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Enhanced Mathematics
Interactive Activity Map · Grades 3–10
Prepared 11 November 2026 • Redgem Edutech / SPSTEM
Planning map — proposed activities. Activity titles, interactions, and exit tasks are proposed adaptations. Grades 4–10 follow the grade/term placement and numbered items in the retrieved Enhanced Mathematics guide. Each activity covers a cluster of competencies; a model supports instruction but does not by itself demonstrate every skill in the cluster.
Week assignments: pending. The source guide is term-based and does not assign weeks. Source item numbers below are competency numbers, not week numbers. Grade 3 is provisional because the retrieved enhanced guide contains tables for Grades 4–10 only.
Wording: The activity titles summarize competency clusters; they are not replacements for official competency wording. The source reference identifies the exact grade, term, and numbered items to retain when developing individual lessons.
Source: 2-SPSTEM-Enhanced-Math-Grades-4-10.pdf, retrieved 11 November 2026. References below use the guide’s visible competency numbering. No official validation or approval is claimed.
Grade 3 · Provisional foundation activities
No Grade 3 Enhanced Mathematics competency table was located. These six activities are candidate designs only: grade alignment, exact competency wording, term, and week require the Grade 3 curriculum/BOW. Regular Grade 3 exemplars were located, but their quarter/week labels must not be assumed to be the enhanced three-term sequence.
| Activity | Interaction | Exit evidence | Status |
|---|
| Fraction Studio | Tap equal pieces of a constant-sized whole and name the selected fraction. | Show 2 of 6 equal parts and explain the numerator and denominator. | Existing preview; alignment pending |
| Place-Value Builder | Group objects into ones, tens, hundreds, and larger places only after source limits are confirmed. | Build a number and explain the value of one digit. | Proposed; alignment pending |
| Multiplication and Sharing Arrays | Arrange equal rows and redistribute objects into equal groups. | Explain how an array represents multiplication and division. | Proposed; alignment pending |
| Measure and Compare | Align a virtual ruler correctly and compare lengths using specified units. | Explain why measuring must begin at zero or account for an offset. | Proposed; alignment pending |
| Shape and Perimeter Builder | Join sides, identify shapes, and trace the outside boundary. | Find a boundary length and explain which edges count. | Proposed; alignment pending |
| Data Picture Board | Sort class objects and construct a simple pictorial/bar display. | Compare two categories using evidence from the display. | Proposed; alignment pending |
Grade 4
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–2 | Angle Explorer | Rotate two rays and position a protractor to draw and measure right, acute, and obtuse angles. | Draw 125° and explain its classification. |
| 3–5 | Triangle and Quadrilateral Sorter | Drag vertices; inspect sides, angles, and diagonals; sort figures by their properties. | Explain why a square also belongs to the rectangle family. |
| 6–7 | Composite Fence Builder | Join triangles and quadrilaterals; trace only the outside boundary and total its length. | Explain why an internal shared edge is not part of the perimeter. |
| 8–13 | Million Place-Value Lab | Build six-digit numbers with place-value disks; compare, round, estimate, and regroup for addition/subtraction. | Show the value of 7 in 472,316 and round to the nearest hundred thousand. |
| 14–18 | Market Operations Lab | Change item quantities and prices; use area arrays and sharing models for multiplication/division and check estimates. | Solve a purchase-and-change problem and justify an estimate. |
| 19–21 | Number Sentence Workshop | Arrange operation cards and evaluate expressions using MDAS, including left-to-right equal-precedence operations. | Build two expressions equal to 24 and explain their evaluation order. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–3 | Measurement and Time Converter | Move linked unit scales and clock hands; compare length, mass, capacity, and elapsed time. | Convert 2.5 L to milliliters and find elapsed time from 9:35 to 11:10. |
