## Mathematical practices

Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

## Related Lessons

Lesson 24

Use the number line to place, compare, and order decimals to the hundredths. Use estimation and an algorithm based on place value to add decimals to hundredths. Use the number line to place, compare, order, and add decimals to the hundredths.

Lesson 23

Match visual models to the numbers they represent in fraction and decimal format. Solve problems with decimal fractions. Match visual models to the numbers they represent in fraction and decimal format.

Lesson 22

Use visual models and equations to solve problems involving multiplying and dividing fractions. Use models & equations to solve problems involving multiplying and dividing fractions.

Lesson 21

Use visual models, repeated addition, and multiplication to solve problems with equal sized groups. Compare the strategies to see which one is most efficient. Use visual models, addition, & multiplication to solve problems with equal sized groups.

Lesson 20

Use estimation and visual models to solve problems involving adding fractions with unlike denominators. Solve problems involving adding fractions with unlike denominators.

Lesson 19

Put together the fraction puzzle pieces by matching the visual model, expression, and fraction representations. Match visual models, expressions, and fractions to explore adding fractions.

Lesson 18

Use visual models and benchmark fractions to help compare and order fractions with unlike numerators and denominators. Use a number line and benchmark fractions to compare and order fractions.

Lesson 12

Mr. Lineberger loves playing games with dice. He needs your help to figure out how many each of his friends will get when they come over to play games. We can use division to help him figure it out.

Lesson 11

Mr. Lineberger wants to plant a garden. Help him visualize and represent his garden. We can use division to help him plan how he'll use all the veggies he plans to grow.

Lesson 10

Explore side length, area, and volume and apply the formulas V = l × w × h and V = B × h for rectangular prisms to solve problems. Explore side length, area, and volume and apply the formulas for volume to solve problems.

Lesson 09

Understand concepts of volume measurement by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Solve problems involving volume. Understand concepts of volume measurement by counting unit cubes or calculating volume.

Lesson 08

Use visual models, decompose shapes, and apply the area formula for rectangles to solve problems in real world contexts. Use visual models & the area formula for rectangles to solve problems.

Lesson 3

Move on a physical place value chart to help understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Move on a physical place value chart to understand the "times 10" pattern.

Lesson 2

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right. Hunt for patterns in the number of zeros of the product when multiplying a number by powers of 10. Hunt for patterns in the product when multiplying a number by 10.

Lesson 01

Multiply a two-digit by a one-digit whole number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply whole numbers using place value strategies & the properties of operations.

Lesson 303

Compare fractions with the same numerator and different denominators. Compare and order fractions using bar models. Represent one whole using a fraction with equal numerator and denominator.