition extends beyond simple putting together to addition of equal groups. This addition of equal groups builds the preliminary understanding of the concept of multiplication of whole numbers.

Here is a question from the Cuemath curriculum where three equal groups of 4 have been given to the student to add.

Here, students can visualize addition of objects arranged in rectangular arrays to find the total as a sum of equal addends. In both the examples, the students add 4 three times and 5 four times without using multiplication. However, this helps in laying a **foundation for multiplication**. This also helps in development of an algebraic approach that is implicitly used to build multiplication tables.

Although in traditional teaching there is a greater emphasis on ensuring students learn multiplication tables by rote than making students understand the meaning of multiplication. However, in Cuemath, through such questions, they develop an intuitive understanding of the meaning of multiplication of whole numbers. This gives a strong foundation of formal multiplication that they eventually learn in grade 3.

**Numbers and Operations in Base ten**

USCC standards stress on the fact that concrete models maximize the initial understanding of numbers in children. Adhering to these standards, in the Cuemath Curriculum Base 10 blocks are used to help students understand how a** number is composed of hundreds, tens, and ones**. The flats are shown as bundles of tens and tens as bundles of ones to show the multiplicative structure of the base ten system to students. This helps them in understanding the place value system easily which in turn makes it easier for students to grasp addition and subtraction of large numbers. Addition and subtraction of numbers using Base 10 blocks helps children visualize the process of operations before the standard algorithm is introduced.

For example, notice how the visual representation of the addition of 126 and 143 simplifies the process for the student.

The students add the ones first, bringing all the blocks together. Next, they bring the tens together.

Lastly, the students put the flats (hundreds) together.

This helps them visualize the sum 269 formed by 2 flats, 6 rods and 9 blocks. This understanding allows for **easy transition to addition of place values **when the standard algorithm is introduced to students.

**Measurement and Data **

In grade 2, standard units of measurement of length such as meters, centimeters, feet and inches are used by the students to identify the length of the given object. The focus also remains on the comparison of lengths by determining how much longer one object is than another and expressing the length difference in terms of a standard length unit.

Take a look at this question:

Here each pen begins at the zero mark on the ruler and hence it will be easy for the student to find the right pen as per the given length.

The Cuemath curriculum is designed to address common misconceptions students usually have. Hence, the above question is taken one step further as shown below where students measure and compare lengths when the starting point of the two objects are not the ‘zero’ mark’ on the scale.

Here, the students often struggle with the measurement of length because in most cases, they focus on the end points, which in this case are 8 inches and 10 inches. Many students overlook the starting point and consider the end point as the length. However, the actual length of the pens is 5 inches and 4 inches respectively. The focus here must shift to both the start point and the end point to find the length of each pen and then compare.

Students also visualize how whole numbers can be shown as lengths from 0 on a number line with equally spaced points corresponding to the numbers 0, 1, 2, and so on. The visualization of whole numbers on the number line plays an integral part in students’ understanding of the number system and proves to be of great help when decimals and fractions are introduced.

Along with the ability to **measure and compare lengths**, students use this skill to **generate measurement data** by measuring lengths of several objects and show the same in the form of a line plot. They learn to represent other forms of data set in bar graphs and picture graphs.

**Geometry**

When students are introduced to **2D shapes**, they often start thinking of these shapes as unique entities that can only exist in isolation. USCC standards challenge this way of thinking and push the students to develop the ideas of composing shapes using various other shapes and **decomposing shapes to form different shapes**.

The simulation below from the Cuemath Curriculum is an example of an activity that the students do to understand the same.

In the simulation, the students get to explore various cases such as formation of a square using two triangles, formation of a rectangle using two squares, and formation of a triangle using two triangles.

A follow up question like the below, after the activity, ensures that the students comprehend and grasp the idea clearly.

USCC standards allow the students to delve into the basic understanding of fractions in preliminary form by showing partition of circles and rectangles into two, three, or four equal shares. The equal shares are described using the words halves, thirds, half of, a third of, whereas the whole are described as two halves, three thirds, and four fourths.

With the focus primarily on the expansion of the number system to three-digit numbers and operation on them, the in-depth understanding of units of length, and the properties of 2D and 3D shapes, the Cuemath curriculum for grade 2 ends on a high-note before moving on to grade 3 where all domains are taken a notch-up.** ****Cuemath curriculum provides learning experiences of important concepts through concrete and pictorial representations and connects mathematics with the lives of students.** **Cuemath conducts Live Online Math classes and Coding classes. **This makes them love math and see its relevance in their day to day lives.

-By Shubhi Mittal

Shubhi is the Project Lead for the primary curriculum for the Asia-Pacific countries at Cuemath. She believes in leveraging simplified and interactive learning approaches to remould the delivery tools of math education. In her spare time, she is a linguaphile who also enjoys gardening and working out.

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