180 Days of Math Connections

36 weeks · 180 short lessons · 5–10 minutes each

Number sense, proportional reasoning, financial decisions, algebra, geometry and data. Open a week to teach its five daily prompts alongside your regular math lessons.

Teach it in 5–10 minutes

Notice (1 min): Invite a prediction. Model (2 min): Draw or think aloud. Try (3–5 min): Partners or whiteboards. Prove it (1 min): Ask for an answer and a reason.

Revisit an older idea each Friday. Money examples use fictional amounts and stated rates.

01 · Number sense

Week 1 · Numbers tell a story

Weekly concept: Numbers tell a story

  1. Day 1: Ask “12 what?” Model students vs minutes; students invent two meanings for 25; check why a bare number is incomplete.
  2. Day 2: Circle distance and time in “40 miles in 1 hour”; students label a price story; check units.
  3. Day 3: Compare $6 for 2 items with $8 for 4; try $9 for 3 vs $10 for 5; check price per item.
  4. Day 4: Show 3 of 4 seats as words, picture, fraction; students represent 5 of 8 two ways.
  5. Day 5: Create two stories for 18÷3=6; students explain what 6 counts.

Friday reflection: I know my answer makes sense because…

Week 2 · Estimate and check

Weekly concept: Estimate and check

  1. Day 6: Estimate 49+31 using 50+30; try 198+403; check near 600.
  2. Day 7: Estimate 803−397 with 800−400; try 59.8−19.7; check near 40.
  3. Day 8: Estimate 19×6 with 20×6; try 298÷6; reject an answer of 500.
  4. Day 9: Spot the error in $3.90+$5.10=$90; give a sensible range.
  5. Day 10: How many $4 tickets can $19 buy? Estimate, compute, and explain the whole-number result.

Friday reflection: I know my answer makes sense because…

Week 3 · Place value still matters

Weekly concept: Place value still matters

  1. Day 11: Compare 40,500 and 405,000; identify value of the 5 in each.
  2. Day 12: Show 0.7=0.70>0.68; compare 2.09 and 2.1; explain digit count.
  3. Day 13: Model 4.2×10=42; try 0.36×100 and 36÷100; describe digit values.
  4. Day 14: Model $3.50+$2.75; try $10−$6.85; estimate to check.
  5. Day 15: Correct 2.4+0.38=0.62 with a place-value chart; explain why result exceeds 2.

Friday reflection: I know my answer makes sense because…

Week 4 · Fractions are numbers

Weekly concept: Fractions are numbers

  1. Day 16: Mark 0, 1/2, 1; place 1/4 and 3/4; explain positions.
  2. Day 17: Use eighths to compare 5/8 to half; try 3/7 against half.
  3. Day 18: Shade 1/2 and 2/4 on equal wholes; rename 3/6; explain equivalence.
  4. Day 19: Compare 2/3 and 3/4 with models; try 3/5 and 2/3; justify.
  5. Day 20: Draw equal-size wholes for 4/9 and 4/7; explain larger piece size.

Friday reflection: I know my answer makes sense because…

Week 5 · Fractions decimals and percents connect

Weekly concept: Fractions decimals and percents connect

  1. Day 21: Shade half a hundred grid: 1/2=0.5=50%; show 1/4 three ways.
  2. Day 22: Match 1/2, 1/4, 3/4, 1/10 with decimals and percents; explain one.
  3. Day 23: Show 3/4=3÷4=0.75; students convert 1/8 by division.
  4. Day 24: Order 0.6, 55%, 2/3 on a number line and explain closest pair.
  5. Day 25: Create a fraction-decimal-percent guide; partner checks equal values.

Friday reflection: I know my answer makes sense because…

Week 6 · Operations have meaning

Weekly concept: Operations have meaning

  1. Day 26: Model 7 students joining 5; invent a story for 7+5; label total.
  2. Day 27: Compare 14-mile and 9-mile routes; find the difference; explain subtraction.
  3. Day 28: Draw four groups of three, then double a recipe; explain two multiplications.
  4. Day 29: Share 12 stickers among 3, then make groups of 3; explain 4 in both.
  5. Day 30: Sketch a word problem before computing; choose and defend an operation.

