How to create DatagridTemplateColumn with checkbox and binding to datasouce?

Apologies in advance if I am missing something - I still find my feet working with Xaml and not with window forms.

I am trying to bind a datasource to a DataGrid where one of the columns is a checkbox. My original solution did a great job with this, but required the user to check the checkbox twice:

<Window x:Class="ExecBoxInvoices.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="MainWindow" Height="507" Width="676">
<Grid Margin="0,0,0,51">
    <DataGrid x:Name="InvoiceDG" HorizontalAlignment="Left" Height="165" Margin="134,251,0,0" VerticalAlignment="Top" Width="400" ItemsSource="{Binding}" AutoGenerateColumns="False">
        <DataGrid.Columns>
            <DataGridCheckBoxColumn Header="Generate" Binding="{Binding Generate}" Width="80"/>
            <DataGridTextColumn Header="Table_Number" Binding="{Binding Table_Number}" Width="120"/>
            <DataGridTextColumn Header="Transaction_Date" Binding="{Binding Transaction_Date}" Width="175"/>
            <DataGridTextColumn Header="Transaction_ID" Visibility="Hidden" Binding="{Binding Transaction_ID}"/>
        </DataGrid.Columns>
    </DataGrid>
</Grid>

      

        
        
        
      

    

New solution for single checkboxes shows below but doesn't work (error shows up in Binding = "{Binding Generate}"):

<Window x:Class="ExecBoxInvoices.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="MainWindow" Height="507" Width="676">
<Grid Margin="0,0,0,51">
    <DataGrid x:Name="InvoiceDG" HorizontalAlignment="Left" Height="165" Margin="134,251,0,0" VerticalAlignment="Top" Width="400" ItemsSource="{Binding}" AutoGenerateColumns="False">
        <DataGrid.Columns>
            <DataGridTemplateColumn Header="Generate" Width="60" Binding="{Binding Generate}">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <CheckBox IsChecked="{Binding Path=IsSelected, UpdateSourceTrigger=PropertyChanged}"/>
                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>
            <DataGridTextColumn Header="Table_Number" Binding="{Binding Table_Number}" Width="120"/>
            <DataGridTextColumn Header="Transaction_Date" Binding="{Binding Transaction_Date}" Width="175"/>
            <DataGridTextColumn Header="Transaction_ID" Visibility="Hidden" Binding="{Binding Transaction_ID}"/>
        </DataGrid.Columns>
    </DataGrid>
</Grid>

      

        
        
        
      

    

For reference, the code used to set the source is:

InvoiceDG.ItemsSource = recordCollection;

      

        
        
        
      

    

Where recordCollection is a list:

class InvoiceRow
{
    public bool Generate { get; set; }
    public string Table_Number { get; set; }
    public string Transaction_Date { get; set; }
    public string Transaction_ID { get; set; }

    public InvoiceRow(bool generate, string table_Number, string transaction_Date, string transaction_ID)
    {
        this.Generate = generate;
        this.Table_Number = table_Number;
        this.Transaction_Date = transaction_Date;
        this.Transaction_ID = transaction_ID;
    }
}