Measure elapsed minutes and calculate money in matching units

Learning goal: Tell time to the nearest minute, solve elapsed-time problems within ninety minutes and calculate money amounts in a consistent unit. A clock and a money collection both require attention to units, but they use different groupings. An hour contains sixty minutes. One dollar has the same value as one hundred cents.

On an analog clock, the minute hand makes one complete turn in sixty minutes. The large numbers mark five-minute positions: at the four, twenty minutes have passed since the hour. Small marks between the large positions each represent one additional minute. At the third small mark after four, the minute hand shows twenty-three minutes.

The hour hand moves continuously as minutes pass. At 2:23, it is between two and three, closer to two. It does not stay exactly on two until 2:59 and then jump. Read the hour already reached and combine it with the minute count. An hour hand between two and three together with twenty-three minutes gives 2:23.

A number line helps find elapsed time across an hour. A reading session begins at 2:47 and ends at 3:22. From 2:47 to 3:00 is thirteen minutes. From 3:00 to 3:22 is twenty-two more minutes. Add 13 + 22 = 35 minutes. Subtracting the written clock digits as though an hour contained one hundred minutes would give a misleading answer.

You can also find an ending or starting time. Starting at 10:38 and working for forty-five minutes, first use twenty-two minutes to reach 11:00. Twenty-three minutes remain, so the ending time is 11:23. To find a starting time, move backward by the known duration, crossing an hour boundary carefully. This sequence stays within ninety minutes of elapsed time.

For money, count values rather than the number of coins. Three quarters and two dimes have a value of 75 + 20 = 95 cents. Five coins are present, but the amount is not five cents. A nickel has a value of five cents and a penny one cent; different coin combinations can have equal total value.

Use matching units in calculations and write the unit symbol correctly. The cent sign follows the number, as in 68¢; the dollar sign comes before the number, as in $245. If a notebook costs 68¢ and you pay 95¢, write 95¢ − 68¢ = 27¢ in change. If a club has $245 and receives $138, write $245 + $138 = $383. Writing 27$ or $27 for twenty-seven cents would misstate the amount. This lesson's computations use cents with cents or dollars with dollars, within one thousand. Mixed dollar-and-cent notation and decimal algorithms belong to a later sequence; do not silently treat dollars as if they were cents.

Worked time example: A walk ends at 4:12 after twenty-five minutes. Move back twelve minutes to 4:00, then thirteen more to 3:47. Check forward: thirteen minutes to four o'clock and twelve more to 4:12 make twenty-five minutes.

Worked money example: A learner has two quarters, three dimes and four pennies. Their values are fifty cents, thirty cents and four cents, for eighty-four cents altogether. Buying an item for 57¢ leaves 84¢ − 57¢ = 27¢. Check 57¢ + 27¢ = 84¢. A quarter and two pennies could represent that change.

Guided performance: Read several real or movable analog-clock faces, including hands between minute labels, then set a clock to a spoken time. Use a time line for beginning-time, ending-time and elapsed-time questions. For coins, sort and count real or clearly marked model coins before calculating a total or change.

Independent evidence: Solve a new elapsed-time story crossing an hour and show the minute intervals. Solve one cents-only purchase problem and one dollars-only addition or subtraction problem, writing ¢ after cent amounts and $ before dollar amounts. If an answer has no unit, add one and check its meaning. A correct written answer does not replace demonstrating that the learner can actually read the clock face or count the coin collection.