Friday reflection: I know my answer makes sense because…

Week 7 · Multiplication changes size

Weekly concept: Multiplication changes size

  1. Day 31: Show 8×1.5 as 8 plus half of 8; try 10×1.5; predict size.
  2. Day 32: Compare 8×1, 8×0.5, 8×2; explain the role of 1.
  3. Day 33: Draw 3/4 of a 12-cup batch; find 3/4 of 20; check smaller.
  4. Day 34: Predict size for 18×0.8, 18×1, 18×1.2; calculate to verify.
  5. Day 35: Give counterexamples to “multiplication always makes bigger”; rewrite claim.

Friday reflection: I know my answer makes sense because…

Week 8 · Division reveals relationships

Weekly concept: Division reveals relationships

  1. Day 36: Share 15 counters among 5, then form groups of 5; explain 3 twice.
  2. Day 37: Ask “6 times what equals 42?”; try 3.6÷0.6; multiply to check.
  3. Day 38: Count quarter-cups in 2 cups; try half-cups in 3; label scoops.
  4. Day 39: Share $10 among 4; try $9 among 4; check by multiplication.
  5. Day 40: Match 12÷3 and 3÷12 to stories; explain why order matters.

Friday reflection: I know my answer makes sense because…

Week 9 · Fluency through strategy

Weekly concept: Fluency through strategy

  1. Day 41: Break 18×5 into 10×5 and 8×5; try 17×6.
  2. Day 42: Use known facts for 48÷6; try 360÷9; explain shortcut.
  3. Day 43: Show 7(20+3); try 6(30−1); explain distribution.
  4. Day 44: Compare two strategies for 25×16; show both yield 400.
  5. Day 45: Choose mental, drawing, written, or calculator check for four calculations; defend.

Friday reflection: I know my answer makes sense because…

02 · Change and proportional reasoning

Week 10 · Negative numbers describe position

Weekly concept: Negative numbers describe position

  1. Day 46: Draw −5 to 5; place −3 and 2; compare positions.
  2. Day 47: Pair opposites 4 and −4; find opposite of −7; explain distance.
  3. Day 48: Compare −2 and −8 as temperatures; order −6, 0, −1.
  4. Day 49: Show absolute value of −5 as distance 5; compare distances of −9 and 4.
  5. Day 50: Plot elevations −20 and 15 around sea level; find distance 35.

Friday reflection: I know my answer makes sense because…

Week 11 · Negative numbers describe change

Weekly concept: Negative numbers describe change

  1. Day 51: Start at −2, move 5 right; model 3+(−6); explain endpoint.
  2. Day 52: Find distance from −4 to 3; explain positive distance.
  3. Day 53: Compare 4−7 and 4+(−7) on a line; explain same endpoint.
  4. Day 54: Fictional $5 balance and $9 purchase; interpret −$4 in words.
  5. Day 55: Track three temperature changes; narrate the final value.

Friday reflection: I know my answer makes sense because…

Week 12 · Signed multiplication and division

Weekly concept: Signed multiplication and division

  1. Day 56: Extend 3×3, 3×2, 3×1, 3×0, 3×(−1); predict next.
  2. Day 57: Interpret (−4)×3 as three negative changes; try (−2)×5.
  3. Day 58: Find number times −3 equals 12; solve 12÷(−3); check.
  4. Day 59: Predict signs of (−8)(−4) and (−32)÷8; calculate and justify.
  5. Day 60: Find a sign error in a worked example; repair with multiplication check.

Friday reflection: I know my answer makes sense because…

Week 13 · Ratios compare quantities

Weekly concept: Ratios compare quantities

  1. Day 61: Draw 2 red, 3 blue; contrast red:blue 2:3 with red:total 2:5.
  2. Day 62: Tape diagram 2 juice to 3 water; draw equivalent 4:6.
  3. Day 63: Double both parts of 2:3; build three equivalent ratios.
  4. Day 64: Compare 2:3, 4:6, and 3:4 mixtures; identify matches with a model.
  5. Day 65: Make 15 cups of a 2:3 mixture: 6 juice and 9 water; check.