| 4–8 | Fraction Number-Line Kitchen | Partition equal wholes; convert improper fractions and mixed numbers; combine or remove like-denominator pieces. | Model 1 1/4 + 2/4 and explain the result. |
| 9–13 | Equivalent Fraction Studio | Overlay equal-sized fraction strips; subdivide without changing shaded quantity; compare and order unlike fractions. | Show why 2/3 and 4/6 are equal. |
| 14–16 | Factor and Multiple Machine | Build arrays, highlight multiples up to 100, and use common factors to simplify fraction models. | Reduce 12/18 and justify the common factor used. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–3 | Unlike-Fraction Builder | Choose equal wholes, create common partitions, and add or subtract fractions and mixed numbers. | Model 1/2 + 1/3 and explain why adding denominators is incorrect. |
| 4–6 | Mirror and Glide Studio | Move a mirror line; complete reflected figures, then translate a reflection along the line. | Complete a symmetric figure and explain equal distances from its axis. |
| 7–10 | Class Data Timeline | Enter time-based observations; switch between a table and a single line graph and pose questions. | Identify the greatest increase and support the answer with two values. |
| 11–12,20 | Pattern and Equality Machine | Extend simple patterns and balance equivalent number sentences with missing values. | Find the missing number in 4 + __ = 6 + 3 and explain. |
| 13–20 | Decimal Grid and Number Line | Shade tenths/hundredths; connect decimals to fractions; compare, order, and round. | Show 0.75 as a fraction and place it between 0.7 and 0.8. |
Grade 5
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–5 | Clock and World-Time Planner | Move 12/24-hour clocks and compare specified time-zone offsets with Philippine time. | Convert 18:45 to 12-hour time and explain a date change across zones. |
| 6 | GMDAS Expression Lab | Group number cards and highlight the next valid operation. | Explain why 6 + 2 × (5 − 1) equals 14. |
| 7–8,12–13 | Fraction Product and Quotient Lab | Overlay fraction areas and count how many fractional groups fit in a quantity. | Use a model to explain 3/4 ÷ 1/4. |
| 9–11 | Area Cut-and-Rearrange Lab | Move heights and rearrange triangles, parallelograms, and trapezoids into equal-area figures. | Explain why a slanted side is not always the height. |
| 14–15 | Decimal Place-Value Zoom | Build decimal numbers through ten-thousandths and expand their place values. | Explain the value of 6 in 2.0364. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–4 | Decimal Compare and Calculate | Link decimal grids, fraction forms, number lines, and regrouping for addition/subtraction. | Explain 2.305 − 0.78 using place values. |
| 5–6 | Prime Sieve and Divisibility Lab | Cross out composite numbers and test divisibility with digit patterns and factor arrays. | Explain why 1 is neither prime nor composite. |
| 7–12 | Two-Series Data Studio | Collect paired categories/time series; build double bar or double line graphs and compare trends. | Choose a suitable graph and write a conclusion supported by the data. |
| 13–14 | Fair Chance Explorer | List equally likely outcomes for fair dice, coins, or equal spinner sectors and count favorable outcomes. | Find the probability of an even number on a fair six-sided die. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–7 | Decimal Shop and Sharing Lab | Model decimal multiplication and division, estimate results, and apply GMDAS to a shopping situation. | Explain why multiplying a positive number by 0.5 makes it smaller. |
| 8–14 | Solid and Net Workshop | Rotate prisms/pyramids, unfold nets, label faces/edges/vertices, and sum face areas. | Choose a valid net and explain how it gives surface area. |
| 15–16 | Cube Packing Preview | Fill cubes and rectangular prisms with equal non-standard cubes and compare counts. | Explain why equal-sized units are needed to compare volumes. |
| 17–18 | Turn and Match Studio | Rotate figures clockwise/counterclockwise and count matching orientations within one turn. | Find the order of rotational symmetry of a square. |
Grade 6
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–3 | Tessellation and Transformation Designer | Tile a plane and apply translations, reflections, rotations, and combinations. | Explain why a tiling has neither gaps nor overlaps. |
