Illinois Grade 6 Math

A negative sign changes how a quantity is ordered, so comparing the digit sizes alone can be misleading. Position on a number line gives a consistent explanation. The temperature labels in this activity are invented and are not observations from Illinois weather stations.

Try the worked activity

Three model temperature readings are −6°C, −2°C, and 3°C. Put them in increasing order, identify the warmest reading, and explain why −2°C is warmer than −6°C even though two is less than six.

Follow the reasoning

On a number line increasing from left to right, −6 lies to the left of −2, and both lie to the left of 3. The increasing order is −6 < −2 < 3. In this context, the reading farther to the right represents the warmer temperature, so 3°C is warmest. The statement −2°C > −6°C compares the signed temperatures; it does not compare the positive digits two and six by themselves. A reading two degrees below zero is closer to zero and warmer than one six degrees below zero.

Check the explanation

The location relative to zero matters, not just whether a number is negative. Two negative readings can be ordered without treating them as equal or automatically less cold when their digits are larger. Also keep temperature order separate from distance to zero: −6 has a larger absolute value than −2, while −6 is the smaller signed number. That distance comparison is a related part of the full expectation, and it answers a different question from which reading is warmer.

Use the next session

1. Place zero and label an increasing number line.
2. Locate each signed reading with equal unit intervals.
3. State an inequality and explain what it means for temperature.

Insert −4°C among the original readings and justify −6 < −4 < −2 < 3 by position. Then compare −4°C with 0°C and state what the inequality means. Use the same number-line order to discuss invented elevations, keeping the context and unit clear. A larger distance below a reference point is not automatically a greater signed value. Extend the work to rational numbers between integers and to the absolute-value parts of the official expectation when those are being taught. This initial integer model selects order and contextual interpretation rather than cover every rational-number task.

Selected references from Illinois’s adopted mathematics document

The Illinois mathematics standards directory links the Illinois Learning Standards document incorporating Common Core. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

Grade 6 is within Illinois’s IAR mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Illinois’s assessment overview.

Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.