Friday reflection: I know my answer makes sense because…

Week 14 · Unit rates make comparisons fair

Weekly concept: Unit rates make comparisons fair

  1. Day 66: Find $6 for 3 notebooks = $2 each; try $12 for 4.
  2. Day 67: Compare 4 bars for $6 with 6 for $8; choose lower per-bar cost.
  3. Day 68: Compare 12 miles in 3 hours with 15 in 5; identify faster rate.
  4. Day 69: Label $9÷3 lb as $3/lb; explain units in another rate.
  5. Day 70: Choose between fictional packages using unit cost and amount needed.

Friday reflection: I know my answer makes sense because…

Week 15 · Proportional relationships scale

Weekly concept: Proportional relationships scale

  1. Day 71: Scale 2 tickets for $10 to 4 and 6 tickets; name factor.
  2. Day 72: Build ticket-cost table and fill missing pairs.
  3. Day 73: Find $5 per ticket; write c=5t and interpret 5.
  4. Day 74: Compare (1,5),(2,10) with (1,5),(2,7); choose proportional set.
  5. Day 75: Scale a 2-serving recipe to 7 servings using a ratio table.

Friday reflection: I know my answer makes sense because…

Week 16 · Graphs tell the same relationship

Weekly concept: Graphs tell the same relationship

  1. Day 76: Plot ticket-cost table; label axes and interpret a point.
  2. Day 77: Interpret origin as zero tickets, zero cost; contrast fixed fee.
  3. Day 78: Interpret (1,5) and (4,20) in the ticket story.
  4. Day 79: Compare a line through origin with a graph starting at $3 fee.
  5. Day 80: For $4 per item create story, table, graph, equation; identify rate.

Friday reflection: I know my answer makes sense because…

Week 17 · Percent is a comparison to 100

Weekly concept: Percent is a comparison to 100

  1. Day 81: Show 10%, 25%, 50% on grid; find each of 80.
  2. Day 82: Find 20% of $30 as two 10% parts; try 30% of $40.
  3. Day 83: If $12 is 25%, find $48 whole; if 10%=7, find whole.
  4. Day 84: Contrast 10% of 20 with 10% of 200; name the whole.
  5. Day 85: Solve 15% of 60 as 10%+5% and 0.15×60; explain 9.

Friday reflection: I know my answer makes sense because…

Week 18 · Percent changes real prices

Weekly concept: Percent changes real prices

  1. Day 86: Take 25% off $40; distinguish $10 savings from $30 price.
  2. Day 87: Use a stated sample 8% tax on $25; find $2 tax and $27 total.
  3. Day 88: Use a chosen 20% tip on $30; find $6 tip and $36 total.
  4. Day 89: Compare 30% off $50 with $12 off; calculate final prices.
  5. Day 90: Plan a fictional $60 purchase with discount and stated tax; verify.

Friday reflection: I know my answer makes sense because…

03 · Financial decisions and algebra

Week 19 · Needs wants and tradeoffs

Weekly concept: Needs wants and tradeoffs

  1. Day 91: Sort fictional expenses as needs, wants, depends; defend one.
  2. Day 92: Give two people different goals and same $20; explain priorities.
  3. Day 93: Choose affordable items under $20 from an over-budget list; prove.
  4. Day 94: Buying a $12 game delays a $12 book; identify the tradeoff.
  5. Day 95: Defend a choice with calculation, reason, and drawback.

Friday reflection: I know my answer makes sense because…

Week 20 · A budget is a plan

Weekly concept: A budget is a plan

  1. Day 96: Start with fictional $100; subtract stated expenses; explain remainder.
  2. Day 97: Sort recurring and changeable expenses; discuss planning.
  3. Day 98: Allocate fictional $60 among three goals; check sum ≤$60.
  4. Day 99: Add unexpected $8 expense; revise plan and name change.
  5. Day 100: Compare two balanced plans; defend one for a stated goal.

