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…

Help with Seventh grade math connections

Seventh grade math connections: a useful next step

Seventh grade math connections work best when students connect a short prompt to a model, a strategy, and an explanation. Use these daily lessons alongside your regular instruction to revisit useful ideas over time.

Choose a purposeful prompt

Open a week that connects to your current learning goal or an earlier skill students need to retrieve. Read the daily prompt before class and decide what evidence would show understanding. Prepare a quick diagram, table, or worked example when it will help students make sense of the situation.

Keep the routine focused

Invite a prediction, model the important relationship, and give students time to try. Ask for an answer and a reason. Encourage them to label units, compare strategies, and check whether the result makes sense in the original situation. A short conversation about the reasoning is more useful than rushing through several unrelated prompts.

Revisit and extend

Use student explanations to decide what to practice next. Return to an earlier representation when a misconception appears, or change one number to test whether a strategy still works. Financial examples use fictional amounts and stated rates. Adapt the context to your lesson while keeping the mathematical relationship clear.

Explore interactive math pathways →