GA Milestones Math Grade 3: Primary measurement, shape attributes and data displays

Measurement

The Measurement domain tests selecting appropriate tools and units, measuring length, liquid volume, mass, and temperature, solving problems with time and elapsed time, and finding perimeter and area. Grade 3 items often include rulers, clocks, and real-world contexts such as gardening, cooking, or travel. Students must choose the right unit and keep the meaning of the measurement.

Core rules and concepts

Choose a unit that matches the object: inches, feet, yards, or miles for length; cups, pints, quarts, or gallons for liquid volume; ounces, pounds, or tons for weight; grams or kilograms for mass; degrees Fahrenheit or Celsius for temperature.
Measure length from the zero mark, not from the edge of the ruler. Read the nearest marked fraction or whole unit required by the problem.
Elapsed time is the difference between a start time and an end time. Count forward in convenient jumps, such as to the next hour, then by minutes.
Perimeter is the distance around a figure. Add all side lengths. For a rectangle, use P = 2l + 2w or P = 2(l + w).
Area is the number of unit squares that cover a figure. For a rectangle, A = length × width. Area is measured in square units; perimeter is measured in linear units.
The same rectangle can have the same perimeter but a different area from another rectangle, so do not substitute one for the other.

Worked example

A rectangle is 6 centimeters long and 4 centimeters wide. Find its perimeter and area. Perimeter: add the four sides, 6 + 4 + 6 + 4 = 20 centimeters, or use 2(6 + 4) = 20 cm. Area: multiply length by width, 6 × 4 = 24 square centimeters. The perimeter describes the distance around the rectangle; the area describes the space inside it.

Traps that cost marks

Reporting area in centimeters instead of square centimeters, or perimeter in square units.
Adding only length and width and forgetting the other two sides for perimeter.
Reading the end mark without subtracting the starting mark when an object does not start at zero. If it starts at 1 and ends at 6, the length is 5 units, not 6.
In elapsed time, forgetting to regroup 60 minutes into 1 hour when crossing an hour.
Choosing a unit that is too large or too small, such as measuring a pencil in miles.

Geometric Reasoning

The Geometric Reasoning domain tests Grade 3 students’ ability to identify and describe two-dimensional figures by their attributes. Items cover points, lines, line segments, rays, parallel and perpendicular lines, angles, quadrilaterals, polygons, and line symmetry. Students also compose and decompose figures and use attributes to classify shapes rather than relying on how a shape looks.

Core rules and concepts

A point names a location. A line goes straight in both directions without ending. A line segment is part of a line with two endpoints. A ray starts at one endpoint and continues in one direction.
Parallel lines never intersect and stay the same distance apart. Perpendicular lines intersect to form right angles.
A polygon is a closed plane figure with straight sides that do not cross. It is named by its number of sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6.
A quadrilateral has 4 sides and 4 angles. Special quadrilaterals include trapezoids, parallelograms, rectangles, rhombuses, and squares. A square is also a rectangle and a rhombus because it has all the required attributes.
A right angle is a square corner. Acute angles are smaller than a right angle; obtuse angles are larger.
Line symmetry means a figure can fold along a line so the two halves match exactly. A figure may have zero, one, or many lines of symmetry.

Worked example

A figure has 4 sides, 4 right angles, and opposite sides equal. What is the most specific name? The figure is a quadrilateral because it has 4 sides. The 4 right angles make it a rectangle. Opposite sides equal fits a rectangle. If all 4 sides were also equal, the most specific name would be a square. Without that extra fact, rectangle is the safest specific name. This reasoning uses attributes, not the orientation of the drawing.

Traps that cost marks

Calling any four-sided shape a rectangle; a rectangle must have four right angles.
Thinking a square is not a rectangle. In the inclusive classification used in Grade 3, a square has all the attributes of a rectangle.
Confusing a line, which continues forever, with a line segment, which has endpoints.
Counting a shape as having symmetry when the fold line does not produce matching halves.
Classifying a quadrilateral by its tilt on the page rather than by side and angle attributes.

Data Analysis and Probability

The Data Analysis and Probability domain tests how Grade 3 students collect, represent, and interpret data. Items use frequency tables, scaled picture graphs, scaled bar graphs, and line plots. Students read the scale, compare categories, find totals and differences, and answer questions that require more than simply reading one number off a graph. Probability at this grade is informal: students may describe events as likely, unlikely, certain, or impossible in simple contexts.

Core rules and concepts

A scaled graph uses each picture or bar unit to stand for more than one item. Read the key or axis scale before counting.
In a picture graph, a half symbol means half of the scale value. If one symbol = 4 books, a half symbol = 2 books.
In a bar graph, read across from the top of the bar to the matching number on the scale. Check whether the grid lines count by 1, 2, 5, or 10.
A line plot shows each data value as an X above a number line. The number of Xs above a value is its frequency.
To compare categories, subtract the smaller value from the larger value. To find a total, add the values for the categories requested.
A table must be read by matching each row or column label with the correct number; do not assume the order of rows is the order of size.

Worked example

A scaled picture graph shows favorite fruits. The key says one apple symbol = 4 votes. Apples have 3 whole symbols and 1 half symbol. How many votes do apples have? Each whole symbol is 4 votes, so 3 whole symbols are 3 × 4 = 12 votes. The half symbol is half of 4, or 2 votes. Add: 12 + 2 = 14 votes. The reasoning is: multiply whole symbols by the scale, then add the value of the partial symbol.

Traps that cost marks

Counting symbols instead of multiplying by the scale.
Reading a bar graph from the wrong grid line or ignoring that the axis starts at 0.
Mixing up “how many more” (subtract) with “how many altogether” (add).
On a line plot, counting the labels instead of the Xs, or missing that a cluster shows frequency.
Treating a half symbol as one whole symbol.