| 4–10 | Decimal Scale and Operation Lab | Shift place values by powers of ten and model decimal arithmetic, including repeating quotients. | Explain the difference between multiplying by 100 and by 0.01. |
| 11–13 | Mixed-Number Recipe Lab | Resize ingredient quantities using fractions, mixed numbers, and combined operations. | Find the amount needed for 1 1/2 batches of a recipe using 2/3 cup each. |
| 14–16 | Ratio Mixer | Drag colored counters to compare part-part and part-whole ratios and scale equivalent mixtures. | For 2 red and 3 blue counters, state red:blue and red:all. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–4 | Proportion Workbench | Link ratio tables and double number lines; change direct/inverse/partitive scenarios. | Explain why doubling workers halves time only when total work and equal work rates are fixed. |
| 5–8 | Percent–Fraction–Decimal Bridge | Shade a hundred grid and align equivalent values on one number line. | Represent 35% as a fraction and decimal and compare it with 1/3. |
| 9–11 | Exponent and GEMDAS Builder | Expand powers as repeated multiplication and step through operation order. | Explain the difference between 3² and 3 × 2. |
| 12–17 | Volume and Capacity Tank Lab | Build cuboid tanks from unit cubes, adjust dimensions, and link cubic centimeters with liters. | Find the capacity of a 10 cm × 10 cm × 20 cm tank in liters. |
| 18–20 | Composite Garden Designer | Split a garden into triangles and quadrilaterals; track area, perimeter, and square-unit conversion. | Explain why multiplying lengths by 100 changes square units by 10,000. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–9 | Circle Measure and Area Lab | Adjust radius, unwrap circumference, rearrange sectors, and combine circular regions. | Predict what happens to circumference and area when radius doubles. |
| 10–15 | Pie-Graph Studio | Change category counts; connect frequencies, percentages, and central angles. | Explain why 25% corresponds to 90° in a pie graph. |
| 16–18 | GCF and LCM Organizer | Compare factor trees, listings, and continuous division with grouping/scheduling contexts. | Choose GCF or LCM for packing identical kits and justify the choice. |
Grade 7
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–7 | Polygon and Angle Lab | Drag polygon vertices, classify shapes, measure angle pairs, and vary regular-polygon side counts. | Explain the relationship between an interior angle and its adjacent exterior angle. |
| 8–10 | Percent Budget Planner | Change discounts, commissions, tax, and simple-interest assumptions in a simulated budget. | Explain why a 20% increase followed by a 20% decrease does not restore the original amount. |
| 11–12 | Rate and Journey Lab | Adjust distance, travel time, and speed and compare linked tables. | Compare two journeys using a common unit of speed. |
| 13–15 | Rational Number Bridge | Link fraction, decimal, percent, number-line, and operation representations. | Order −0.5, 1/4, and 20% and justify the order. |
| 16–17 | Roots and Real-Number Explorer | Build square/cube arrays and bracket irrational roots between known integer values. | Locate √10 between consecutive integers and explain. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–2 | Unit and Currency Converter | Change measurement units and use an explicitly supplied sample exchange rate. | Convert a sample currency amount and state the rate used; do not treat it as a live rate. |
| 3–8 | Cylinder and Pyramid Fill Lab | Compare solids with equal base area and height; fill a prism/cylinder/pyramid and connect volume formulas. | Explain the one-third relationship for a pyramid and matching prism. |
| 9–12 | Venn Set Studio | Drag objects into two or three sets; toggle union, intersection, complement, and difference. | Shade A minus B and explain which objects are excluded. |
| 13–17,22–25 | Integer and Real-Number Map | Locate signed values and sort numbers into nested real-number subsets. | Explain why every integer is rational but not every rational number is an integer. |
| 18–21 | Sampling and Data Display Lab | Choose samples from a modeled population; organize frequencies and select suitable charts. | Compare a convenience sample and a random sample and identify a possible bias. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–5 | Integer Chips and Number-Line Lab | Cancel zero pairs, move on a signed number line, and connect multiplication/division and absolute value. | Explain −3 − 2 and distinguish it from the distance between −3 and 2. |
