Students use number lines to place and compare positive and negative integers, including activities that require marking +4 and -4 and plotting integers on horizontal and vertical number lines. Students justify which number is greater by referencing position on the number line (for example, explaining that -$75 is farther to the left of zero than -$50, so -75 is less than -50). The skills list and activities ask students to write, interpret, and explain statements of order for rational numbers and include an optional game for practice with comparing and ordering positive and negative integers.

Students are asked to plot pairs of numbers on number lines and determine which is larger (Activity 1 and Number Lines and Distances pages). Activity 4 (Inequality Notation) explains > and <, shows examples such as (-2) > (-18) and asks students to write inequalities comparing pairs like -3 and -9, including reversible inequalities. Multiple places (e.g., comparing 7 and -12, comparing -9 and -12) require students to state that a number is larger because it is to the right of another on a number line.

Students are instructed that positive numbers are to the right of the origin and negative numbers are to the left, and they plot numbers and points on horizontal number lines and the coordinate plane (Activity 1, Activity 2, Activity 3). Students fold number lines to compare opposites (e.g., plotting 6 and -6) and draw lines from zero to see that opposite numbers are the same distance from zero. Several activities require students to move points left or right by specified units and to determine new coordinates after such horizontal moves (Problems in Points in the Coordinate Plane and the map/grid activities).

Students plot and locate integers and rational numbers on number lines and the coordinate plane in multiple activities (Activities 1–3 and the Coordinate Pictures task). A Basic Skills Review item asks students to write an inequality comparing two board lengths, and a number-line problem asks for the distance between -3 and 5, which has students work with negative and positive positions. The Parent Plan and Skills sections explicitly state students will extend number line diagrams and position pairs of integers and other rational numbers on a coordinate plane.

Students practice comparing integers and filling in >, <, or = for pairs that include negative numbers (several Problem 16/Fill-in items and other comparison items). Students plot numbers on a number line and identify which is closest to zero (e.g., plotting 2, -1, 4, -3 and identifying -1). Skills and activities explicitly ask students to plot rational numbers on number lines and to recognize that opposite signs indicate locations on opposite sides of 0, and several problems use absolute value in comparison statements.

The Basic Skills Review (#7) asks students to compare numbers using >, <, or = (e.g., -8 < 2, |(-)3| = |+3|, 4 < |(-)9|), so students practice comparing signed numbers and absolute values. Several activities require plotting points on coordinate grids and using number-line-style diagrams (double number lines and the coordinate plane in Activities 2 and 3), so students practice placing numeric values on scales and graphs.

Students are taught to graph inequalities on number lines with open dots for > and < and closed dots for ≥ and ≤, and shown that the arrow points right for greater-than relationships and left for less-than relationships (examples: x > 5 with an open circle and arrow to the right; n ≤ 2 with closed dot and arrow to the left). Students practice writing inequalities from number-line graphs and writing number-line graphs from inequalities in activities and interactive-notebook tasks. The materials include examples with negative numbers (n ≥ -4) and explicit steps that tell students to use the dot position and arrow direction to determine the inequality.

The student activity pages repeatedly require students to graph inequality solution sets on number lines (open/closed dots and arrows) and to check solutions by selecting values from those graphs. The answer key explicitly describes number-line graphs (for example: open dot at 3 with arrow right, closed dot at 3 with arrow left) and the Parent Plan lists "Represent solutions of inequalities on number line diagrams" as a skill. The lesson also instructs students to switch the direction of the inequality sign when switching the placement of expressions, which relates to understanding direction on a number line.

The lesson explicitly contrasts equations and inequalities using number lines, showing x = 2 as a filled dot and x < 2 as an open circle with an arrow, on a number line ranging from -5 to 5. Activity 4 gives inequality practice (e.g., p + 7 > 5, 2a + 4 ≤ 4) and requires students to solve each inequality and graph the solution on a number line; the answer key shows p > -2 graphed with an open dot at -2 and an arrow to the right. Multiple images and tasks ask students to graph solution sets on number lines and note the direction of the arrow for inequalities, including examples with negative values.

Students solve inequalities and are asked to graph their solution sets on number lines that range from -8 to 8 (examples: 4 < n + 6 giving n > -2, n - 7 > -12 giving n > -5). The answer key shows specific number-line graphs with open and closed dots and arrows (open dot at -2 with arrow to the right for n > -2; closed dot at 3 with arrow left for n ≤ 3). Several activity pages require students to represent solutions of inequalities on number line diagrams and to list reasonable solution sets for contextual inequalities.

Students are required to create multiple inequalities and to represent solutions of inequalities on number line diagrams (Parent Plan skills and project checklist). The project explicitly requires at least one inequality to be shown on a number line and includes a sample image showing an inequality graphed with an arrow indicating values greater than 5. Instructions prompt students to discuss and explain the number-line solution when sharing the poster, encouraging interpretation of the graphed solution in context.

The Basic Skills Review includes an inequality problem: 4y - 7 < 5, solved to y < 3, and students are asked to graph the solution on a number line from -5 to 5 with an open dot at 3 and an arrow extending left. The review explicitly shows the algebraic solution y < 3 and a number-line graph of that solution, which links an inequality to a spatial representation on a number line.

