Each lesson has a prediction prompt and a model matched to its topic. Use these notes to turn a slider, diagram, or data plot into a short math conversation. Let the learner make a prediction, change one value, describe the evidence, and connect it to a written equation or claim.
Unit 01
Ratios, rates, and proportional relationships
Visuals: Grouped ratio bars, ratio tables, unit-rate comparisons, and a three-view equivalent-ratio explorer.
Ask: What do the two quantities count, and what must happen to both quantities to keep the comparison equivalent?
Listen for: The learner names the order and units of the quantities, then identifies one shared scale factor across the bars, table, or number line.
Watch for: A learner may reverse the order, scale only one term, or treat an equivalent ratio as unrelated numbers.
Open a sample lesson: Equivalent Ratios ↗Unit 02
Fractions and fraction operations
Visuals: Equal-part fraction strips, area overlaps, common-unit strips, regrouped mixed-number strips, and a number line that measures divisor-size groups.
Ask: What is one whole in this picture, and what does one equal piece represent before you operate?
Listen for: The learner keeps the unit fraction visible, renames unlike pieces before combining, and explains fraction division as counting divisor-size groups.
Watch for: A learner may add denominators, ignore piece size, or invert-and-multiply without connecting it to the model.
Open a sample lesson: Dividing Fractions ↗Unit 03
Decimal place value and operations
Visuals: Place-value charts, decimal number lines, aligned operation columns, equal-group division, hundred grids, and fraction-decimal links.
Ask: Which place does each digit represent, and what changes when a digit moves one place left or right?
Listen for: The learner aligns decimal points by place value and explains a product or quotient with equivalent tenths, hundredths, or thousandths.
Watch for: A learner may compare decimals by counting digits, align the last digits instead of decimal points, or scale only one number.
Open a sample lesson: Adding and Subtracting Decimals ↗Unit 04
Negative numbers and the coordinate plane
Visuals: Integer number lines and coordinate grids with reflected points and labeled ordered pairs.
Ask: Are you describing a point’s position, its distance from zero, or the distance between two points?
Listen for: The learner uses left/right for order, absolute value for distance from zero, and names which coordinate changes in a reflection.
Watch for: A learner may assume a larger absolute value is always greater, or change both coordinates when reflecting across one axis.
Open a sample lesson: Reflecting Points on the Coordinate Plane ↗Unit 05
Factors, multiples, and number structure
Visuals: Factor arrays and paired factor rows that connect rectangular arrangements to factor pairs, prime factors, GCF, and LCM.
Ask: How can you prove this list of factor pairs is complete without repeating a pair?
Listen for: The learner links each factor pair to a rectangular array and checks factors against the original number.
Watch for: A learner may list multiples when asked for factors, confuse prime with odd, or omit 1 and the number itself.
Open a sample lesson: Prime Factorization ↗Unit 06
Percents and real situations
Visuals: Percent grids, part-whole bars, and before/after bars for percent increase, decrease, tax, tip, and discount contexts.
Ask: Which amount is the whole, which amount is the part or change, and what does 100% represent here?
Listen for: The learner anchors 100% to the correct whole before finding a part, finding the whole, or applying a change.
Watch for: A learner may use the changed amount as the original whole or confuse the percent amount with the rate.
Open a sample lesson: Finding the Percent of a Number ↗Unit 07
Expressions, equations, and inequalities
Visuals: Expression tiles, substitution, area arrays for distribution, balance steps, equal groups, two-quantity tables and graphs, story-to-equation prompts, and inequality solution lines.
Ask: Which variable is the input, which depends on it, and how does the same pair appear in the table and graph?
Listen for: The learner connects a fixed starting amount and per-unit change to an equation, then matches a table row with its graph point.
Watch for: A learner may reverse the variables, omit the starting value, or treat each table row as a separate rule.
Open a sample lesson: Writing Equations from Word Problems ↗Unit 08
Area and polygons
Visuals: Adjustable rectangles, parallelograms, triangles, trapezoids, coordinate-plane polygons, and split-or-subtract composite figures.
Ask: Which segment is the perpendicular height, and how could a cut or rearrangement make the area easier to see?
Listen for: The learner distinguishes base from slanted side and can show why the formula counts square units.
Watch for: A learner may use a slanted edge as height or add outside side lengths when the task asks for area.
Open a sample lesson: Area of Triangles ↗Unit 09
Nets, surface area, and volume
Visuals: Unfoldable nets for prisms and pyramids, face-by-face surface area, whole-cube layers, and fractional-edge unit prisms.
Ask: Are we covering the outside faces or filling the solid, and what unit should the answer use?
Listen for: The learner matches each net face to a solid face and explains volume as unit cubes or the product of three edge lengths.
Watch for: A learner may confuse square units with cubic units, count a hidden face incorrectly, or treat fractional edges as whole cubes.
Open a sample lesson: Volume with Fractional Edge Lengths ↗Unit 10
Statistics and data
Visuals: Editable data sets that update dot plots, a fractional-measurement line plot, mean and median, mean absolute deviation, histograms, box plots, and distribution summaries.
Ask: What changes if one value moves, and which feature of the distribution answers the question?
Listen for: The learner connects marks or intervals to data and describes center and spread with evidence, not only one statistic.
Watch for: A learner may treat a histogram bar as one observation, assume the mean must be a data value, or miss variability in a statistical question.
Open a sample lesson: Histograms ↗