Friday reflection: I know my answer makes sense because…

Week 21 · Saving connects goals and time

Weekly concept: Saving connects goals and time

  1. Day 101: Set fictional $48 goal and current savings; find remaining gap.
  2. Day 102: Save $48 in 8 weeks: $6/week; try a 6-week plan.
  3. Day 103: Table $6 per week; find week-five total and connect to 6w.
  4. Day 104: Pause saving for one week; revise schedule and check goal.
  5. Day 105: Present goal, timeline, weekly amount, adjustment; partner checks.

Friday reflection: I know my answer makes sense because…

Week 22 · Compare the full cost

Weekly concept: Compare the full cost

  1. Day 106: Compare 3 for $9 with 5 for $12 using unit prices.
  2. Day 107: Add stated $4 fee to $16 offer; compare all-in $19.
  3. Day 108: Compare $8/month for 6 months with $45 one-time price.
  4. Day 109: Read an offer with quantity limit; identify which price applies.
  5. Day 110: Recommend option for stated need and budget using final cost.

Friday reflection: I know my answer makes sense because…

Week 23 · Earned money has limits

Weekly concept: Earned money has limits

  1. Day 111: Find 4 hours at $12/hour; try 6 hours; label dollars.
  2. Day 112: Compare 5 hours at $10 with 4 at $13; total both.
  3. Day 113: Fictional $100 gross minus stated $15 deductions = $85 take-home.
  4. Day 114: Plan expenses from take-home pay rather than gross amount.
  5. Day 115: Track two-week earnings; decide when a purchase is affordable.

Friday reflection: I know my answer makes sense because…

Week 24 · Borrowing has a cost

Weekly concept: Borrowing has a cost

  1. Day 116: Borrow fictional $50, repay $55; identify $5 extra.
  2. Day 117: Simple interest: $100 at 5% for one year means $5 interest.
  3. Day 118: Compare two stated repayment offers; total every payment.
  4. Day 119: Compare $12/month for 12 months ($144) with $120 once.
  5. Day 120: Compare saving with stated borrowing offer by cost and timing.

Friday reflection: I know my answer makes sense because…

Week 25 · Patterns become expressions

Weekly concept: Patterns become expressions

  1. Day 121: Draw pattern growing by 3 tiles each stage; predict later count.
  2. Day 122: Let b be marbles per bag; write 3b for three bags.
  3. Day 123: Model $4 entry plus $3 per game as 4+3g; create similar expression.
  4. Day 124: Evaluate 4+3g when g=5; interpret $19 in the story.
  5. Day 125: Show three groups of g+2 as 3g+6; test at g=4.

Friday reflection: I know my answer makes sense because…

Week 26 · Equations preserve balance

Weekly concept: Equations preserve balance

  1. Day 126: Draw x+3=8 as balanced sides; remove 3 from both and check.
  2. Day 127: Solve x−7=12 and x+9=15 using inverse operations.
  3. Day 128: Four boxes total 28 means 4x=28; also solve x/3=5.
  4. Day 129: Undo +2 then ×3 in 3x+2=17; try 2x+5=19.
  5. Day 130: Story: $5 entry + $2 per game totals $17; solve and check.

Friday reflection: I know my answer makes sense because…

Week 27 · Inequalities describe limits

Weekly concept: Inequalities describe limits

  1. Day 131: Translate “at most $20” and “at least 12”; test equality.
  2. Day 132: Graph x≥4 versus x<7; explain open and closed circles.
  3. Day 133: With $30 and $5 tickets, write 5t≤30; find maximum.
  4. Day 134: Test 5, 6, 7 tickets in 5t≤30; show substitutions.
  5. Day 135: Explain why “no more than $30” includes exactly $30.

Friday reflection: I know my answer makes sense because…

04 · Geometry, data and application

Week 28 · Units prevent mistakes

Weekly concept: Units prevent mistakes

  1. Day 136: Choose centimeters for pencil, kilometers for trip; defend.
  2. Day 137: Use 100 cm=1 m; convert 250 cm and 0.7 m.
  3. Day 138: Show 12 miles÷3 hours=4 miles/hour; label another rate.
  4. Day 139: Match rectangle edge, surface, box capacity to length, area, volume.
  5. Day 140: Correct garden area “24 feet” to 24 square feet; explain.