| 6–10,12–15 | Equation Balance Workshop | Move equal operations on both sides; use bar models, substitution, and formula rearrangement. | Solve 3x + 2 = 14 and justify each equality-preserving step. |
| 11 | Changing Quantities Machine | Change an input and inspect patterns, a table, and a simple coordinate plot. | Describe how the output changes when the input increases by one. |
| 16–18 | Experimental Outcomes Lab | Run coin/die trials, retain trial counts, and build tables and graphs. | Describe an observed pattern without claiming the next random result is guaranteed. |
| 19–20 | Scientific Notation Zoom | Move between decimal and scientific notation and combine scales using operations. | Explain why 4.2 × 10⁻³ is less than 1. |
Grade 8
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–2 | Mean–Median–Mode Data Lab | Drag data values and observe the effects of outliers on central tendency. | Choose a representative measure for a skewed dataset and justify it. |
| 3–9 | Algebra Tiles and Factoring Lab | Build expressions, combine like terms, multiply area models, and factor with tiles or symbolic extensions. | Explain (x + 3)(x + 2) with an area model and verify expansion. |
| 10–12 | Rational Algebra Lab | Link factor cancellation to algebraic forms and display excluded denominator values. | Simplify an expression and state why a canceled denominator still restricts the original domain. |
| 13–21,23 | Arithmetic and Geometric Sequence Explorer | Adjust first term, common difference, and ratio; connect terms, sums where specified, equations, and discrete graphs. | Explain how changing common difference differs from changing common ratio. |
| 22,24 | Coordinate Distance and Midpoint Lab | Drag points on a grid and reveal horizontal/vertical changes, distance, and midpoint. | Find and verify the midpoint of (−2, 4) and (6, 0). |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–6,8 | Pyramid, Cone, and Sphere Volume Lab | Compare matched solids, change dimensions, and apply volume formulas with right-triangle measurements. | Compare a cone and cylinder with the same base radius and height. |
| 7,9–10 (MG) | Right-Triangle and Triangle-Inequality Lab | Change side lengths; test existence of a triangle and classify it using squares of side lengths. | Explain why lengths 2, 3, and 6 cannot form a triangle. |
| 10–13 (NA) | Linear Equation and Inequality Balance | Apply operations to equations/inequalities and shade their number-line solutions. | Explain why dividing an inequality by a negative number reverses its sign. |
| 14–19 | Slope and Line Studio | Drag two points or change slope/intercept; compare equations, tables, and parallel/perpendicular lines. | Predict the graph change from y = 2x + 1 to y = 2x − 3. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–5 | Two-Line Systems Lab | Adjust two equations to show one, zero, or infinitely many solutions; connect graphing to algebra. | Explain why parallel distinct lines have no common solution. |
| 6 | Three-Variable Systems Lab | Use linked equations, elimination steps, and optional plane views. | Verify a proposed ordered triple in all three equations. |
| 7–8 | Feasible Region and Optimization Lab | Drag constraint lines, shade valid regions, and compare objective values at vertices. | Choose an optimal feasible point and explain the constraints it satisfies. |
| 9–12 | Scatterplot and Regression Lab | Move data points; inspect correlation, ranks, fitted line, and predictions. | Explain why a strong correlation does not establish causation. |
| 13–15 | Data Spread and Graph Critique | Compare datasets with equal means, calculate variability, and inspect axis choices. | Explain how two datasets can have the same mean but different spread. |
| 16–22 | Probability and Sample-Space Lab | Build tree diagrams; run trials; compare theory with experiment and explore unions, intersections, complements, and conditions. | Explain why conditional probability uses a restricted sample space. |
Grade 9
