Develop and understand the concept of surface area and volume of rectangular… | Students find the total area covering the outside of a box and the space inside it, using measurements that include fractions or decimals. This builds the skills needed to solve real problems involving packaging, storage, or construction. | 7.GM.1 |
Recognize that the surface area of a rectangular prism can be found by finding… | Students find the total surface area of a box by adding up the area of each flat face. Two boxes with different shapes can still have the same total surface area. | 7.GM.1.1 |
Using a variety of tools and strategies, develop the concept that surface area… | Surface area measures all the flat faces of a box added together. Students figure out how many same-size squares it would take to cover every face, then record that total in square units like cm². | 7.GM.1.2 |
Using a variety of tools and strategies, develop the concept that the volume of… | Students figure out the volume of a box by imagining how many same-sized cubes would fill it completely, with no gaps. The answer is written in cubic units like cm³. | 7.GM.1.3 |
Use mathematical models and problems to calculate and justify the area of… | Students find the area of trapezoids and figure out the perimeter and area of shapes built from simpler pieces, like rectangles and triangles combined. They work with measurements that include fractions and decimals. | 7.GM.2 |
Develop and use the formula to determine the area of a trapezoid | Students learn the formula for finding the area of a trapezoid, a four-sided shape with one pair of parallel sides. They practice applying it with measurements that include fractions and decimals. | 7.GM.2.1 |
Find the area and perimeter of composite figures | Students find the total area and perimeter of shapes made by combining simpler shapes, such as rectangles and triangles. Measurements include fractions and decimals. | 7.GM.2.2 |
Use mathematical models and reasoning with proportions and ratios to determine… | Students use ratios and proportions to find unknown measurements, like a missing side length or scale distance, and explain why area and volume formulas work. | 7.GM.3 |
Solve problems that require the conversion of weights and capacities within the… | Students convert measurements within the same system, like changing pounds to ounces or gallons to cups, to solve everyday problems. They choose the right unit for the job and do the math to switch between them. | 7.GM.3.1 |
Demonstrate an understanding of the proportional relationship between the… | Students learn that a circle's distance around is always a little more than 3 times its width across, and that this ratio never changes. That fixed relationship is called pi, often approximated as 3.14. | 7.GM.3.2 |
Calculate the circumference and area of circles to solve problems in various… | Students calculate the distance around a circle and the space inside it, using pi (roughly 3.14) to get the answer. These skills show up in real problems, like figuring out how much fencing wraps a circular garden or how much tile covers a round floor. | 7.GM.3.3 |
Analyze the effect of translations, reflections, rotations | Sliding, flipping, turning, and resizing shapes changes where they sit or how big they are, but usually keeps their angles and proportions intact. Students study how each of these moves affects a shape's size, position, and overall form. | 7.GM.4 |
Describe the properties of similarity, compare geometric figures for similarity | Students learn what makes two shapes "similar" (same shape, different size) and figure out the scale factor: the number that shows how much bigger or smaller one shape is than the other. | 7.GM.4.1 |
Apply proportions, ratios | Students use scale factors and ratios to read scale drawings and find the real side lengths and areas of similar triangles and rectangles. | 7.GM.4.2 |
Graph and describe translations | Students plot shapes on a grid, then slide, flip, or rotate them and find the new corner points. They follow both written directions and algebraic rules to describe each move. | 7.GM.4.3 |