Friday reflection: I know my answer makes sense because…

Week 29 · Geometry solves practical problems

Weekly concept: Geometry solves practical problems

  1. Day 141: Trace boundary of 4-by-6-foot garden; find 20 feet of fencing.
  2. Day 142: Cover same garden; find 24 square feet of surface.
  3. Day 143: Split L-shaped floor into rectangles; sum without overlap.
  4. Day 144: For 24 square feet sold in 5-square-foot packs, buy five packs.
  5. Day 145: Find trim and flooring for a room separately; label units.

Friday reflection: I know my answer makes sense because…

Week 30 · Circles have relationships

Weekly concept: Circles have relationships

  1. Day 146: Mark center, radius, diameter; radius 4 cm means diameter 8 cm.
  2. Day 147: Measure around and across circles; compare circumference÷diameter.
  3. Day 148: For diameter 10 cm, estimate above 30, then calculate 10π cm.
  4. Day 149: For radius 3 cm, calculate area 9π square centimeters.
  5. Day 150: Choose circumference for path, area for tabletop; solve one.

Friday reflection: I know my answer makes sense because…

Week 31 · Scale drawings represent reality

Weekly concept: Scale drawings represent reality

  1. Day 151: At scale 1 cm:2 m, 3 cm represents 6 m.
  2. Day 152: At same scale, 5 cm represents 10 m; try another.
  3. Day 153: Draw 8-by-6-m room as 4-by-3-cm rectangle.
  4. Day 154: Spot one incorrectly scaled side; repair consistently.
  5. Day 155: Fit two furnishings on a scaled classroom sketch by dimensions.

Friday reflection: I know my answer makes sense because…

Week 32 · Data describes a group

Weekly concept: Data describes a group

  1. Day 156: Ask whether reading minutes vary; frame a statistical question.
  2. Day 157: Collect reading minutes with units, or use fictional data.
  3. Day 158: Make dot plot, include every observation, read a fact.
  4. Day 159: Compare two datasets using median and range; explain both.
  5. Day 160: Write “In this sample…” claim supported by a number.

Friday reflection: I know my answer makes sense because…

Week 33 · Samples can mislead

Weekly concept: Samples can mislead

  1. Day 161: Define whole seventh grade as population and selected students as sample.
  2. Day 162: Critique favorite-sport survey of only basketball players.
  3. Day 163: Compare first ten at lunch with random selection across classes.
  4. Day 164: Take two small random counter samples; discuss variation.
  5. Day 165: Critique “8 of 10 surveyed prefer X, so 80% of school does.”

Friday reflection: I know my answer makes sense because…

Week 34 · Probability measures uncertainty

Weekly concept: Probability measures uncertainty

  1. Day 166: Place certain, likely, unlikely, impossible on likelihood line.
  2. Day 167: Bag 3 red and 2 blue: probability red = 3/5.
  3. Day 168: Simulate 20 draws with replacement; tally reds.
  4. Day 169: Compare experimental red fraction with theoretical 3/5.
  5. Day 170: Compare supplied 5-trial and 100-trial results; explain variation.

Friday reflection: I know my answer makes sense because…

Week 35 · Math helps evaluate claims

Weekly concept: Math helps evaluate claims

  1. Day 171: Correct false “50% off $40 saves $25” to $20 savings.
  2. Day 172: Compare identical data graphed with different vertical scales.
  3. Day 173: Ask starting and ending quantities for “Sales doubled.”
  4. Day 174: Check a claim against a data table and quote relevant numbers.
  5. Day 175: Rewrite exaggerated claim naming sample group and time.

Friday reflection: I know my answer makes sense because…

Week 36 · Apply and explain what you know

Weekly concept: Apply and explain what you know

  1. Day 176: Choose supplies for fictional class event under budget; total.
  2. Day 177: Compare packages with unit rates and a stated discount.
  3. Day 178: Make cost-versus-participants table or graph; label and interpret.
  4. Day 179: Revise for smaller budget or more participants; prove constraints.
  5. Day 180: Present choice, calculation, and check in one minute.

Friday reflection: I know my answer makes sense because…