Grade4 measurement, data, shapes and angles
The Measurement and Data domain tests converting units within a measurement system, solving problems involving perimeter and area, and interpreting data on line plots. Questions expect accurate unit labels and attention to whether a measurement is a length, a liquid volume, a mass, or a time interval.
Unit conversions
- Length: 1 kilometer = 1,000 meters; 1 meter = 100 centimeters; 1 centimeter = 10 millimeters.
- Mass: 1 kilogram = 1,000 grams. Liquid volume: 1 liter = 1,000 milliliters.
- Time: 1 hour = 60 minutes; 1 minute = 60 seconds.
- Converting from a larger unit to a smaller unit multiplies. Converting from a smaller unit to a larger unit divides.
Perimeter and area
- Perimeter is the distance around a figure and is measured in linear units. For a rectangle, P = 2 × (length + width).
- Area is the number of square units covering a figure. For a rectangle, A = length × width.
- The same dimensions can produce different numerical perimeter and area values, so keep the units and the formulas separate.
Line plots
- Each mark on a line plot represents one data value. Count marks carefully, especially when several marks stack above the same fraction.
- Read the scale before counting. A line plot may be divided into halves, fourths, or eighths.
- Use the line plot to answer questions about the most common value, the difference between the greatest and least values, or the total number of observations.
Worked example
A jug contains 3.25 liters of juice. How many milliliters is that? Since 1 liter = 1,000 milliliters, multiply by 1,000. 3.25 × 1,000 = 3,250 milliliters. Reason it out: 3 liters = 3,000 milliliters, and 0.25 liter = 250 milliliters, for a total of 3,250 milliliters.
Traps that cost marks
- Mixing units, such as subtracting centimeters from meters without converting first.
- Labeling area in linear units or perimeter in square units.
- Using the area formula when the question asks for distance around a figure.
- Miscounting stacked marks on a line plot or reading the wrong fractional interval.
- Multiplying when converting from milliliters to liters instead of dividing.
The Geometry and Geometric Measurement domain tests lines, line segments, rays, angles, parallel and perpendicular lines, classification of two-dimensional figures, lines of symmetry, and angle measurement. Questions often combine naming a figure with measuring or reasoning about its angles.
Lines, rays, and angles
- A line extends in both directions without endpoints. A line segment has two endpoints. A ray has one endpoint and extends in one direction.
- An angle is formed by two rays that share a vertex. Angle size is measured in degrees and does not depend on the lengths of the rays.
- A right angle measures 90°, an acute angle is less than 90°, and an obtuse angle is greater than 90° but less than 180°. A straight angle measures 180°.
- Parallel lines never meet and stay the same distance apart. Perpendicular lines meet at a right angle.
Classifying figures
- Triangles can be classified by sides: equilateral (three equal sides), isosceles (at least two equal sides), and scalene (no equal sides). They can also be classified by angles: acute, right, or obtuse.
- Quadrilaterals include trapezoids, parallelograms, rectangles, rhombuses, and squares. A square is also a rectangle, a rhombus, and a parallelogram because it satisfies each definition.
- A line of symmetry divides a figure into two matching halves that fold onto each other.
Angle measurement
- Place the protractor center on the vertex and align one ray with the zero mark. Read the scale that starts at zero on that ray.
- Adjacent angles that form a right angle add to 90°. Adjacent angles that form a straight angle add to 180°.
Worked example
Two adjacent angles form a right angle. One angle measures 37°. Find the other angle. A right angle is 90°, so subtract: 90° − 37° = 53°. The second angle measures 53°, and 37° + 53° = 90° checks the result.
Traps that cost marks
- Judging an angle by the length of its rays rather than by the opening between them.
- Reading the wrong protractor scale, especially when the ray does not point to zero on the outer scale.
- Calling a square only a square and not recognizing it as a rectangle and rhombus.
- Confusing a line, ray, and segment when naming a figure.
- Assuming every quadrilateral has a line of symmetry or that every triangle is equilateral.