Reading a scale and a table

I can read a plotted point as a month and a number.

A dot on a line graph is a pair. The month comes from underneath and the value from the side, and a reader who takes only one of the two has not read the graph.

The child rules and labels the grid, plots both stated values, joins them, and reads a dot on somebody else's grid back as a month and a number of miles.

First lesson. Put one dot on a ruled grid and ask what it says. Take the answers and count how many of them named two things.

The book explains that a line graph records facts as dots joined by lines, and then prints the answers a reader would get from four of its own graphs.

Children read the two sentences saying how a line graph is made and put a finger on the dot and on the joining line, say aloud what one dot holds, then write the months along the bottom and the miles up the side counting by fifties, place a dot at three hundred eighty for May and at forty for June, and join them.

A labelled grid with both of the book's values plotted and joined, and a partner's grid read back — a finger run down to the month and across to the miles for each dot.

Children write one sentence for each dot in the book's own shape, the month then the miles, and read both to a partner who points at the matching dot — and if the partner points at the wrong dot, they find which half of the sentence sent them there.

I can answer a most question and a fewest question off the same graph.

The graph does not change when the question does. One word sends a finger to the highest dot and another sends it to the lowest, and noticing which word is doing that is the reading skill.

The child answers both questions off their own line, checks both against the book's printed answers, swaps the two words on one question, and says what moved.

Yesterday the dots were read. Today the same line is asked two questions that differ by one word, and the answers are different.

Every graph in the book is asked the same two questions, and the only thing that changes between them is one word.

Children take a card for each of the two words that make the questions different, lay them one above the other and say what each tells a finger to do, then find the dot the word most sends them to and write the month beside the card, and do the same for fewest — checking both against the book's own answers.

Both questions answered off one line and checked against the printed answers, then the word fewest laid over the word most and the new answer pointed at.

Children write one question of their own about their line using either word and hand it to another pair with the graph but not the answer; when the pair answers, they decide together whether the graph or the wording sent them wrong.

I can compare two tables line by line and say where a difference ends up.

Two tables are compared by matching rows, not by scanning totals. When every line but two is identical, the difference has only one place it can go, and that is a conclusion rather than a guess.

The child joins each matching pair of lines, names and subtracts the two unmatched pairs, and states where the extra forty dollars ends up using numbers from the cards.

Graphs have been read for two lessons. Put two ledgers side by side and ask which costs more to make — then ask how much of the price difference that explains.

The book prints two ledgers back to back whose cost columns are identical line for line and whose prices differ by forty dollars.

Children lay the two cards side by side cost line against cost line, read each pair aloud together working down the column, draw one joining line for every pair carrying the same amount and count the joining lines, then find the two lines with no joining line and subtract each pair.

Two differences written side by side, and the sentence on the strip completed with a number from the cards in each blank.

Children run the same test on the second pair of ledgers — joining the lines that match, naming the ones that do not, subtracting each unmatched pair — and say whether these two behave the way the first pair did, naming one cost line that changes here and did not change there.

I can rebuild missing rows of a table and say which row each one depended on.

A table built on a rule has no independent rows. Each one is reachable only from the one above it, which is why the order of the rows is part of the information.

The child orders the events, builds the table with running totals, checks a stated total at the checkpoint, and shows that a row cannot be written while the row above it is covered.

Two tables were compared yesterday and every row was there. Today three totals are given and the rows between them are missing.

The book reports totals at three points of a doubling wage and never prints the rows between them.

Children spread the seven event cards, read each aloud and place them left to right in the order they happen, set the card that says how to get from one day's pay to the next slightly above the line, then build the day table from day one with the running total beside it and stop at day five to check against the stated figure.

The table built to day eleven with running totals, checked at the reported figure, and the seven cards ordered with the rule-setting card identified.

Children cover day seven with a blank card and hand the strip to a partner, who has to try to write day eight without uncovering it — then they uncover it, finish the table, and say aloud what the partner needed before day eight could be written.