The Basic Skills Review includes Problem 3 asking students to graph the inequality y < 2 on a number line, and an accompanying image shows an open circle at 2 with the line shaded to the left. Students also plot points with negative coordinates in Problem 5 (e.g., (-3, 2), (-5, -1)), so they practice locating negative numbers on a number line or coordinate grid. These items require students to place values and regions relative to a number line.

Students are asked to solve the inequality n + 3 < 5 and graph the solution on a number line that ranges from -5 to 5, which requires locating solution values on a number line. The Basic Skills Review includes problems that require working with negative numbers and graphing an inequality, so students practice placing values relative to a number line and using open/closed dots to show solutions.

Students are asked to arrange numerical values in order (e.g., the dog heights are arranged from smallest to largest and ferris wheel rides are to be ordered highest to lowest). Students draw and label a number line for dot plots (the dog heights dot plot uses a number line from 10 to 34) and place dots above the appropriate numeric positions. Students compare numeric positions on the dot plots to answer questions such as identifying the shortest and tallest dog or asking how many more campers voted for one meal than another.

Students are instructed to write data values in order from least to greatest and to fill stems and leaves in order, which requires ordering numbers. Students answer questions that ask for the lowest and highest values in a data set and count how many values fall in specified numeric ranges (e.g., less than 60, at least 65). The Parent Plan Skills section also lists displaying numerical data in plots on a number line (dot plots, histograms, box plots).

Students organize numerical data from smallest to largest and create dot plots that require placing data values on a number line. Students draw box plots and label the five-number summary (minimum, first quartile, median, third quartile, maximum), placing those values along a number line and marking outliers as points outside the box. The project repeatedly requires plotting and interpreting positions of numeric values on number-line-based graphs.

The unit's Skills list explicitly includes "Understand ordering and absolute value of rational numbers." The Wrapping Up section directs students to play a Balloon Pop Math game to practice ordering positive and negative numbers and to complete an online "Ordering and Absolute Value" exercise. These activities provide students with practice ordering signed numbers and working with absolute value.

Students plot points with negative and positive coordinates (e.g., plot (-2, 4) and (3, 5)) and reflect points over axes, producing new coordinates (e.g., (-2,4) → (2,4)). Students are asked to describe whether a point moved left or right after a reflection and to compute horizontal distances between points. The coordinate tasks require students to reason about positions on a horizontal number axis (the x-axis) and to compare locations in different quadrants.

Students solve the inequality n + 2 > 5 (leading to n > 3) and are asked to graph the solution on a provided number line that spans -9 to 9; the answer key shows an open dot at 3 with an arrow extending to the right. The Skills list explicitly includes writing inequalities of the form x > c or x < c and representing solutions of such inequalities on number line diagrams. The Activities prompt reflection on how solving an inequality is similar to solving an equation, and a number line is provided specifically for graphing inequalities.

Students write and use inequalities such as 5 < <1a;30 < 6 after squaring values to compare numbers (Activity 3 and example steps). Students place square roots on number lines and are explicitly instructed to place √30 to the right of 5 and to place other approximated roots between their nearest perfect squares (Activity 5). Several activities ask students to identify which whole number an irrational root is closer to and to mark its position on a number line (Activity 5 and Activity 6). The review quiz asks students to compare and order numbers (√10, 3, √12) and show steps, reinforcing translating comparisons into inequality statements.

Students are asked to compare and order numbers in multiple problems (for example, "Compare and order the following numbers: √36, 5.5, and 6.1" and "compare and order √49, 6.8, and 7"), which requires judging relative magnitude. The Parent Plan explicitly states that students should "locate [irrational numbers] approximately on a number line diagram" and "use rational approximations to compare the size of irrational numbers," indicating attention to positioning numbers. Several estimation items (approximating square roots) and ordering tasks require students to reason about which numbers are greater or smaller.

Students draw and label a Probability Line with 0 (Impossible), 0.5 (Equal Chance), and 1 (Certain) and then place events along that line. They convert probabilities to fractions, decimals, and percents (spinner and coin activities) and use those numeric values to decide where outcomes belong on the line. The materials explicitly state that larger numbers indicate greater likelihood, and students compare probabilities to decide relative placement.

Students label a horizontal probability line with 0, 0.5, and 1 and place seven events along the line from Impossible to Certain. They decide where each event falls between 0 and 1 (e.g., equal chance, likely, unlikely) and justify placements using counts and percentages from the shelter data. The activity asks students to compare probabilities (e.g., which event is more likely) and to compute and interpret percentages like 50% or 75% for positioning on the line.

Students plot and read coordinates on a number line–style x-axis, including negative values, and are repeatedly told to read graphs left to right. In multiple activities they compare x-values (e.g., moving from (1,3) to (2,2): x increases by 1 while y changes) and use the idea that points further right have larger x-values when determining rise/run and slope. Tasks require students to identify whether lines rise or fall as you move right, which links position on the horizontal axis to numerical increase or decrease.

Students approximate irrational square roots by identifying intervals (e.g., √15 between 3 and 4, √20 between 4 and 5) and indicate which integer the value is closer to, which locates numbers approximately on a number line. Students determine final positions for situations with signed results (e.g., −12 + 7 = −5 means 5 meters below sea level) and write equations that express movement relative to zero. Several tasks ask students to compare magnitudes of numbers implicitly through approximation and classification (rational vs. irrational).