A graph that answers a question

I can tally a count in crossed groups of five.

A tally is a record made while counting, not afterwards. The fifth mark goes across the other four so that a reader never has to count inside a group.

The child's strip shows three crossed groups and a part group of three, and they say five, ten, fifteen at each close and eighteen at the end.

First lesson. Count a line of eighteen cubes as a class and lose count on purpose halfway. Ask what could be written down to stop that happening.

The back of the book teaches the tally completely: four single marks, a fifth laid across them, the same again to ten and to fifteen, and a last group that stops at three.

Children lay cubes in a line and draw one tally mark per cube, touching the cube as the mark is made, then put the fifth mark across the other four rather than beside them and cover the group with a finger to say how many without counting the marks.

A tally strip carrying the whole run to eighteen, checked against the cubes by a partner.

Children put three more cubes down, make three more marks and leave that group uncrossed, say how many cubes they counted in all, and swap strips to check a partner's marks against their cubes.

I can read a tally somebody else made.

Reading a tally is two different hand movements: a flat finger for each five, a single touch for each leftover. Recounting inside a crossed group throws away the reason it was crossed.

The child reads a card by fives and then counts on by ones, and says the finished number with the thing being counted named in it.

Yesterday the marks were yours and you knew what they meant. Today the cards arrive already marked by somebody else.

The book states the crossing rule and then prints the numbers its own chart is supposed to give.

Children lay a finger flat across each crossed group saying five, ten, fifteen and moving group to group without touching a single mark inside them, then from the number they stopped on touch each leftover mark and count on by ones.

Several cards read as numbers, each said again as a sentence with the food name in it, and the hamburger card checked against the number the book states.

Children point at a crossed group and say what those five marks are — five people who each said the same food — then point at one single mark and say what that one is, and say why crossing helps a reader with a long row.

I can sort a whole group so every person is in exactly one column.

A count is only worth having when every member is somewhere and nobody is in two places. The tick is what makes that checkable.

No card is left in the pile and no card carries two ticks, and the child counts each column and the tray at the end.

Reading somebody else's record is one thing. Today the class makes the record, and it has to be a record of everybody.

Kip's chart is a census of a group he can name: fifteen singers, three columns, and every singer belongs in exactly one of them.

Children deal fifteen name cards face up and count them, place the four the book decides for them, then take the pile one card at a time as a partner reads each singer's answer, putting the card in its column and ticking it once so it cannot move.

A three-column board holding every card once, with each column counted and the still-to-ask tray counted too.

Children put every card they have no answer for in the tray, count them, say how many singers are still to be asked, then say it again after two more answers arrive and check both numbers against the ones Kip says.

I can say what a board of marks cannot tell me, and fix it.

The display has to survive the data changing. Marks cannot say which three singers are absent; a name on a note can be picked up and moved.

The child works both of the book's changes in order, recounts after each, and says each number before checking it against the book.

Yesterday's board was right on the day it was made. Today three singers fall ill and the board has to be asked a question it cannot answer.

Kip's chart works until the data moves — marks in a column give a count and nothing else, and he says so. Alice's answer is a name on every note.

Children try to answer which three singers are absent from a board of marks with no names, say what the marks can and cannot tell them, then write one singer's name on each of fifteen notes and stick them where the marks were, checking that no count has changed.

A named board, recounted after three singers move each way, with the count of singers who can sing said aloud.

Children move Kelly and Jackson, count again, say the new number before the book says it, and say what each move did to two columns at once.

I can ask everybody, tally the answers and say why my sentence is true.

A statement about data is defended by pointing at the part of the record that proves it. A sentence the chart cannot settle is not an answer, and saying so is the right answer.

The child says two sentences about their chart and defends each with a finger on the row that proves it, and can say which of the book's five sentences need names rather than numbers.

The last two lessons used somebody else's data. Today the class collects its own, from everybody in the room.

The back of the book hands a class a question and a job: Amy and Fred asked some friends whether they would sing a solo, and the reader is told to say why five sentences about the answers are true.

Children ask every person in the room the book's question exactly as printed, writing each answer as yes, no or maybe and asking nobody twice, then build a three-row tally chart, crossing each answer off the list as it is marked, and check the total marks against the number of people asked.

A tally chart whose row counts match the survey list, and two defended sentences, one about a single row and one putting two rows side by side.

Children hear the book's five sentences one at a time and say for each whether their chart can settle it, saying what the chart would need where it cannot, and name the two of the five that need names rather than numbers.

I can read a bar graph to find the most, and answer the question with it.

A bar is tall because a number is large, so the answer is read off the picture rather than computed. The category is the answer, not the number.

The child finds the tallest tower by looking along the tops and answers in a full sentence naming the category.

Tallies have been marks in rows. Today the same counts stand up as towers, and the answer can be seen from across the table.

The mosquito spread prints a graph with three labelled categories and asks a question the graph alone answers: where the mosquitoes should lay their eggs.

Children build three cube towers on a labelled base with their bottoms level, say each label aloud with a hand on its tower, then find the tallest by looking along the tops and answer the book's question in a sentence naming the category, counting only if a partner disagrees.

Two three-tower graphs, the mosquito graph and the peeper vote, each with its question answered in a full sentence.

Children look at the mosquito towers again and say one thing the graph does tell them and one thing it does not, beginning the second with the graph does not say, and a partner says whether that thing could be found by looking at the towers.

I can record a reading every day and count the two groups at the end.

The counting has somewhere to go. Two counts answer a question somebody actually asked, which is what makes the month of recording worth doing.

The child fills every box, separates the two colours, counts both lines aloud with one touch per cube, and says which group has more with both counts inside the answer.

Every record so far has been made in one sitting. Today the record is made a day at a time and only means something at the end of the month.

The book's closing pages set the class a job in its own words: read a thermometer each day, record it, and at the end of the month count how many days were above freezing and how many below.

Children take the day cards in order and place a cube in each day box — light if the reading is above the blue line at 32, dark if below — saying the number and the colour aloud so a partner can check, and working straight through without going back.

A filled month grid, the two colours separated into two lines, and both counts said as whole sentences.

Children look at their two lines and say which group has more days in it, then say whether this was a month when snow could be expected, pointing at the lines as the reason and saying both counts inside the answer.