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–4,12 | Parallel-Line and Transversal Lab | Construct lines and drag a transversal; compare corresponding and supplementary angles. | Justify a missing angle using a named angle relationship. |
| 5–11 | Function Input–Output Studio | Switch among mappings, equations, tables, and graphs; inspect domain, range, and linear rates. | Decide whether a relation is a function and explain why. |
| 13–18 | Quadrilateral Property Lab | Drag constrained quadrilaterals, measure diagonals and angles, and support coordinate proofs. | Explain which additional property makes a parallelogram a rectangle. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–5 | Logic and Proof Builder | Sort hypothesis/conclusion cards and form converse, inverse, and contrapositive statements. | Give a counterexample to a false converse. |
| 6–9 | Triangle Congruence Construction Lab | Lock selected sides/angles, construct triangles and centers, and assemble two-column proof steps. | Explain why matching two angles alone does not establish congruence. |
| 10–18 | Quadratic Transformation Studio | Adjust a, h, and k; connect standard/vertex forms, vertex, axis, roots, direction, and intervals. | Explain the effect of changing h in y = a(x − h)² + k. |
| 19–21 | Quadratic Roots and Equation Lab | Link graph intersections with factoring, square-root extraction, and quadratic-formula steps. | Solve x² − 5x + 6 = 0 and verify both roots. |
| 22–25 | Position and Box-Plot Lab | Sort data, move values, and connect quartiles, percentiles, IQR, and cumulative displays. | Interpret a percentile rank without confusing it with percent correct. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–4 | Similarity and Pythagorean Reasoning Lab | Dilate polygons, compare corresponding ratios, and build a similarity-based proof. | Explain why similar triangles need not be congruent. |
| 5–10 | Right-Triangle Trigonometry Lab | Adjust right triangles and model elevation/depression measurements using sine, cosine, and tangent. | Choose a ratio for an inaccessible height and justify the selected sides. |
| 11–13 | Direct and Inverse Variation Lab | Move linked quantities and compare tables, equations, and graphs. | Distinguish constant ratio from constant product. |
| 14–20 | Statistical Position and Media Critique | Compare box plots and cumulative distributions; inspect outliers and misleading displays. | Challenge a claim using the data, scale, and representativeness of its sample. |
Grade 10
First Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–4 | Radicals and Rational Exponents Lab | Connect powers and roots, simplify expressions, and check candidate equation solutions. | Explain why a solution obtained by squaring must be checked in the original equation. |
| 5–7 | Inverse Function Mirror | Reflect one-to-one graphs across y = x and swap ordered pairs with domain restrictions. | Explain why a function must be one-to-one to have an inverse function on its domain. |
| 8–13 | Exponential and Logarithmic Explorer | Change base and parameters; link inverse graphs, domain/range, equations, and contextual models. | Explain the relationship between 2³ = 8 and log₂8 = 3. |
| 14–17 | Interest and Depreciation Simulator | Compare simple/compound growth and depreciation under user-supplied classroom rates and periods. | Explain why equal nominal rates can give different totals with different compounding periods. |
Second Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1 | Absolute Value Distance Lab | Move reference points and distance thresholds and display solution sets in several notations. | Solve |x − 3| = 2 using distance on a number line. |
| 2–6 | Inequality Sign and Region Lab | Move roots/poles; inspect sign intervals, open/closed endpoints, and shaded quadratic regions. | Explain why an undefined denominator value cannot belong to a solution set. |
| 7–13 | Polynomial Roots and Graph Lab | Set roots, degree, multiplicity, and leading coefficient; connect division/theorems with graph features. | Predict whether a graph crosses or touches the axis at a repeated root and verify. |
| 14–16 | Rational Function and Rate Lab | Change numerator/denominator; display zeros, excluded values, holes, asymptotes, and contextual solutions. | Explain the difference between a vertical asymptote and a removable hole. |
Third Term
