What does a student learn in
New York, Grade 7, Mathematics ?

Students combine and simplify algebraic expressions that include fractions or decimals. They use rules like the distributive property to rewrite expressions in a different but equivalent form.

Rewriting a math expression in a different but equal form can show a relationship that was hidden. For example, rewriting a price plus tax as a single multiplier shows the total cost in one step.

Students solve real-world problems that mix whole numbers, fractions, and decimals, including negatives. They pick the right form for each number, do the math, and then check whether the answer actually makes sense.

Scale drawings shrink or stretch real objects onto paper. Students read a map or blueprint's scale to figure out actual distances and areas, then redraw the same figure at a new scale.

Students draw triangles from given angle and side measurements, then figure out whether those measurements can only produce one triangle, could produce several different triangles, or make a triangle impossible.

Students slice through 3-D shapes, like a cube or cone, and name the flat shape the cut reveals. A horizontal slice through a cylinder makes a circle; a vertical slice makes a rectangle.

Students use the formulas for area and circumference to find the size and distance around circles in real problems, like figuring out how much pizza fits on a plate or how far a wheel travels in one turn.

Students use what they know about angle pairs to write and solve equations that find a missing angle. For example, if two angles together form a straight line, they add to 180 degrees, so students write an equation and solve for the unknown.

Students find the area of flat shapes made from triangles and trapezoids, then figure out the surface area and volume of 3-D objects like prisms and pyramids. The problems use real measurements, not just diagrams.

Adding and subtracting negative numbers, fractions, and decimals. Students use a number line to show why a problem like -3 + 5 or 1/2 - (-2) lands where it does.

Multiplying and dividing negative numbers, like -3 times 4 or -12 divided by -2. Students use the same rules they already know for fractions and whole numbers, now applied to negatives and positives together.

Working with positive and negative numbers, fractions, and decimals, students add, subtract, multiply, and divide to solve real problems. Think splitting a bill, tracking a bank balance, or figuring out a temperature change.

Students figure out the rate for one unit when both numbers in the ratio are fractions. For example, finding miles per hour when the trip covers a fraction of a mile in a fraction of an hour.

Students learn to spot when two quantities grow at a constant rate together, like miles per hour or price per item. They find that rate in tables, graphs, and equations, then explain what specific points on the graph mean in real terms.

Students use percentages to solve real problems: figuring out a sale price, calculating interest, or finding how much something grew or shrank. The math takes more than one step.

Students learn to read and build box plots, calculate the spread of the middle half of a data set, and spot values that fall unusually far from the rest.

Students compare two sets of data on a graph and describe how much the groups overlap or differ. For example, they might look at two dot plots side by side and explain whether the numbers are clustered in the same range or spread far apart.

Students compare two groups using averages and spread, like how the typical height of 7th graders in one school stacks up against another. The goal is to draw reasonable conclusions about which group tends to be higher, lower, or more consistent.

Students figure out the chances of two things happening together, like flipping a coin and rolling a die. They list out every possible result using charts or tree diagrams, then use that list to find the probability.