I can turn a count of seconds into miles and mark it on a scale.

A converted number means more once it is on a scale. Two marks on one scale turn two separate answers into a distance that can be measured and seen closing in.

The child writes the rule as a division, converts both counts and marks them in two colours, measures the distance between the marks, and marks the distance at which the whistle goes.

Tables and graphs have both been read. Ask how far away a storm is if the bang comes sixty-five seconds after the flash — and what would let anybody say.

The book gives a rule for locating a storm — sound covers a mile every five seconds — works one case, thirty seconds being about six miles, and leaves two.

Children read what flash to bang means and the speed of sound rule, write the division they would use to get from seconds to miles, then convert the sixty-five second count and mark it on their scale, and convert the later count and mark that in a different colour.

A scale of miles carrying two marks in two colours, with the distance between them measured and written beside the two counts.

Children read the rule about halting the game, mark the distance that matches it on the scale, and say how many more miles the storm has to travel before the whistle goes.

I can change feet to inches before subtracting, and subtract both ends of a range.

Two numbers in different units cannot be subtracted. The conversion comes first, and when the amount taken away is a range the subtraction gets done twice.

The child converts each depth from feet to inches and subtracts both the smaller and the larger amount, and rings any row where the most that could melt would leave nothing at all.

Yesterday one number went onto a scale. Today two numbers arrive in different units and one of them is a range. Read the sentence and ask what has to happen first.

Half a foot of snow falls and a warm spell is expected to melt two to four inches of it.

Children read what the storm produced and the reminder about feet and inches, write the snowfall in inches saying what they multiplied, then subtract the smaller amount of melting from the total and then the larger, writing both answers.

Eight depths converted and reduced twice each, with the rows that would melt away entirely ringed.

Children take one row and show it on the ruler — marking the snowfall, marking what melts, reading off what is left — and say whether the ruler agrees with the arithmetic.

I can work the least and the most a forecast allows and answer with both numbers.

When one piece of a sum is a range, the total is a range. If it straddles the rule, then two numbers are the honest answer and one number is a guess.

The child writes the rule, adds the fixed pieces into both columns, carries the hourly range through for the right number of hours, and answers with both numbers in the sentence.

The range was subtracted twice yesterday. Today it is added, and the answer lands on both sides of a rule.

A forecast arrives in pieces — a fifth of an inch already down, two more inches by midnight, then one to two inches an hour until three in the morning — and the rule for a snow day is six inches.

Children write the snow day rule at the top of the sheet and say how many hours the amount has to fall in, add what is on the ground to what is expected by midnight and write that total in both columns because so far the least and the most are the same, then read the hourly rate, work out how many hours it runs, and add the least it could give to the least column and the most to the most.

A two-column sheet carried to the end, with both totals placed on the snow strip beside the six-inch mark.

Children say what each end means for the two characters and answer the book's question with both numbers in the sentence.

I can carry a rate given as a range through a multiplication and turn both ends into hours.

A rate can be a range, and multiplying it by a weight gives two times rather than one. Reporting an about-figure in hours is fair only once both ends are known.

The child multiplies both ends of the rate by the weight, divides both minute totals by sixty, reports the time as a range in minutes and as one about-figure in hours, and says what happens at each end of the range.

A range has been subtracted and added. Read the label and ask what happens when the range has to be multiplied.

The label gives a cooking rate as a range, twenty-three to twenty-five minutes per pound, and the roast weighs five pounds.

Children read the label sentences aloud, write the weight in the weight box and the two rates on the two rate rows with the smaller on top, then multiply the top rate by five pounds and the bottom rate by five pounds, circling both and writing the word to between them so the card reads as a range.

Two cooking times in minutes and both of them divided by sixty into hours, with the whole number of hours both answers sit closest to said aloud.

Children point at each end of the range and say what happens to the meat there using the book's own two words, then say one sentence naming the number of minutes between the two ends and what a cook gains by knowing it.