| Source items | Competency cluster / proposed activity | Student interaction | Exit task / evidence |
|---|
| 1–5 | Circle Equation Studio | Move center/radius, switch equation forms, and construct a circle through three non-collinear points. | Determine center and radius from a circle equation and verify a point. |
| 6–8 | Line–Parabola–Circle Intersection Lab | Move curves and connect intersections with algebraic solutions and contextual constraints. | Predict and verify the number of intersections of a line and a circle. |
| 9–12 | Circle Theorem Investigation Lab | Drag chords, secants, tangents, and inscribed vertices; measure relationships and build proof steps. | State a conjecture and support it with a theorem-based argument, not measurement alone. |
| 13–14 | Sector and Segment Designer | Adjust radius and central angle in a circular garden and compare sector/segment areas. | Explain which triangle area is subtracted from a sector to obtain a minor segment. |
| 15–16 | Oblique Triangle Solver | Vary known sides/angles and inspect sine/cosine laws, including zero/one/two-triangle SSA cases. | Explain why an SSA case can have two valid solutions. |
| 17–18 | Bearing and Coordinate Transformation Lab | Set bearings clockwise from north and apply translations, reflections, and rotations on a coordinate map. | Describe a rotation using center, direction, angle, and resulting coordinates. |
Implementation and alignment notes
- Preserve exact source wording: each future activity page should display the relevant competency verbatim, separately from the learner-friendly target and original activity instructions.
- Learning sequence: predict → manipulate → record → explain → apply → exit task. Require an explanation or worked solution; automatic correctness alone is insufficient.
- Visual approach: use realistic familiar objects for contexts (measuring tools, containers, coins, gardens) while keeping equal partitions, scales, coordinates, and geometric relationships mathematically exact. Decorative perspective must not distort measurement.
- Accessible interactions: provide numeric inputs and buttons alongside dragging, keyboard operation, readable labels, and information beyond color alone.
- Construction and proof: a digital model supports conjecture; pair it with compass/protractor practice or written reasoning where the competency requires construction or proof.
- Probability: clearly identify fair/equally likely models; retain trial counts and avoid implying a short-run frequency must match theoretical probability.
- Money and clocks: use classroom sample exchange/interest rates, not claimed live rates. Time-zone activities should state date and offset assumptions.
- Units: use correct squared/cubed units. Do not teach weeks-to-months as one fixed conversion for calendar dates; state an approximation or use an actual calendar.
Source issues to retain for review
| Location | Issue | Handling |
|---|
| Grade 8, Second Term | Item 10 appears in both geometry and algebra sequences. | References distinguish 10 (MG) and 10 (NA). |
| Grade 7, Second Term | Integer competencies recur at items 13–16 and 22–25. | One activity links to both sets; do not count them as different required simulations. |
| Grade 9, Second/Third Terms | Measures of position recur; Second Term quadratic graph properties have irregular numbering at 14–15. | Retain source ranges; use a shared statistics model with term-specific tasks. Verify exact wording before student-page publication. |
| Performance standards | Some term standards use “quarter” or cover topics positioned elsewhere in competency tables. | Map this catalog to competency tables; flag standards for editorial reconciliation without silently rewriting them. |
Recommended first build in each grade
Grade 3: refine Fraction Studio after source confirmation. Grade 4: Equivalent Fraction Studio. Grade 5: Area Cut-and-Rearrange Lab. Grade 6: Ratio Mixer. Grade 7: Integer Chips and Equation Balance. Grade 8: Slope and Line Studio. Grade 9: Quadratic Transformation Studio. Grade 10: Circle Equation Studio.
Remaining source need: Grade 3 Enhanced Mathematics guide and the approved weekly BOW for Grades 3–10. These are needed to finalize Grade 3 alignment and week placement. Activity implementation status is shown in the Mathematics catalog.